<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2024 Workiva-->
<!--r:8cdb58fd-4801-4927-8001-b7d32b49f943,g:f287e148-ef87-4472-bb01-3c8c361cfed7-->
<link:linkbase xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedPeriodStartLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedPeriodStartLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/netLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/net-2009-12-16.xsd#netLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedNetLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedNetLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedTerseLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedPeriodEndLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedPeriodEndLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedTotalLabel"/>
  <link:labelLink xlink:role="http://www.xbrl.org/2003/role/link" xlink:type="extended">
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear_a2bb18c8-7750-4b3d-96a0-baebd3e93774_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Four, Originated, Three Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrualNoAllowance_77023837-1666-41e0-bf65-1c0bf7826b63_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrualNoAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nonaccrual loans with no associated allowance</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrualNoAllowance_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrualNoAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Nonaccrual, No Allowance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrualNoAllowance" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrualNoAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrualNoAllowance" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrualNoAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_terseLabel_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs)</link:label>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_label_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockAppreciationRightsSARSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:to="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ExcessCapital_ca80bf4a-0ee5-48bf-92b9-7c5cd0532478_terseLabel_en-US" xlink:label="lab_us-gaap_ExcessCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Excess capital</link:label>
    <link:label id="lab_us-gaap_ExcessCapital_label_en-US" xlink:label="lab_us-gaap_ExcessCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Total Risk-Based Capital, Excess, Actual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ExcessCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ExcessCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ExcessCapital" xlink:to="lab_us-gaap_ExcessCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt_e44f1f51-a8a8-404d-a2b3-df08f26c3a8d_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale of available-for-sale investment</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Debt Securities, Available-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt" xlink:to="lab_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward_99bd1608-f8a7-4c41-9c8c-85e91473c778_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Losses [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:to="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LoansHeldForInvestmentTransferredToConsolidatedTrusts_cfd84a39-6b1e-485d-b1bf-c39f242a3101_terseLabel_en-US" xlink:label="lab_agm_LoansHeldForInvestmentTransferredToConsolidatedTrusts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans held for investment transferred to consolidated trusts</link:label>
    <link:label id="lab_agm_LoansHeldForInvestmentTransferredToConsolidatedTrusts_label_en-US" xlink:label="lab_agm_LoansHeldForInvestmentTransferredToConsolidatedTrusts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Held for Investment Transferred to Consolidated Trusts</link:label>
    <link:label id="lab_agm_LoansHeldForInvestmentTransferredToConsolidatedTrusts_documentation_en-US" xlink:label="lab_agm_LoansHeldForInvestmentTransferredToConsolidatedTrusts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loans Held for Investment Transferred to Consolidated Trusts</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LoansHeldForInvestmentTransferredToConsolidatedTrusts" xlink:href="agm-20240331.xsd#agm_LoansHeldForInvestmentTransferredToConsolidatedTrusts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LoansHeldForInvestmentTransferredToConsolidatedTrusts" xlink:to="lab_agm_LoansHeldForInvestmentTransferredToConsolidatedTrusts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_b48af459-ea2c-4faf-8d8c-18c1b31d420f_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum borrowing capacity from U.S. Treasury</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DueYearTwoMember_40325d7e-e116-4e83-b7f6-9ebbd4802ec5_terseLabel_en-US" xlink:label="lab_agm_DueYearTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year two</link:label>
    <link:label id="lab_agm_DueYearTwoMember_label_en-US" xlink:label="lab_agm_DueYearTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Due year two [Member]</link:label>
    <link:label id="lab_agm_DueYearTwoMember_documentation_en-US" xlink:label="lab_agm_DueYearTwoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Due year two [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DueYearTwoMember" xlink:href="agm-20240331.xsd#agm_DueYearTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DueYearTwoMember" xlink:to="lab_agm_DueYearTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_4d89ccad-59c1-4f59-aa6c-23bcd7dea248_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net change in:</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Operating Capital [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInOperatingCapitalAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Award Types</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValueAbstract_b4e8c567-cdfd-4978-8c10-2c5f523ae013_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValueAbstract_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Maturity, Allocated and Single Maturity Date, Fair Value [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValueAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValueAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValueAbstract" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValueAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesYearSixThroughTenWeightedAverageYield_5c9279e1-3027-41c0-a049-05eb47fc1fc9_terseLabel_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesYearSixThroughTenWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after five years through ten years</link:label>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesYearSixThroughTenWeightedAverageYield_label_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesYearSixThroughTenWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Available-for-sale Securities, Debt Maturities, Year Six Through Ten, Weighted-Average Yield</link:label>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesYearSixThroughTenWeightedAverageYield_documentation_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesYearSixThroughTenWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Available-for-sale Securities, Debt Maturities, Year Six Through Ten, Weighted-Average Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_AvailableForSaleSecuritiesDebtMaturitiesYearSixThroughTenWeightedAverageYield" xlink:href="agm-20240331.xsd#agm_AvailableForSaleSecuritiesDebtMaturitiesYearSixThroughTenWeightedAverageYield"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_AvailableForSaleSecuritiesDebtMaturitiesYearSixThroughTenWeightedAverageYield" xlink:to="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesYearSixThroughTenWeightedAverageYield" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardGrantDateFairValue_terseLabel_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value as of Grant Date</link:label>
    <link:label id="lab_ecd_AwardGrantDateFairValue_label_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardGrantDateFairValue" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AwardGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardGrantDateFairValue" xlink:to="lab_ecd_AwardGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfShortTermDebt_665afd8d-eed5-4597-911b-0c0ea1839ec6_negatedLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfShortTermDebt" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Payments to redeem discount notes</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfShortTermDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfShortTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Short-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfShortTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RepaymentsOfShortTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfShortTermDebt" xlink:to="lab_us-gaap_RepaymentsOfShortTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_InterestRateSwapReceiveFixedCallableMember_67c124e5-a09e-4537-b357-9c3a52897153_terseLabel_en-US" xlink:label="lab_agm_InterestRateSwapReceiveFixedCallableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receive fixed callable</link:label>
    <link:label id="lab_agm_InterestRateSwapReceiveFixedCallableMember_label_en-US" xlink:label="lab_agm_InterestRateSwapReceiveFixedCallableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swap, Receive Fixed Callable [Member]</link:label>
    <link:label id="lab_agm_InterestRateSwapReceiveFixedCallableMember_documentation_en-US" xlink:label="lab_agm_InterestRateSwapReceiveFixedCallableMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Rate Swap, Receive Fixed Callable [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_InterestRateSwapReceiveFixedCallableMember" xlink:href="agm-20240331.xsd#agm_InterestRateSwapReceiveFixedCallableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_InterestRateSwapReceiveFixedCallableMember" xlink:to="lab_agm_InterestRateSwapReceiveFixedCallableMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAbstract_dd96da48-4c9b-489f-a50b-5fd0af013bf2_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Held-to-Maturity Securities</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAbstract_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAbstract" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet_a5cd4fe4-c4fa-4827-8138-0130cf059e5a_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax liability, net</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Liabilities, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DeferredIncomeTaxLiabilitiesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:to="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_NetChangeInFairValueTradingSecuritiesHedgedAssetsFinancialDerivativesAndLoansHeldForSale_dcf64024-cce5-461f-a738-dbfc01509462_negatedTerseLabel_en-US" xlink:label="lab_agm_NetChangeInFairValueTradingSecuritiesHedgedAssetsFinancialDerivativesAndLoansHeldForSale" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net change in fair value of trading securities, hedged items, and financial derivatives</link:label>
    <link:label id="lab_agm_NetChangeInFairValueTradingSecuritiesHedgedAssetsFinancialDerivativesAndLoansHeldForSale_label_en-US" xlink:label="lab_agm_NetChangeInFairValueTradingSecuritiesHedgedAssetsFinancialDerivativesAndLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Change In Fair Value, Trading Securities, Hedged Assets, Financial Derivatives And Loans Held For Sale</link:label>
    <link:label id="lab_agm_NetChangeInFairValueTradingSecuritiesHedgedAssetsFinancialDerivativesAndLoansHeldForSale_documentation_en-US" xlink:label="lab_agm_NetChangeInFairValueTradingSecuritiesHedgedAssetsFinancialDerivativesAndLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Change In Fair Value, Trading Securities, Hedged Assets, Financial Derivatives And Loans Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_NetChangeInFairValueTradingSecuritiesHedgedAssetsFinancialDerivativesAndLoansHeldForSale" xlink:href="agm-20240331.xsd#agm_NetChangeInFairValueTradingSecuritiesHedgedAssetsFinancialDerivativesAndLoansHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_NetChangeInFairValueTradingSecuritiesHedgedAssetsFinancialDerivativesAndLoansHeldForSale" xlink:to="lab_agm_NetChangeInFairValueTradingSecuritiesHedgedAssetsFinancialDerivativesAndLoansHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_9f1ea0db-209a-4b34-914f-c4478ff0d5ee_periodStartLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning Balance</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_4c78bfdc-58df-4f83-b527-cfbde51aacf4_periodEndLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending Balance</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss_7cebf075-b1e2-4849-933e-9793559aea9c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Available-for-sale, accrued interest excluded</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accrued Interest, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain_c607b681-1de3-47c7-8cd6-c23a8c09e90a_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:to="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingPoliciesProcLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_InsiderTradingPoliciesProcLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:to="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_Rule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:to="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_terseLabel_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement does not require Recovery</link:label>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_label_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Does Not Require Recovery [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_RestatementDoesNotRequireRecoveryTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:to="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_6dc8d93c-5720-495b-9713-acfcc2669bf0_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EQUITY</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialAssetNotPastDueMember_fb17e6da-8f1c-44a1-a777-a3ce007e2a67_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialAssetNotPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current</link:label>
    <link:label id="lab_us-gaap_FinancialAssetNotPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancialAssetNotPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Not Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialAssetNotPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialAssetNotPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialAssetNotPastDueMember" xlink:to="lab_us-gaap_FinancialAssetNotPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityLineItems_ff183bc3-d6de-4046-9abc-f1c27e6cf8e7_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Line Items]</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityLineItems_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_VariableInterestEntityLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityLineItems" xlink:to="lab_us-gaap_VariableInterestEntityLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockValue_505d3de4-499e-4cd4-a4b6-0fad6f42ffe8_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock</link:label>
    <link:label id="lab_us-gaap_PreferredStockValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockValue" xlink:to="lab_us-gaap_PreferredStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossLineItems_ebc9db06-5bbe-4fbd-9209-c154c934ede9_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeInstrumentsGainLossLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:to="lab_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_14092ba2-031e-4950-b844-738856a955fb_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted earnings per common share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_7a0aaded-632e-421a-b149-9fe7ce8c0067_totalLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Diluted EPS (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EarningsPerShareDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareDiluted" xlink:to="lab_us-gaap_EarningsPerShareDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossExcludingAccruedInterest_5bd4873e-ac00-4089-a426-3667be7bd54d_negatedLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Allowance for losses</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossExcludingAccruedInterest_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Allowance for Credit Loss, Excluding Accrued Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossExcludingAccruedInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossExcludingAccruedInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossExcludingAccruedInterest" xlink:to="lab_us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossExcludingAccruedInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax_27310cd1-4e91-4384-b128-8ed1b244ed2b_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Expense recognized on cash flow hedges</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), Reclassification, after Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ExtinguishmentOfDebtAmount_ba7a4fc7-c462-40e2-bb55-97033c3ed7d8_terseLabel_en-US" xlink:label="lab_us-gaap_ExtinguishmentOfDebtAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding debt repurchases</link:label>
    <link:label id="lab_us-gaap_ExtinguishmentOfDebtAmount_label_en-US" xlink:label="lab_us-gaap_ExtinguishmentOfDebtAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Extinguishment of Debt, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ExtinguishmentOfDebtAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ExtinguishmentOfDebtAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ExtinguishmentOfDebtAmount" xlink:to="lab_us-gaap_ExtinguishmentOfDebtAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract_70b1ef94-283d-4df5-a7d7-8cb4b6151ceb_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Maturity, Allocated and Single Maturity Date, Amortized Cost [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsBeforeTax_fc424593-bf44-4471-9212-6910e52f51b4_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized gain/(losses), before tax</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsBeforeTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), before Reclassifications, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsBeforeTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_TradingSymbol_13347c94-80ab-4689-9ef5-dc71c8eb9923_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:label id="lab_dei_TradingSymbol_label_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_TradingSymbol"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_TradingSymbol" xlink:to="lab_dei_TradingSymbol" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember_18d3fb44-31d8-42e9-acf2-4d62ac1b82c6_terseLabel_en-US" xlink:label="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">USDA Securities:</link:label>
    <link:label id="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember_a3323e57-f269-4efb-b002-4062cf8c01a9_verboseLabel_en-US" xlink:label="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">USDA Securities</link:label>
    <link:label id="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Government Agencies Debt Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_USGovernmentAgenciesDebtSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:to="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MarketApproachValuationTechniqueMember_dcd946ca-e765-43aa-ad35-ac48264c4da4_terseLabel_en-US" xlink:label="lab_us-gaap_MarketApproachValuationTechniqueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Indicative bids</link:label>
    <link:label id="lab_us-gaap_MarketApproachValuationTechniqueMember_label_en-US" xlink:label="lab_us-gaap_MarketApproachValuationTechniqueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation, Market Approach [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MarketApproachValuationTechniqueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MarketApproachValuationTechniqueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MarketApproachValuationTechniqueMember" xlink:to="lab_us-gaap_MarketApproachValuationTechniqueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GuaranteeObligationsNatureDomain_b1b0cc3d-64d6-444e-901c-02a633fa57ad_terseLabel_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsNatureDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantor Obligations, Nature [Domain]</link:label>
    <link:label id="lab_us-gaap_GuaranteeObligationsNatureDomain_label_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsNatureDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guarantor Obligations, Nature [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GuaranteeObligationsNatureDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GuaranteeObligationsNatureDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GuaranteeObligationsNatureDomain" xlink:to="lab_us-gaap_GuaranteeObligationsNatureDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TradingSecuritiesDebtAmortizedCost_5928246b-5b22-487b-9466-5e5096a720ab_terseLabel_en-US" xlink:label="lab_us-gaap_TradingSecuritiesDebtAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost</link:label>
    <link:label id="lab_us-gaap_TradingSecuritiesDebtAmortizedCost_label_en-US" xlink:label="lab_us-gaap_TradingSecuritiesDebtAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, Amortized Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradingSecuritiesDebtAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TradingSecuritiesDebtAmortizedCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TradingSecuritiesDebtAmortizedCost" xlink:to="lab_us-gaap_TradingSecuritiesDebtAmortizedCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesMember_24f4fb61-20e6-43fc-847c-e134b61b51bb_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Securities</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesMember_4bd96ae0-8a27-4645-964f-387e6d467a71_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Available-for-sale securities</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesMember" xlink:to="lab_us-gaap_DebtSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_c90254f9-70f3-4e61-a7c8-12c595a5929a_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_HedgedItemsinFairValueHedgingRelationshipTable_d86403df-8041-4fee-84c6-ac9d6cac9029_terseLabel_en-US" xlink:label="lab_agm_HedgedItemsinFairValueHedgingRelationshipTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">HedgedItemsinFairValueHedgingRelationship [Table]</link:label>
    <link:label id="lab_agm_HedgedItemsinFairValueHedgingRelationshipTable_label_en-US" xlink:label="lab_agm_HedgedItemsinFairValueHedgingRelationshipTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">HedgedItemsinFairValueHedgingRelationship [Table]</link:label>
    <link:label id="lab_agm_HedgedItemsinFairValueHedgingRelationshipTable_documentation_en-US" xlink:label="lab_agm_HedgedItemsinFairValueHedgingRelationshipTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Hedged Items in Fair Value Hedging Relationship [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_HedgedItemsinFairValueHedgingRelationshipTable" xlink:href="agm-20240331.xsd#agm_HedgedItemsinFairValueHedgingRelationshipTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_HedgedItemsinFairValueHedgingRelationshipTable" xlink:to="lab_agm_HedgedItemsinFairValueHedgingRelationshipTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_7e1117c8-98c2-4a41-b12c-524a281bd47f_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">INVESTMENT SECURITIES</link:label>
    <link:label id="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_02e43fdc-e1cf-42b8-8d8f-cbc495991329_verboseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">FARMER MAC GUARANTEED SECURITIES AND USDA SECURITIES</link:label>
    <link:label id="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments in Debt and Marketable Equity Securities (and Certain Trading Assets) Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:to="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DebtSecuritiesTradingAllowanceForCreditLoss_b8948e5a-df88-48fe-a455-1ad220d999dc_negatedLabel_en-US" xlink:label="lab_agm_DebtSecuritiesTradingAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Allowance for losses</link:label>
    <link:label id="lab_agm_DebtSecuritiesTradingAllowanceForCreditLoss_label_en-US" xlink:label="lab_agm_DebtSecuritiesTradingAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, Allowance for Credit Loss</link:label>
    <link:label id="lab_agm_DebtSecuritiesTradingAllowanceForCreditLoss_documentation_en-US" xlink:label="lab_agm_DebtSecuritiesTradingAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DebtSecuritiesTradingAllowanceForCreditLoss" xlink:href="agm-20240331.xsd#agm_DebtSecuritiesTradingAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DebtSecuritiesTradingAllowanceForCreditLoss" xlink:to="lab_agm_DebtSecuritiesTradingAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems_9557b65f-24bc-47b7-b753-c728de3db17d_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]</link:label>
    <link:label id="lab_us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems_label_en-US" xlink:label="lab_us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems" xlink:to="lab_us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_ef681f0a-f689-400a-bacc-38d66e6f3470_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Basic and Diluted EPS</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_terseLabel_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Executive Category:</link:label>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_label_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Executive Category [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ExecutiveCategoryAxis" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_ExecutiveCategoryAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ExecutiveCategoryAxis" xlink:to="lab_ecd_ExecutiveCategoryAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_828c633d-3115-4d8f-b7b8-8766dcb8c6bf_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Unobservable Input Reconciliation</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_TradingSecuritiesWeightedAverageYield_2a2658de-33cf-4dbb-ac75-3758ca549369_terseLabel_en-US" xlink:label="lab_agm_TradingSecuritiesWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading securities, weighted-average yield</link:label>
    <link:label id="lab_agm_TradingSecuritiesWeightedAverageYield_label_en-US" xlink:label="lab_agm_TradingSecuritiesWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Securities, Weighted-Average Yield</link:label>
    <link:label id="lab_agm_TradingSecuritiesWeightedAverageYield_documentation_en-US" xlink:label="lab_agm_TradingSecuritiesWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Trading Securities, Weighted-Average Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_TradingSecuritiesWeightedAverageYield" xlink:href="agm-20240331.xsd#agm_TradingSecuritiesWeightedAverageYield"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_TradingSecuritiesWeightedAverageYield" xlink:to="lab_agm_TradingSecuritiesWeightedAverageYield" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_9abe533b-a5c1-4e6d-a756-6ee456daae5d_terseLabel_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES</link:label>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_label_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Significant Accounting Policies [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SignificantAccountingPoliciesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_546d9f71-c6f2-4c86-bbb9-69c9c3c8c17e_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 1</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel1Member" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueInputsLevel1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel1Member" xlink:to="lab_us-gaap_FairValueInputsLevel1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeSecurities_f083744f-abe7-4c71-b754-f31374b0bee8_terseLabel_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments and cash equivalents</link:label>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeSecurities_label_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Dividend Income, Securities, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestAndDividendIncomeSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestAndDividendIncomeSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestAndDividendIncomeSecurities" xlink:to="lab_us-gaap_InterestAndDividendIncomeSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_e325a0d3-1de9-4d7b-bf51-465f16e69dfe_terseLabel_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying Amount</link:label>
    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reported Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CarryingReportedAmountFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:to="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GuaranteeObligationsMaximumExposure_269432fd-1c2a-4f2a-8388-a349cd0f2daf_terseLabel_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsMaximumExposure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total off-balance sheet Farmer Mac Guaranteed Securities</link:label>
    <link:label id="lab_us-gaap_GuaranteeObligationsMaximumExposure_4d4fccc9-f279-4a30-a03e-27fe479069ea_verboseLabel_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsMaximumExposure" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Maximum principal amount</link:label>
    <link:label id="lab_us-gaap_GuaranteeObligationsMaximumExposure_label_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsMaximumExposure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guarantor Obligations, Maximum Exposure, Undiscounted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GuaranteeObligationsMaximumExposure" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GuaranteeObligationsMaximumExposure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GuaranteeObligationsMaximumExposure" xlink:to="lab_us-gaap_GuaranteeObligationsMaximumExposure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_79db47d6-8ca5-4ecd-8749-9bbb3b3d2198_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_5941c983-cc4b-4196-9db0-241fb87168e5_terseLabel_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_label_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:to="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure</link:label>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_label_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Additional402vDisclosureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_Additional402vDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Additional402vDisclosureTextBlock" xlink:to="lab_ecd_Additional402vDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities_a6de9414-cc3c-456a-8408-c8a945e39323_verboseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest payable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInAccruedLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgingRelationshipDomain_3ac6a06f-a5ea-4af9-85a6-3f377f84a867_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingRelationshipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging Relationship [Domain]</link:label>
    <link:label id="lab_us-gaap_HedgingRelationshipDomain_label_en-US" xlink:label="lab_us-gaap_HedgingRelationshipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Relationship [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingRelationshipDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_HedgingRelationshipDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgingRelationshipDomain" xlink:to="lab_us-gaap_HedgingRelationshipDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_f4e47574-3e9a-4004-b3f0-8c70c20b92b0_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Two years</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_820d229a-f1a2-4ef4-b94b-e730a3caa2dd_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_HedgedItemsInFairValueHedgingRelationshipsTableTextBlock_d506e924-9bad-4a9e-a303-56ad09bcf693_terseLabel_en-US" xlink:label="lab_agm_HedgedItemsInFairValueHedgingRelationshipsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Hedged Items in Fair Value Hedging Relationships</link:label>
    <link:label id="lab_agm_HedgedItemsInFairValueHedgingRelationshipsTableTextBlock_label_en-US" xlink:label="lab_agm_HedgedItemsInFairValueHedgingRelationshipsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedged Items In Fair Value Hedging Relationships [Table Text Block]</link:label>
    <link:label id="lab_agm_HedgedItemsInFairValueHedgingRelationshipsTableTextBlock_documentation_en-US" xlink:label="lab_agm_HedgedItemsInFairValueHedgingRelationshipsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Hedged Items in Fair Value Hedging Relationships [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_HedgedItemsInFairValueHedgingRelationshipsTableTextBlock" xlink:href="agm-20240331.xsd#agm_HedgedItemsInFairValueHedgingRelationshipsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_HedgedItemsInFairValueHedgingRelationshipsTableTextBlock" xlink:to="lab_agm_HedgedItemsInFairValueHedgingRelationshipsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_3d015a07-489f-49b6-b69a-c310a686239d_negatedLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Allowance for losses</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_b1f2cbca-5fad-4db1-bfaa-b31c0e41c39e_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_23df0a94-adc6-42be-8b12-47a904e42796_periodStartLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_392f21e3-c622-422d-8a82-92e4da35a963_periodEndLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss, Excluding Accrued Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:to="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitySmallBusiness_8fd3c3c0-1095-4b3c-b49a-c2181eed938b_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitySmallBusiness" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntitySmallBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitySmallBusiness" xlink:to="lab_dei_EntitySmallBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_ff2e6fdb-113f-40dc-b6c4-dc58933fa9be_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_LocalPhoneNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LocalPhoneNumber" xlink:to="lab_dei_LocalPhoneNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RecoveryOfErrCompDisclosureLineItems_label_en-US" xlink:label="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Erroneously Awarded Compensation Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_RecoveryOfErrCompDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:to="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_MeasurementInputRangeOfBrokerQuotesMember_1cdb5f4e-6667-4e92-a52a-e4135daf976f_terseLabel_en-US" xlink:label="lab_agm_MeasurementInputRangeOfBrokerQuotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Range of broker quotes</link:label>
    <link:label id="lab_agm_MeasurementInputRangeOfBrokerQuotesMember_label_en-US" xlink:label="lab_agm_MeasurementInputRangeOfBrokerQuotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Range Of Broker Quotes [Member]</link:label>
    <link:label id="lab_agm_MeasurementInputRangeOfBrokerQuotesMember_documentation_en-US" xlink:label="lab_agm_MeasurementInputRangeOfBrokerQuotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Range Of Broker Quotes [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_MeasurementInputRangeOfBrokerQuotesMember" xlink:href="agm-20240331.xsd#agm_MeasurementInputRangeOfBrokerQuotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_MeasurementInputRangeOfBrokerQuotesMember" xlink:to="lab_agm_MeasurementInputRangeOfBrokerQuotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_VariableInterestEntityConsolidatedFairValueDisclosureLiabilities_a4994a45-125e-4d83-850e-6ac0d1171f73_terseLabel_en-US" xlink:label="lab_agm_VariableInterestEntityConsolidatedFairValueDisclosureLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt securities of consolidated trusts held by third parties</link:label>
    <link:label id="lab_agm_VariableInterestEntityConsolidatedFairValueDisclosureLiabilities_label_en-US" xlink:label="lab_agm_VariableInterestEntityConsolidatedFairValueDisclosureLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Consolidated, Fair Value Disclosure, Liabilities</link:label>
    <link:label id="lab_agm_VariableInterestEntityConsolidatedFairValueDisclosureLiabilities_documentation_en-US" xlink:label="lab_agm_VariableInterestEntityConsolidatedFairValueDisclosureLiabilities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Consolidated, Fair Value Disclosure, Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_VariableInterestEntityConsolidatedFairValueDisclosureLiabilities" xlink:href="agm-20240331.xsd#agm_VariableInterestEntityConsolidatedFairValueDisclosureLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_VariableInterestEntityConsolidatedFairValueDisclosureLiabilities" xlink:to="lab_agm_VariableInterestEntityConsolidatedFairValueDisclosureLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_8e0bb46d-cac7-45f9-8e7d-a2c92b8c5d84_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative, notional amount</link:label>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_label_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Notional Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeNotionalAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeNotionalAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeNotionalAmount" xlink:to="lab_us-gaap_DerivativeNotionalAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_NoncashOrPartNoncashAcquisitionLoansAcquiredAndSecuritized_329b77e0-cc07-434a-a941-ab1aca07b872_terseLabel_en-US" xlink:label="lab_agm_NoncashOrPartNoncashAcquisitionLoansAcquiredAndSecuritized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans securitized as Farmer Mac Guaranteed Securities</link:label>
    <link:label id="lab_agm_NoncashOrPartNoncashAcquisitionLoansAcquiredAndSecuritized_label_en-US" xlink:label="lab_agm_NoncashOrPartNoncashAcquisitionLoansAcquiredAndSecuritized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncash Or Part Noncash Acquisition, Loans Acquired And Securitized</link:label>
    <link:label id="lab_agm_NoncashOrPartNoncashAcquisitionLoansAcquiredAndSecuritized_documentation_en-US" xlink:label="lab_agm_NoncashOrPartNoncashAcquisitionLoansAcquiredAndSecuritized" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Noncash Or Part Noncash Acquisition, Loans Acquired And Securitized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_NoncashOrPartNoncashAcquisitionLoansAcquiredAndSecuritized" xlink:href="agm-20240331.xsd#agm_NoncashOrPartNoncashAcquisitionLoansAcquiredAndSecuritized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_NoncashOrPartNoncashAcquisitionLoansAcquiredAndSecuritized" xlink:to="lab_agm_NoncashOrPartNoncashAcquisitionLoansAcquiredAndSecuritized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_ab0aeee6-2e51-47ef-b35f-66bad9075a31_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueByMeasurementFrequencyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:to="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_ScheduleofHeldtoMaturityAvailableforsaleandTradingSecuritiesLineItems_d40fc293-143d-40f2-a80a-05a5465f8eca_terseLabel_en-US" xlink:label="lab_agm_ScheduleofHeldtoMaturityAvailableforsaleandTradingSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Held-to-Maturity, Available-for-sale, and Trading Securities [Line Items]</link:label>
    <link:label id="lab_agm_ScheduleofHeldtoMaturityAvailableforsaleandTradingSecuritiesLineItems_label_en-US" xlink:label="lab_agm_ScheduleofHeldtoMaturityAvailableforsaleandTradingSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Held-to-Maturity, Available-for-sale, and Trading Securities [Line Items]</link:label>
    <link:label id="lab_agm_ScheduleofHeldtoMaturityAvailableforsaleandTradingSecuritiesLineItems_documentation_en-US" xlink:label="lab_agm_ScheduleofHeldtoMaturityAvailableforsaleandTradingSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">[Line Items] for Schedule of held to maturity, available for sale, and trading securities which includes, but is not limited to changes in the cost basis and fair value, fair value and gross unrealized gain (loss), fair values by type of security, contractual maturity and classification, amortized cost basis and other related disclosures</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_ScheduleofHeldtoMaturityAvailableforsaleandTradingSecuritiesLineItems" xlink:href="agm-20240331.xsd#agm_ScheduleofHeldtoMaturityAvailableforsaleandTradingSecuritiesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_ScheduleofHeldtoMaturityAvailableforsaleandTradingSecuritiesLineItems" xlink:to="lab_agm_ScheduleofHeldtoMaturityAvailableforsaleandTradingSecuritiesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MarketableSecuritiesTextBlock_88476194-23e1-40c8-8885-6b2860f055c4_terseLabel_en-US" xlink:label="lab_us-gaap_MarketableSecuritiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Farmer Mac Investment Securities</link:label>
    <link:label id="lab_us-gaap_MarketableSecuritiesTextBlock_02cc5a04-6da5-4568-a171-b928e064885b_verboseLabel_en-US" xlink:label="lab_us-gaap_MarketableSecuritiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Farmer Mac Guaranteed Securities and USDA Securities</link:label>
    <link:label id="lab_us-gaap_MarketableSecuritiesTextBlock_label_en-US" xlink:label="lab_us-gaap_MarketableSecuritiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketable Securities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MarketableSecuritiesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MarketableSecuritiesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MarketableSecuritiesTextBlock" xlink:to="lab_us-gaap_MarketableSecuritiesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_e50e5361-3b75-4ac2-9e06-e7327531725a_terseLabel_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement</link:label>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransactionTypeAxis_f05af510-2056-4292-8b76-de91964ee93d_terseLabel_en-US" xlink:label="lab_us-gaap_TransactionTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transaction Type [Axis]</link:label>
    <link:label id="lab_us-gaap_TransactionTypeAxis_label_en-US" xlink:label="lab_us-gaap_TransactionTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transaction Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransactionTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TransactionTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransactionTypeAxis" xlink:to="lab_us-gaap_TransactionTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock_e817f352-83f1-44b2-9764-7a5e487d9170_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfDebtInstrumentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposure_5bf83729-ab49-43b0-a8ed-2d8a7c239d52_terseLabel_en-US" xlink:label="lab_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative, additional net exposure</link:label>
    <link:label id="lab_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposure_label_en-US" xlink:label="lab_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Collateral Exceeding Derivative Position, Additional Net Exposure</link:label>
    <link:label id="lab_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposure_documentation_en-US" xlink:label="lab_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative, Collateral Exceeding Derivative Position, Additional Net Exposure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposure" xlink:href="agm-20240331.xsd#agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposure" xlink:to="lab_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposure" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield_a9afdd8f-304a-4836-b07f-9952d83af780_terseLabel_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due within one year</link:label>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield_label_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Available-for-sale Securities, Debt Maturities, Next Twelve Months, Weighted-Average Yield</link:label>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield_documentation_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Available-for-sale Securities, Debt Maturities, Next Twelve Months, Weighted-Average Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_AvailableForSaleSecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield" xlink:href="agm-20240331.xsd#agm_AvailableForSaleSecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_AvailableForSaleSecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield" xlink:to="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_b935d392-0cdb-4843-82ab-98cc7164ac59_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after one year through five years</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Fair Value, Maturity, Allocated and Single Maturity Date, after Year One Through Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DueWithinOneYearMember_2f7ace8b-852b-4e5c-bf87-22c547140b9c_terseLabel_en-US" xlink:label="lab_agm_DueWithinOneYearMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due within one year</link:label>
    <link:label id="lab_agm_DueWithinOneYearMember_label_en-US" xlink:label="lab_agm_DueWithinOneYearMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Due within one year [Member]</link:label>
    <link:label id="lab_agm_DueWithinOneYearMember_documentation_en-US" xlink:label="lab_agm_DueWithinOneYearMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Due within one year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DueWithinOneYearMember" xlink:href="agm-20240331.xsd#agm_DueWithinOneYearMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DueWithinOneYearMember" xlink:to="lab_agm_DueWithinOneYearMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation_967ba046-8594-4f64-92be-8fcf873608bf_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tax payments related to share-based awards</link:label>
    <link:label id="lab_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Decrease for Tax Withholding Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:to="lab_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss_d7333b9f-dcf0-44d6-99b9-bbc0904e4dec_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Unrealized Loss</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Continuous Unrealized Loss Position, Less than 12 Months, Accumulated Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAccumulatedLossAbstract_9ffe9f16-3933-4c67-9382-8ce7099cbb83_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized&#160;loss&#160;position for more&#160;than&#160;12&#160;months</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAccumulatedLossAbstract_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Unrealized Loss Position, Accumulated Loss [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAccumulatedLossAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost_95745a60-8201-4f47-a86d-5c5d4ac646ec_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after ten years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, after Year 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DueYearFourMember_7bd8187d-bd34-47aa-a6ea-23ae34a8e2dd_terseLabel_en-US" xlink:label="lab_agm_DueYearFourMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year four</link:label>
    <link:label id="lab_agm_DueYearFourMember_label_en-US" xlink:label="lab_agm_DueYearFourMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Due year four [Member]</link:label>
    <link:label id="lab_agm_DueYearFourMember_documentation_en-US" xlink:label="lab_agm_DueYearFourMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Due year four [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DueYearFourMember" xlink:href="agm-20240331.xsd#agm_DueYearFourMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DueYearFourMember" xlink:to="lab_agm_DueYearFourMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_terseLabel_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Available</link:label>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_label_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Securities Aggregate Available Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_TrdArrSecuritiesAggAvailAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:to="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_ProvisionForLoanAndSecuritiesLosses_907b42d9-8d99-4d26-a4f0-cb86cd993509_negatedTerseLabel_en-US" xlink:label="lab_agm_ProvisionForLoanAndSecuritiesLosses" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Release of/(provision for) losses</link:label>
    <link:label id="lab_agm_ProvisionForLoanAndSecuritiesLosses_label_en-US" xlink:label="lab_agm_ProvisionForLoanAndSecuritiesLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Provision for Loan And Securities Losses</link:label>
    <link:label id="lab_agm_ProvisionForLoanAndSecuritiesLosses_documentation_en-US" xlink:label="lab_agm_ProvisionForLoanAndSecuritiesLosses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Provision for Loan And Securities Losses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_ProvisionForLoanAndSecuritiesLosses" xlink:href="agm-20240331.xsd#agm_ProvisionForLoanAndSecuritiesLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_ProvisionForLoanAndSecuritiesLosses" xlink:to="lab_agm_ProvisionForLoanAndSecuritiesLosses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockNumberOfSharesParValueAndOtherDisclosuresAbstract_5784e7f2-036a-4168-afbe-1075a353740b_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockNumberOfSharesParValueAndOtherDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common stock:</link:label>
    <link:label id="lab_us-gaap_CommonStockNumberOfSharesParValueAndOtherDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_CommonStockNumberOfSharesParValueAndOtherDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Number of Shares, Par Value and Other Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockNumberOfSharesParValueAndOtherDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockNumberOfSharesParValueAndOtherDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockNumberOfSharesParValueAndOtherDisclosuresAbstract" xlink:to="lab_us-gaap_CommonStockNumberOfSharesParValueAndOtherDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:to="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotesPayableFairValueDisclosure_75177812-f4b5-49a7-a455-e140ba892e74_terseLabel_en-US" xlink:label="lab_us-gaap_NotesPayableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notes payable</link:label>
    <link:label id="lab_us-gaap_NotesPayableFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_NotesPayableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Payable, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesPayableFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NotesPayableFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotesPayableFairValueDisclosure" xlink:to="lab_us-gaap_NotesPayableFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AwardTypeAxis_terseLabel_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type</link:label>
    <link:label id="lab_us-gaap_AwardTypeAxis_label_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AwardTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AwardTypeAxis" xlink:to="lab_us-gaap_AwardTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SpecialMentionMember_435ddfd6-d497-42c7-8323-e79785145096_terseLabel_en-US" xlink:label="lab_us-gaap_SpecialMentionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Special mention</link:label>
    <link:label id="lab_us-gaap_SpecialMentionMember_label_en-US" xlink:label="lab_us-gaap_SpecialMentionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Special Mention [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SpecialMentionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SpecialMentionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SpecialMentionMember" xlink:to="lab_us-gaap_SpecialMentionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_0f913b6a-ad45-4135-a0ce-ebb36c91e57e_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive securities excluded from earnings per share (in shares)</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear_27c51a79-cc17-4ccb-a458-1d2d80d1ffbf_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Originated, More than Five Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentQuarterlyReport_38c1d026-c792-452a-9312-e679e10ecce2_terseLabel_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Annual Report</link:label>
    <link:label id="lab_dei_DocumentQuarterlyReport_label_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentQuarterlyReport" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentQuarterlyReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentQuarterlyReport" xlink:to="lab_dei_DocumentQuarterlyReport" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetCollateralObligationToReturnCashOffset_59130dd5-dfb5-4480-afb1-be6ef66cd606_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetCollateralObligationToReturnCashOffset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral received</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetCollateralObligationToReturnCashOffset_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetCollateralObligationToReturnCashOffset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, Collateral, Obligation to Return Cash, Offset Against Derivative Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetCollateralObligationToReturnCashOffset" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeAssetCollateralObligationToReturnCashOffset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetCollateralObligationToReturnCashOffset" xlink:to="lab_us-gaap_DerivativeAssetCollateralObligationToReturnCashOffset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract_16f875b6-6125-4ab2-9b1f-22df71830da5_terseLabel_en-US" xlink:label="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-cash activity:</link:label>
    <link:label id="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract_label_en-US" xlink:label="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncash Investing and Financing Items [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NoncashInvestingAndFinancingItemsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:to="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_RuralInfrastructureRuralUtilitiesSegementMember_654db1da-3b68-4f91-94fb-59b6c7e38b90_terseLabel_en-US" xlink:label="lab_agm_RuralInfrastructureRuralUtilitiesSegementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rural&#160; Utilities</link:label>
    <link:label id="lab_agm_RuralInfrastructureRuralUtilitiesSegementMember_label_en-US" xlink:label="lab_agm_RuralInfrastructureRuralUtilitiesSegementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rural Infrastructure, Rural Utilities Segement [Member]</link:label>
    <link:label id="lab_agm_RuralInfrastructureRuralUtilitiesSegementMember_documentation_en-US" xlink:label="lab_agm_RuralInfrastructureRuralUtilitiesSegementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Rural Utilities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_RuralInfrastructureRuralUtilitiesSegementMember" xlink:href="agm-20240331.xsd#agm_RuralInfrastructureRuralUtilitiesSegementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_RuralInfrastructureRuralUtilitiesSegementMember" xlink:to="lab_agm_RuralInfrastructureRuralUtilitiesSegementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_d32f7081-3f74-48f3-8709-11236a28c718_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgingDesignationAxis_a5fc7362-57b4-44e0-9673-f05beb55b995_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingDesignationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging Designation [Axis]</link:label>
    <link:label id="lab_us-gaap_HedgingDesignationAxis_label_en-US" xlink:label="lab_us-gaap_HedgingDesignationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Designation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingDesignationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_HedgingDesignationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgingDesignationAxis" xlink:to="lab_us-gaap_HedgingDesignationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_label_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoActuallyPaidCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_PeoActuallyPaidCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoActuallyPaidCompAmt" xlink:to="lab_ecd_PeoActuallyPaidCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_ed56f813-a2b4-4072-883b-9edaa6618220_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:to="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_OtherNonInterestIncomeExpenseExcludingGuaranteeAndCommitmentFees_e37f8d0b-ea4a-40f2-9e53-a31649047605_terseLabel_en-US" xlink:label="lab_agm_OtherNonInterestIncomeExpenseExcludingGuaranteeAndCommitmentFees" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income/(expense)</link:label>
    <link:label id="lab_agm_OtherNonInterestIncomeExpenseExcludingGuaranteeAndCommitmentFees_label_en-US" xlink:label="lab_agm_OtherNonInterestIncomeExpenseExcludingGuaranteeAndCommitmentFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Non-Interest Income (Expense), Excluding Guarantee and Commitment Fees</link:label>
    <link:label id="lab_agm_OtherNonInterestIncomeExpenseExcludingGuaranteeAndCommitmentFees_documentation_en-US" xlink:label="lab_agm_OtherNonInterestIncomeExpenseExcludingGuaranteeAndCommitmentFees" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Non-Interest Income (Expense), Excluding Guarantee and Commitment Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_OtherNonInterestIncomeExpenseExcludingGuaranteeAndCommitmentFees" xlink:href="agm-20240331.xsd#agm_OtherNonInterestIncomeExpenseExcludingGuaranteeAndCommitmentFees"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_OtherNonInterestIncomeExpenseExcludingGuaranteeAndCommitmentFees" xlink:to="lab_agm_OtherNonInterestIncomeExpenseExcludingGuaranteeAndCommitmentFees" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingDerivativeLiabilitiesAbstract_b8d330b9-3551-44e5-887a-c8838c911068_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingDerivativeLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities:</link:label>
    <link:label id="lab_us-gaap_OffsettingDerivativeLiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_OffsettingDerivativeLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Derivative Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingDerivativeLiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OffsettingDerivativeLiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingDerivativeLiabilitiesAbstract" xlink:to="lab_us-gaap_OffsettingDerivativeLiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BasisSwapMember_e53997af-16cd-47d1-a7be-ad31e2c1351e_terseLabel_en-US" xlink:label="lab_us-gaap_BasisSwapMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basis swaps</link:label>
    <link:label id="lab_us-gaap_BasisSwapMember_label_en-US" xlink:label="lab_us-gaap_BasisSwapMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Basis Swap [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BasisSwapMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_BasisSwapMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BasisSwapMember" xlink:to="lab_us-gaap_BasisSwapMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_6b97410b-2e44-4939-8b81-d46f835d7c31_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New Accounting Standards</link:label>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_UnsecuritizedMember_04469622-dd89-4407-8ade-8f0a02513f9f_terseLabel_en-US" xlink:label="lab_agm_UnsecuritizedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecuritized</link:label>
    <link:label id="lab_agm_UnsecuritizedMember_label_en-US" xlink:label="lab_agm_UnsecuritizedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecuritized [Member]</link:label>
    <link:label id="lab_agm_UnsecuritizedMember_documentation_en-US" xlink:label="lab_agm_UnsecuritizedMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unsecuritized, no in a trust[Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_UnsecuritizedMember" xlink:href="agm-20240331.xsd#agm_UnsecuritizedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_UnsecuritizedMember" xlink:to="lab_agm_UnsecuritizedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingLiabilitiesTableTextBlock_bfdc4c28-a6ed-4a0d-8161-836884b1b013_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Offsetting Liabilities</link:label>
    <link:label id="lab_us-gaap_OffsettingLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OffsettingLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:to="lab_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetFairValueNetAbstract_7dc86676-d293-4db6-b1ad-01f482d6523f_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair&#160;Value</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetFairValueNetAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, before Offset of Collateral [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetFairValueNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeAssetFairValueNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetFairValueNetAbstract" xlink:to="lab_us-gaap_DerivativeAssetFairValueNetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InternalCreditAssessmentAxis_ecd53cb2-e018-408f-9cf5-8c931e86399c_terseLabel_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Axis]</link:label>
    <link:label id="lab_us-gaap_InternalCreditAssessmentAxis_label_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InternalCreditAssessmentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InternalCreditAssessmentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InternalCreditAssessmentAxis" xlink:to="lab_us-gaap_InternalCreditAssessmentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetNotionalAmount_947c1731-5363-45bf-9e0e-3da1ce1590f6_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Notional amount</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetNotionalAmount_f4ce72ac-287b-4883-908c-1de7e40357d2_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notional Amount</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetNotionalAmount_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Notional Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetNotionalAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeAssetNotionalAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetNotionalAmount" xlink:to="lab_us-gaap_DerivativeAssetNotionalAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_USGovernmentSponsoredEnterprisesDebtSecuritiesMember_29fccd4f-f2c3-4310-85df-55d1c9dbb6b7_terseLabel_en-US" xlink:label="lab_us-gaap_USGovernmentSponsoredEnterprisesDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Farmer Mac Guaranteed Securities</link:label>
    <link:label id="lab_us-gaap_USGovernmentSponsoredEnterprisesDebtSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_USGovernmentSponsoredEnterprisesDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Government-sponsored Enterprises Debt Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USGovernmentSponsoredEnterprisesDebtSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_USGovernmentSponsoredEnterprisesDebtSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_USGovernmentSponsoredEnterprisesDebtSecuritiesMember" xlink:to="lab_us-gaap_USGovernmentSponsoredEnterprisesDebtSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeInterest_e78e60ae-849a-4ea7-b5ae-2f5b50f1a0bd_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Farmer Mac Guaranteed Securities and USDA Securities</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeInterest_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income, Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InvestmentIncomeInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeInterest" xlink:to="lab_us-gaap_InvestmentIncomeInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss_6cc47165-7108-4e5c-814e-73bbd200f83f_verboseLabel_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Held-to-maturity, at amortized cost</link:label>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss_876ccbbd-3d5c-410a-a631-451d6cfad402_terseLabel_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost</link:label>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss_label_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Amortized Cost, Excluding Accrued Interest, before Allowance for Credit Loss</link:label>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss_documentation_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Amortized Cost, Excluding Accrued Interest, before Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:href="agm-20240331.xsd#agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:to="lab_agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method</link:label>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_label_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_StkPrcOrTsrEstimationMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:to="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DueAfterYearFourMember_faad9b74-5632-4d11-8288-84d25c7c7639_terseLabel_en-US" xlink:label="lab_agm_DueAfterYearFourMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_agm_DueAfterYearFourMember_label_en-US" xlink:label="lab_agm_DueAfterYearFourMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Due After Year Four [Member]</link:label>
    <link:label id="lab_agm_DueAfterYearFourMember_documentation_en-US" xlink:label="lab_agm_DueAfterYearFourMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Due After Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DueAfterYearFourMember" xlink:href="agm-20240331.xsd#agm_DueAfterYearFourMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DueAfterYearFourMember" xlink:to="lab_agm_DueAfterYearFourMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_81ecf9dc-62ed-4594-a228-5c1b3502c16c_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_SecurityExchangeName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_SecurityExchangeName" xlink:to="lab_dei_SecurityExchangeName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions_76049ab1-bc99-4add-ba16-a5be9a03f82c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized loss position for more than 12 months, Number of securities in loss position</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Continuous Unrealized Loss Position, 12 Months or Longer, Number of Positions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_10b32cff-8a13-4a53-bd5b-baa1c9fa2101_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated other comprehensive loss, net of tax</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax_74b180db-f8b6-408d-a103-d64a716b5ffd_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income/(loss) before reclassifications</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax_f595ce8b-01b3-4179-bdff-9424429dc929_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Unrealized gains/(losses), after tax</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), before Reclassifications, Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock Option</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Employee Stock Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_HedgedItemsinFairValueHedgingRelationshipLineItems_006c1d23-ac5c-4a4c-8552-ec7ca12d6191_terseLabel_en-US" xlink:label="lab_agm_HedgedItemsinFairValueHedgingRelationshipLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">HedgedItemsinFairValueHedgingRelationship [Line Items]</link:label>
    <link:label id="lab_agm_HedgedItemsinFairValueHedgingRelationshipLineItems_label_en-US" xlink:label="lab_agm_HedgedItemsinFairValueHedgingRelationshipLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">HedgedItemsinFairValueHedgingRelationship [Line Items]</link:label>
    <link:label id="lab_agm_HedgedItemsinFairValueHedgingRelationshipLineItems_documentation_en-US" xlink:label="lab_agm_HedgedItemsinFairValueHedgingRelationshipLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">[Line Items] for HedgedItemsinFairValueHedgingRelationship [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_HedgedItemsinFairValueHedgingRelationshipLineItems" xlink:href="agm-20240331.xsd#agm_HedgedItemsinFairValueHedgingRelationshipLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_HedgedItemsinFairValueHedgingRelationshipLineItems" xlink:to="lab_agm_HedgedItemsinFairValueHedgingRelationshipLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_4a51f256-2772-40b3-82bb-7a0a92c32611_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">FINANCIAL DERIVATIVES</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:to="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction_83374358-13e3-4976-a6fa-90eab154e469_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Netting Adjustments</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, Deduction of Financial Instrument Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction" xlink:to="lab_us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_USDAGuaranteesMember_f37151f1-f9bc-4c4d-a3c3-7cd76a14d58a_terseLabel_en-US" xlink:label="lab_agm_USDAGuaranteesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">USDA Securities</link:label>
    <link:label id="lab_agm_USDAGuaranteesMember_label_en-US" xlink:label="lab_agm_USDAGuaranteesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">USDA Guarantees [Member]</link:label>
    <link:label id="lab_agm_USDAGuaranteesMember_documentation_en-US" xlink:label="lab_agm_USDAGuaranteesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">USDA Guarantees [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_USDAGuaranteesMember" xlink:href="agm-20240331.xsd#agm_USDAGuaranteesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_USDAGuaranteesMember" xlink:to="lab_agm_USDAGuaranteesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MaximumMember_193dc5b8-9658-4c10-859f-c65a242749c5_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum</link:label>
    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_MaximumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MaximumMember" xlink:to="lab_srt_MaximumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentType_6dff8be7-ced5-4ec7-94ef-82605edd879f_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:label id="lab_dei_DocumentType_label_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentType"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentType" xlink:to="lab_dei_DocumentType" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable_e47d8616-9b29-461c-9d28-946cb860ccff_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Table]</link:label>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable_label_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable" xlink:to="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TabularListTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tabular List, Table</link:label>
    <link:label id="lab_ecd_TabularListTableTextBlock_label_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tabular List [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TabularListTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_TabularListTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TabularListTableTextBlock" xlink:to="lab_ecd_TabularListTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DebtSecuritiesAvailableForSaleUnpaidPrincipalBalance_5363a9f0-0f88-47b0-902a-75e65bcb3319_terseLabel_en-US" xlink:label="lab_agm_DebtSecuritiesAvailableForSaleUnpaidPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amount Outstanding</link:label>
    <link:label id="lab_agm_DebtSecuritiesAvailableForSaleUnpaidPrincipalBalance_caf92708-354a-4e3d-9e5f-97d4e6ecf209_verboseLabel_en-US" xlink:label="lab_agm_DebtSecuritiesAvailableForSaleUnpaidPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unpaid Principal Balance</link:label>
    <link:label id="lab_agm_DebtSecuritiesAvailableForSaleUnpaidPrincipalBalance_label_en-US" xlink:label="lab_agm_DebtSecuritiesAvailableForSaleUnpaidPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-For-Sale, Unpaid Principal Balance</link:label>
    <link:label id="lab_agm_DebtSecuritiesAvailableForSaleUnpaidPrincipalBalance_documentation_en-US" xlink:label="lab_agm_DebtSecuritiesAvailableForSaleUnpaidPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-For-Sale, Unpaid Principal Balance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DebtSecuritiesAvailableForSaleUnpaidPrincipalBalance" xlink:href="agm-20240331.xsd#agm_DebtSecuritiesAvailableForSaleUnpaidPrincipalBalance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DebtSecuritiesAvailableForSaleUnpaidPrincipalBalance" xlink:to="lab_agm_DebtSecuritiesAvailableForSaleUnpaidPrincipalBalance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_a4182f1a-77aa-4f2a-8d71-729749fed3bf_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, after Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount_fbff76af-8285-492b-a3a6-496ec362b7bc_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum exposure to loss</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount" xlink:to="lab_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingGain_0934beb7-35b7-48fb-b5b4-950bb04942bf_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingGain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized Gains</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingGain_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingGain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Accumulated Unrecognized Gain</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingGain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingGain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingGain" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingGain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_6df35d8d-e211-465d-a421-9d26b1e6ce16_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AntidilutiveSecuritiesNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:to="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt_12cc86ee-39ad-447a-b5b5-8c2ec4ac7da3_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Purchases of Farmer Mac Guaranteed Securities and USDA Securities</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Debt Securities, Available-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:to="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_RuralInfrastructureFinanceMember_d5571bd8-8dec-4d16-828a-a9960a41652f_terseLabel_en-US" xlink:label="lab_agm_RuralInfrastructureFinanceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rural Infrastructure Finance</link:label>
    <link:label id="lab_agm_RuralInfrastructureFinanceMember_label_en-US" xlink:label="lab_agm_RuralInfrastructureFinanceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rural Infrastructure Finance [Member]</link:label>
    <link:label id="lab_agm_RuralInfrastructureFinanceMember_documentation_en-US" xlink:label="lab_agm_RuralInfrastructureFinanceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Rural Infrastructure Finance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_RuralInfrastructureFinanceMember" xlink:href="agm-20240331.xsd#agm_RuralInfrastructureFinanceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_RuralInfrastructureFinanceMember" xlink:to="lab_agm_RuralInfrastructureFinanceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_58f80470-a01f-4cb9-b694-c1f07dc0dc43_negatedTerseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Current period charge-offs</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_c22f4366-26aa-4a1b-a074-4ced23ae62ee_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current period charge-offs</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_label_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated Five Or More Years Before Latest Fiscal Year, Excluding Accrued Interest, Allowance For Credit Loss, Write Off</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_documentation_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated Five Or More Years Before Latest Fiscal Year, Excluding Accrued Interest, Allowance For Credit Loss, Write Off</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:href="agm-20240331.xsd#agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:to="lab_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeTable_74ef5cd0-b8d6-4d32-8a30-5bad2463d71b_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
    <link:label id="lab_us-gaap_DerivativeTable_label_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeTable" xlink:to="lab_us-gaap_DerivativeTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_Security12bTitle_bbe83b8c-ba6a-4882-be61-b52ff9225e80_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:label id="lab_dei_Security12bTitle_label_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_Security12bTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_Security12bTitle" xlink:to="lab_dei_Security12bTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_PremiumDiscountRecognizedOnHedgedInstrument_8760357f-a153-46e2-8ae6-97dc987871d0_negatedLabel_en-US" xlink:label="lab_agm_PremiumDiscountRecognizedOnHedgedInstrument" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Premium/discount amortization recognized on hedged items</link:label>
    <link:label id="lab_agm_PremiumDiscountRecognizedOnHedgedInstrument_label_en-US" xlink:label="lab_agm_PremiumDiscountRecognizedOnHedgedInstrument" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premium (Discount), Recognized on Hedged Instrument</link:label>
    <link:label id="lab_agm_PremiumDiscountRecognizedOnHedgedInstrument_documentation_en-US" xlink:label="lab_agm_PremiumDiscountRecognizedOnHedgedInstrument" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Premium (Discount), Recognized on Hedged Instrument</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_PremiumDiscountRecognizedOnHedgedInstrument" xlink:href="agm-20240331.xsd#agm_PremiumDiscountRecognizedOnHedgedInstrument"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_PremiumDiscountRecognizedOnHedgedInstrument" xlink:to="lab_agm_PremiumDiscountRecognizedOnHedgedInstrument" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestIncomeOperating_ebef3f5a-15cc-43ea-a327-13c8cbd66021_terseLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Income Farmer Mac Guaranteed Securities and USDA Securities</link:label>
    <link:label id="lab_us-gaap_InterestIncomeOperating_label_en-US" xlink:label="lab_us-gaap_InterestIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestIncomeOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestIncomeOperating" xlink:to="lab_us-gaap_InterestIncomeOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_NoninterestIncomeExcludingProvisionForOtherCreditLosses_b17d2f13-541a-479e-8093-65032da275c3_totalLabel_en-US" xlink:label="lab_agm_NoninterestIncomeExcludingProvisionForOtherCreditLosses" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total revenues</link:label>
    <link:label id="lab_agm_NoninterestIncomeExcludingProvisionForOtherCreditLosses_label_en-US" xlink:label="lab_agm_NoninterestIncomeExcludingProvisionForOtherCreditLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Income, Excluding Provision for Other Credit Losses</link:label>
    <link:label id="lab_agm_NoninterestIncomeExcludingProvisionForOtherCreditLosses_documentation_en-US" xlink:label="lab_agm_NoninterestIncomeExcludingProvisionForOtherCreditLosses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Noninterest Income, Excluding Provision for Other Credit Losses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_NoninterestIncomeExcludingProvisionForOtherCreditLosses" xlink:href="agm-20240331.xsd#agm_NoninterestIncomeExcludingProvisionForOtherCreditLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_NoninterestIncomeExcludingProvisionForOtherCreditLosses" xlink:to="lab_agm_NoninterestIncomeExcludingProvisionForOtherCreditLosses" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined</link:label>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_label_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AggtErrCompNotYetDeterminedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:to="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_531c4229-a79f-4202-bf49-541c71a846eb_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Segments</link:label>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_label_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Segments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingSegmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OperatingSegmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingSegmentsMember" xlink:to="lab_us-gaap_OperatingSegmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfMediumTermNotes_91c212e8-86a2-4451-9e68-caededd7e8f7_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfMediumTermNotes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from issuance of medium-term notes</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfMediumTermNotes_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfMediumTermNotes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Medium-term Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfMediumTermNotes" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromIssuanceOfMediumTermNotes"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfMediumTermNotes" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfMediumTermNotes" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_82d6e78d-5c52-4d81-acf3-33c16fca6497_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Composition of Loan Balances</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accounts, Notes, Loans and Financing Receivable [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_ba2297da-22dc-4673-a3dc-77ee6e85afdc_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_label_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityTaxIdentificationNumber" xlink:to="lab_dei_EntityTaxIdentificationNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_e28fa32d-012a-4e46-a91b-3e418de77afa_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Range [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BalanceSheetLocationDomain_edecc202-19c8-4490-8764-fcb89df0da65_terseLabel_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Balance Sheet Location [Domain]</link:label>
    <link:label id="lab_us-gaap_BalanceSheetLocationDomain_label_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Balance Sheet Location [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BalanceSheetLocationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_BalanceSheetLocationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BalanceSheetLocationDomain" xlink:to="lab_us-gaap_BalanceSheetLocationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_9d6e07cd-afa8-49fb-990a-17c3fd00711f_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_label_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityInteractiveDataCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_GuaranteeAssetMember_a7cb1e9e-13b0-4159-9acf-0b81492c29a4_terseLabel_en-US" xlink:label="lab_agm_GuaranteeAssetMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantee Asset</link:label>
    <link:label id="lab_agm_GuaranteeAssetMember_label_en-US" xlink:label="lab_agm_GuaranteeAssetMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guarantee Asset [Member]</link:label>
    <link:label id="lab_agm_GuaranteeAssetMember_documentation_en-US" xlink:label="lab_agm_GuaranteeAssetMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Guarantee Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_GuaranteeAssetMember" xlink:href="agm-20240331.xsd#agm_GuaranteeAssetMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_GuaranteeAssetMember" xlink:to="lab_agm_GuaranteeAssetMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTable_08f6b692-12a4-4c24-bdbc-d68478828eb8_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-sale Securities [Table]</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTable_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesAvailableForSaleTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_TreasuryFundingSegmentMember_b0e3795a-a37b-47e7-82c0-126c12f1864e_terseLabel_en-US" xlink:label="lab_agm_TreasuryFundingSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Funding</link:label>
    <link:label id="lab_agm_TreasuryFundingSegmentMember_label_en-US" xlink:label="lab_agm_TreasuryFundingSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury, Funding Segment [Member]</link:label>
    <link:label id="lab_agm_TreasuryFundingSegmentMember_documentation_en-US" xlink:label="lab_agm_TreasuryFundingSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Treasury, Funding Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_TreasuryFundingSegmentMember" xlink:href="agm-20240331.xsd#agm_TreasuryFundingSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_TreasuryFundingSegmentMember" xlink:to="lab_agm_TreasuryFundingSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract_2fa671f1-b980-4570-b0cc-6a11e8fa1216_terseLabel_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted- Average Yield</link:label>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract_label_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Held-To-Maturity Securities, Debt Maturities, Weighted Average Yield, Single Maturity Date [Abstract]</link:label>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract_documentation_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Held-to-Maturity Securities, Debt Maturities, Weighted Average Yield, Single Maturity Date [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:href="agm-20240331.xsd#agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:to="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissions_c00b3daf-915e-41fa-a636-b89302ff23c2_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantee and commitment fees</link:label>
    <link:label id="lab_us-gaap_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissions_label_en-US" xlink:label="lab_us-gaap_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Banking, Advisory, Brokerage, and Underwriting Fees and Commissions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissions" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissions" xlink:to="lab_us-gaap_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissions" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureAxis_terseLabel_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measure:</link:label>
    <link:label id="lab_ecd_MeasureAxis_label_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureAxis" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_MeasureAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureAxis" xlink:to="lab_ecd_MeasureAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_32a609bd-0fe9-489c-aec4-7d5bb7e12939_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommitmentsAndContingenciesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_OutstandingRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryIndName" xlink:to="lab_ecd_OutstandingRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDate_f02719d1-fba4-48f1-af9d-dd61ec31af4c_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDate" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total, Amortized Cost</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDate_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Amortized Cost Excluding Accrued Interest, after Allowance for Credit Loss, Maturity, Allocated and Single Maturity Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDate" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDate" xlink:to="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDate" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DebtInstrumentRedemptionAfterPeriodFiveMember_fa6cd50e-8645-4035-98a3-51c5c1d52664_terseLabel_en-US" xlink:label="lab_agm_DebtInstrumentRedemptionAfterPeriodFiveMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_agm_DebtInstrumentRedemptionAfterPeriodFiveMember_label_en-US" xlink:label="lab_agm_DebtInstrumentRedemptionAfterPeriodFiveMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, After Period Five [Member]</link:label>
    <link:label id="lab_agm_DebtInstrumentRedemptionAfterPeriodFiveMember_documentation_en-US" xlink:label="lab_agm_DebtInstrumentRedemptionAfterPeriodFiveMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Period after five representing period after fifth most current period of debt redemption features under terms of the debt agreement.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DebtInstrumentRedemptionAfterPeriodFiveMember" xlink:href="agm-20240331.xsd#agm_DebtInstrumentRedemptionAfterPeriodFiveMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DebtInstrumentRedemptionAfterPeriodFiveMember" xlink:to="lab_agm_DebtInstrumentRedemptionAfterPeriodFiveMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction_a7f658e2-a4ef-4104-8cbb-93ac0a8f5438_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Netting Adjustments</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, Deduction of Financial Instrument Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction" xlink:to="lab_us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_4e3d9eb6-e6da-4c19-af08-02e8406f9cb8_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityIncorporationStateCountryCode" xlink:to="lab_dei_EntityIncorporationStateCountryCode" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoninterestIncome_b5f0089c-8127-42a6-a72d-108d28bdba34_totalLabel_en-US" xlink:label="lab_us-gaap_NoninterestIncome" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Non-interest income</link:label>
    <link:label id="lab_us-gaap_NoninterestIncome_8e8ed6eb-f927-43cf-a002-e45a2e2d716d_terseLabel_en-US" xlink:label="lab_us-gaap_NoninterestIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest expense on interest rate swaps</link:label>
    <link:label id="lab_us-gaap_NoninterestIncome_label_en-US" xlink:label="lab_us-gaap_NoninterestIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoninterestIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NoninterestIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoninterestIncome" xlink:to="lab_us-gaap_NoninterestIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_InstitutionalCreditMember_9c8a8214-cc47-407a-bacd-1e1fb6f3c6f5_terseLabel_en-US" xlink:label="lab_agm_InstitutionalCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AgVantage</link:label>
    <link:label id="lab_agm_InstitutionalCreditMember_36ef1ddd-4e69-48b9-b9ac-e57660c8ab45_verboseLabel_en-US" xlink:label="lab_agm_InstitutionalCreditMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">AgVantage Securities</link:label>
    <link:label id="lab_agm_InstitutionalCreditMember_label_en-US" xlink:label="lab_agm_InstitutionalCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Institutional Credit [Member]</link:label>
    <link:label id="lab_agm_InstitutionalCreditMember_documentation_en-US" xlink:label="lab_agm_InstitutionalCreditMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Institutional Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_InstitutionalCreditMember" xlink:href="agm-20240331.xsd#agm_InstitutionalCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_InstitutionalCreditMember" xlink:to="lab_agm_InstitutionalCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_2b990ac8-4dd8-4e21-b823-47717cf68f40_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_AvailableforsaleSecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract_80406392-6a13-4ee3-9529-8e9f47f6f866_terseLabel_en-US" xlink:label="lab_agm_AvailableforsaleSecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted- Average Yield</link:label>
    <link:label id="lab_agm_AvailableforsaleSecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract_label_en-US" xlink:label="lab_agm_AvailableforsaleSecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Available-for-sale Securities, Debt Maturities, Weighted Average Yield, Single Maturity Date [Abstract]</link:label>
    <link:label id="lab_agm_AvailableforsaleSecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract_documentation_en-US" xlink:label="lab_agm_AvailableforsaleSecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Available-for-sale Securities, Debt Maturities, Weighted Average Yield, Single Maturity Date [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_AvailableforsaleSecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:href="agm-20240331.xsd#agm_AvailableforsaleSecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_AvailableforsaleSecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:to="lab_agm_AvailableforsaleSecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InternalCreditAssessmentDomain_7550f20e-b0f2-4c10-a82c-0c864596cb32_terseLabel_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Domain]</link:label>
    <link:label id="lab_us-gaap_InternalCreditAssessmentDomain_label_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InternalCreditAssessmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InternalCreditAssessmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InternalCreditAssessmentDomain" xlink:to="lab_us-gaap_InternalCreditAssessmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_5e2dc488-04b3-4f52-84fe-95ed45f9213a_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherInvestments_8c4ba939-e113-40d1-bf80-832e00eef11a_terseLabel_en-US" xlink:label="lab_us-gaap_OtherInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other investments</link:label>
    <link:label id="lab_us-gaap_OtherInvestments_label_en-US" xlink:label="lab_us-gaap_OtherInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherInvestments" xlink:to="lab_us-gaap_OtherInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_e443da81-c907-4059-9c34-54336be94962_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gains on financial derivatives</link:label>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_label_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Derivative Instruments, Net, Pretax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GainLossOnDerivativeInstrumentsNetPretax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:to="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoMember_terseLabel_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO</link:label>
    <link:label id="lab_ecd_PeoMember_label_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoMember" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_PeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoMember" xlink:to="lab_ecd_PeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesAbstract_610d30ac-1dea-4704-9691-76de87ce1252_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Held-to-maturity:</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesAbstract_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Fair Value to Amortized Cost, after Allowance for Credit Loss [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_HeldToMaturitySecuritiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesAbstract" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationOtherLongtermIncentivePlansRequisiteServicePeriodRecognition_664f41ca-d6c0-466a-a412-c0d7c78ea5de_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationOtherLongtermIncentivePlansRequisiteServicePeriodRecognition" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other stock-based award activity</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationOtherLongtermIncentivePlansRequisiteServicePeriodRecognition_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationOtherLongtermIncentivePlansRequisiteServicePeriodRecognition" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">APIC, Share-Based Payment Arrangement, Other, Increase for Cost Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationOtherLongtermIncentivePlansRequisiteServicePeriodRecognition" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationOtherLongtermIncentivePlansRequisiteServicePeriodRecognition"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationOtherLongtermIncentivePlansRequisiteServicePeriodRecognition" xlink:to="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationOtherLongtermIncentivePlansRequisiteServicePeriodRecognition" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharesOutstanding_6bd5eb12-c97b-4ffb-8657-208116511e21_periodStartLabel_en-US" xlink:label="lab_us-gaap_SharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance ( in shares)</link:label>
    <link:label id="lab_us-gaap_SharesOutstanding_dc5fb915-5ec8-43b4-9702-268e876de0b8_periodEndLabel_en-US" xlink:label="lab_us-gaap_SharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_SharesOutstanding_label_en-US" xlink:label="lab_us-gaap_SharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharesOutstanding" xlink:to="lab_us-gaap_SharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_baaa397a-82e9-4549-8901-74adfc39cf0f_negatedTerseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Current period charge-offs</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_1d834ecd-e660-4542-b904-54929b581fb4_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current period charge-offs</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_label_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated Two Years Before Latest Fiscal Year, Excluding Accrued Interest, Allowance For Credit Loss, Write Off</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_documentation_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated Two Years Before Latest Fiscal Year, Excluding Accrued Interest, Allowance For Credit Loss, Write Off</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:href="agm-20240331.xsd#agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:to="lab_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable_f8445e5b-3e8a-4194-9c37-26ffefe3286f_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Variable Interest Entities [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Variable Interest Entities [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:to="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CallOptionMember_ac03740f-f137-4692-b3ce-2f3ce8694092_terseLabel_en-US" xlink:label="lab_us-gaap_CallOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Call Option</link:label>
    <link:label id="lab_us-gaap_CallOptionMember_label_en-US" xlink:label="lab_us-gaap_CallOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Call Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CallOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CallOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CallOptionMember" xlink:to="lab_us-gaap_CallOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_eb64b44c-77a6-4847-85a6-39571308348e_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_f1002388-eba0-4db5-9284-8406219f8ecd_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash used in investing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Investing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_HeldToMaturityUnpaidPrincipalBalance_ab5bc7c1-5ec5-4f6e-9fb2-3f5b9af5dc8d_terseLabel_en-US" xlink:label="lab_agm_HeldToMaturityUnpaidPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amount Outstanding</link:label>
    <link:label id="lab_agm_HeldToMaturityUnpaidPrincipalBalance_e696ba6f-5bda-494e-99e2-f229fe7577f0_verboseLabel_en-US" xlink:label="lab_agm_HeldToMaturityUnpaidPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unpaid Principal Balance</link:label>
    <link:label id="lab_agm_HeldToMaturityUnpaidPrincipalBalance_label_en-US" xlink:label="lab_agm_HeldToMaturityUnpaidPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Held-To-Maturity Unpaid Principal Balance</link:label>
    <link:label id="lab_agm_HeldToMaturityUnpaidPrincipalBalance_documentation_en-US" xlink:label="lab_agm_HeldToMaturityUnpaidPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Held-To-Maturity Unpaid Principal Balance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_HeldToMaturityUnpaidPrincipalBalance" xlink:href="agm-20240331.xsd#agm_HeldToMaturityUnpaidPrincipalBalance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_HeldToMaturityUnpaidPrincipalBalance" xlink:to="lab_agm_HeldToMaturityUnpaidPrincipalBalance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestRateSwapMember_00482364-59c1-41af-9a87-639f94b166bf_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateSwapMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate Swap</link:label>
    <link:label id="lab_us-gaap_InterestRateSwapMember_label_en-US" xlink:label="lab_us-gaap_InterestRateSwapMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swap [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestRateSwapMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestRateSwapMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestRateSwapMember" xlink:to="lab_us-gaap_InterestRateSwapMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_cb8d8c5d-6d81-4d5d-9941-90b9f1574143_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentAxis" xlink:to="lab_us-gaap_DebtInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions_478b0bfb-d455-4aba-be62-3484c48b5feb_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Available-for-sale, securities in unrealized loss positions</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Unrealized Loss Position, Number of Positions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingAggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_OutstandingAggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingAggtErrCompAmt" xlink:to="lab_ecd_OutstandingAggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputTypeDomain_dfaa4c6e-8bf7-4099-b1ac-47816005974c_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Domain]</link:label>
    <link:label id="lab_us-gaap_MeasurementInputTypeDomain_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MeasurementInputTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputTypeDomain" xlink:to="lab_us-gaap_MeasurementInputTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeCollateralRightToReclaimSecurities_1091835d-823f-47ec-9cbd-0101bbc097fa_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeCollateralRightToReclaimSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial instruments pledged</link:label>
    <link:label id="lab_us-gaap_DerivativeCollateralRightToReclaimSecurities_label_en-US" xlink:label="lab_us-gaap_DerivativeCollateralRightToReclaimSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, Collateral, Right to Reclaim Security Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeCollateralRightToReclaimSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeCollateralRightToReclaimSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeCollateralRightToReclaimSecurities" xlink:to="lab_us-gaap_DerivativeCollateralRightToReclaimSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Liabilities_83839eeb-e337-4083-9f3f-3afba2a56a1a_totalLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_label_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_Liabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Liabilities" xlink:to="lab_us-gaap_Liabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromFeesReceived_17708dba-1a42-4335-b595-94f9ede36f1d_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromFeesReceived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantee fees received</link:label>
    <link:label id="lab_us-gaap_ProceedsFromFeesReceived_label_en-US" xlink:label="lab_us-gaap_ProceedsFromFeesReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Fees Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromFeesReceived" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromFeesReceived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromFeesReceived" xlink:to="lab_us-gaap_ProceedsFromFeesReceived" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementFrequencyDomain_6667833b-ef95-4ae4-bf3c-bcab8ef68bae_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement Frequency [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementFrequencyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementFrequencyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueMeasurementFrequencyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementFrequencyDomain" xlink:to="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CorporateMember_bf954b41-cc8f-4a93-8436-f77f749628d3_terseLabel_en-US" xlink:label="lab_us-gaap_CorporateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Corporate</link:label>
    <link:label id="lab_us-gaap_CorporateMember_label_en-US" xlink:label="lab_us-gaap_CorporateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Corporate Segment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CorporateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CorporateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CorporateMember" xlink:to="lab_us-gaap_CorporateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract_91d18db9-1d9e-4da8-b0e3-4720d2a9e390_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, before Allowance for Credit Loss [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract" xlink:to="lab_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis_e27bcfd9-0a0c-4864-8347-cfeddb7450f8_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:to="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesTradingUnrealizedLoss_fe73c6b2-eed9-4107-9143-81ec9c6ab9fd_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesTradingUnrealizedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Unrealized Losses</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesTradingUnrealizedLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesTradingUnrealizedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, Unrealized Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesTradingUnrealizedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesTradingUnrealizedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesTradingUnrealizedLoss" xlink:to="lab_us-gaap_DebtSecuritiesTradingUnrealizedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProvisionForOtherCreditLosses_f9573a75-33da-47cc-86fd-839056a6bb75_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ProvisionForOtherCreditLosses" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Release of/(provision for) reserve for losses</link:label>
    <link:label id="lab_us-gaap_ProvisionForOtherCreditLosses_8b85244c-2cc5-4ea1-8bcc-d8015c8afd87_verboseLabel_en-US" xlink:label="lab_us-gaap_ProvisionForOtherCreditLosses" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Release of losses</link:label>
    <link:label id="lab_us-gaap_ProvisionForOtherCreditLosses_label_en-US" xlink:label="lab_us-gaap_ProvisionForOtherCreditLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Provision for Other Credit Losses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProvisionForOtherCreditLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProvisionForOtherCreditLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProvisionForOtherCreditLosses" xlink:to="lab_us-gaap_ProvisionForOtherCreditLosses" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_NonRule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:to="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTax_1314b452-893a-4ff6-869c-ff0f1728164b_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income/(loss) before tax</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months_fb8c5ca1-cb66-4614-9659-4654d8dd2c5e_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized loss position for less than 12 months, Fair Value</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Continuous Unrealized Loss Position, Less than 12 Months</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_ab34c27d-374d-413a-881c-6a0d71cbfb19_terseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General and administrative</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:to="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases_e5d5955f-d277-49d0-bbb0-498700d18850_terseLabel_en-US" xlink:label="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans</link:label>
    <link:label id="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases_961e7fcb-c981-4e35-8ad9-6ba115e3db2b_verboseLabel_en-US" xlink:label="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Interest Income Loans</link:label>
    <link:label id="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases_label_en-US" xlink:label="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Fee Income, Loans and Leases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestAndFeeIncomeLoansAndLeases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:to="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShortTermDebtWeightedAverageInterestRate_5c206981-bcf0-4c0a-a8a4-cbc0e7fb747e_terseLabel_en-US" xlink:label="lab_us-gaap_ShortTermDebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding, Weighted - average rate</link:label>
    <link:label id="lab_us-gaap_ShortTermDebtWeightedAverageInterestRate_6f1b6752-1b8b-4dbb-97c8-e62569d75fdc_verboseLabel_en-US" xlink:label="lab_us-gaap_ShortTermDebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Short-term debt, weighted average rate (as a percent)</link:label>
    <link:label id="lab_us-gaap_ShortTermDebtWeightedAverageInterestRate_label_en-US" xlink:label="lab_us-gaap_ShortTermDebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Debt, Weighted Average Interest Rate, at Point in Time</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermDebtWeightedAverageInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShortTermDebtWeightedAverageInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortTermDebtWeightedAverageInterestRate" xlink:to="lab_us-gaap_ShortTermDebtWeightedAverageInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoninterestExpenseAbstract_6dbb6f9b-efe4-4253-87d1-4f20c504e51a_terseLabel_en-US" xlink:label="lab_us-gaap_NoninterestExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating expenses:</link:label>
    <link:label id="lab_us-gaap_NoninterestExpenseAbstract_label_en-US" xlink:label="lab_us-gaap_NoninterestExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Expense [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoninterestExpenseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NoninterestExpenseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoninterestExpenseAbstract" xlink:to="lab_us-gaap_NoninterestExpenseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_TreasuryInvestmentsSegmentMember_a56d978a-a2aa-4bdb-8b36-f5b27678603e_terseLabel_en-US" xlink:label="lab_agm_TreasuryInvestmentsSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments</link:label>
    <link:label id="lab_agm_TreasuryInvestmentsSegmentMember_label_en-US" xlink:label="lab_agm_TreasuryInvestmentsSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury, Investments Segment [Member]</link:label>
    <link:label id="lab_agm_TreasuryInvestmentsSegmentMember_documentation_en-US" xlink:label="lab_agm_TreasuryInvestmentsSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Treasury, Investments Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_TreasuryInvestmentsSegmentMember" xlink:href="agm-20240331.xsd#agm_TreasuryInvestmentsSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_TreasuryInvestmentsSegmentMember" xlink:to="lab_agm_TreasuryInvestmentsSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Table</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AwardsCloseToMnpiDiscTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockMember_181820a3-f772-4a06-8957-e573e4f31dae_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Stock</link:label>
    <link:label id="lab_us-gaap_PreferredStockMember_label_en-US" xlink:label="lab_us-gaap_PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockMember" xlink:to="lab_us-gaap_PreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract_cf6fd2b9-7eee-4bb7-86c0-6e5f30f4c193_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income/(loss):</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), before Tax [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TradingSecuritiesDebt_090ff7b3-4cfa-43c7-96d9-31a252f7451b_terseLabel_en-US" xlink:label="lab_us-gaap_TradingSecuritiesDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading</link:label>
    <link:label id="lab_us-gaap_TradingSecuritiesDebt_label_en-US" xlink:label="lab_us-gaap_TradingSecuritiesDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradingSecuritiesDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TradingSecuritiesDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TradingSecuritiesDebt" xlink:to="lab_us-gaap_TradingSecuritiesDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_TotalAmountsOfLineItemsPresentedInTheConsolidatedStatementOfIncome_b6c104e1-a783-4c48-b102-4762223ad65b_terseLabel_en-US" xlink:label="lab_agm_TotalAmountsOfLineItemsPresentedInTheConsolidatedStatementOfIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_agm_TotalAmountsOfLineItemsPresentedInTheConsolidatedStatementOfIncome_label_en-US" xlink:label="lab_agm_TotalAmountsOfLineItemsPresentedInTheConsolidatedStatementOfIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Amounts of Line Items Presented in the Consolidated Statement of Income</link:label>
    <link:label id="lab_agm_TotalAmountsOfLineItemsPresentedInTheConsolidatedStatementOfIncome_documentation_en-US" xlink:label="lab_agm_TotalAmountsOfLineItemsPresentedInTheConsolidatedStatementOfIncome" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Total Amounts of Line Items Presented in the Consolidated Statement of Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_TotalAmountsOfLineItemsPresentedInTheConsolidatedStatementOfIncome" xlink:href="agm-20240331.xsd#agm_TotalAmountsOfLineItemsPresentedInTheConsolidatedStatementOfIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_TotalAmountsOfLineItemsPresentedInTheConsolidatedStatementOfIncome" xlink:to="lab_agm_TotalAmountsOfLineItemsPresentedInTheConsolidatedStatementOfIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember_bf57890b-f56e-4b3f-9476-6858f2eb25b3_terseLabel_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Farmer Mac Guaranteed Securities</link:label>
    <link:label id="lab_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember_8b2278e3-2017-41a0-a44f-3d3cd145bef2_verboseLabel_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Farmer Mac Guaranteed Securities</link:label>
    <link:label id="lab_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember_label_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage-Backed Securities, Issued by US Government Sponsored Enterprises [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember" xlink:to="lab_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock_95270228-4a61-4680-a189-e5a1862ebff9_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Financing Receivable Credit Quality Indicators</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable Credit Quality Indicators [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:to="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff_4e5aa26c-204d-4474-bb0b-8d51d7b2f869_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Charge-offs</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff_4c98a2ef-59cf-4be9-8ba5-ad2f6f7f15a5_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Current period charge-offs</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff_6c3c04de-bb9f-42c7-a212-05f880b5158d_totalLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Current period charge-offs</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Allowance for Credit Loss, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAllowanceForCreditLoss_2cbc7165-9360-440c-b6be-ff6390c52849_negatedLabel_en-US" xlink:label="lab_agm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Allowance for Losses</link:label>
    <link:label id="lab_agm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAllowanceForCreditLoss_label_en-US" xlink:label="lab_agm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Allowance for Credit Loss</link:label>
    <link:label id="lab_agm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAllowanceForCreditLoss_documentation_en-US" xlink:label="lab_agm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAllowanceForCreditLoss" xlink:href="agm-20240331.xsd#agm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAllowanceForCreditLoss" xlink:to="lab_agm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilities_588e8a2b-8c80-4ea5-9db6-1be062351664_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrower remittances</link:label>
    <link:label id="lab_us-gaap_OtherLiabilities_label_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilities" xlink:to="lab_us-gaap_OtherLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerSharePolicyTextBlock_7a20c6ff-5b59-400b-ad11-934c1af9994d_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Common Share</link:label>
    <link:label id="lab_us-gaap_EarningsPerSharePolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerSharePolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EarningsPerSharePolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerSharePolicyTextBlock" xlink:to="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodShares_b40086b1-3e20-46f1-8a07-d08cbae0c702_terseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares repurchased (in shares)</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodShares_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased During Period, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedDuringPeriodShares" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockRepurchasedDuringPeriodShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchasedDuringPeriodShares" xlink:to="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_fb08b1e8-84cf-455e-8dab-ff3308376d93_negatedTerseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Current period charge-offs</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_cf92643e-8a76-44b9-80a2-462c199eb9fa_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current period charge-offs</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_label_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated In Fiscal Year Before Latest Fiscal Year, Excluding Accrued Interest, Allowance For Credit Loss, Write Off</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_documentation_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated In Fiscal Year Before Latest Fiscal Year, Excluding Accrued Interest, Allowance For Credit Loss, Write Off</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:href="agm-20240331.xsd#agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:to="lab_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock_02d845fd-718f-4518-adb7-55ebec3e1fa5_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Accumulated Other Comprehensive Income, Net of Tax</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accumulated Other Comprehensive Income (Loss) [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_263ff2da-9beb-496d-b760-cf20f1c50fb8_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_USTreasuryAndGovernmentMember_c57a3d9b-465d-4b15-85e1-a679bfdafcf3_terseLabel_en-US" xlink:label="lab_us-gaap_USTreasuryAndGovernmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Farmer Mac Guaranteed Securities and USDA Securities</link:label>
    <link:label id="lab_us-gaap_USTreasuryAndGovernmentMember_label_en-US" xlink:label="lab_us-gaap_USTreasuryAndGovernmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Treasury and Government [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USTreasuryAndGovernmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_USTreasuryAndGovernmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_USTreasuryAndGovernmentMember" xlink:to="lab_us-gaap_USTreasuryAndGovernmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_MediumTermNotesCalledDuringThePeriod_7cbc8fc8-8596-4ebd-bb73-fcfc521e1442_terseLabel_en-US" xlink:label="lab_agm_MediumTermNotesCalledDuringThePeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Medium term notes called during the period</link:label>
    <link:label id="lab_agm_MediumTermNotesCalledDuringThePeriod_label_en-US" xlink:label="lab_agm_MediumTermNotesCalledDuringThePeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Medium Term Notes Called During the Period</link:label>
    <link:label id="lab_agm_MediumTermNotesCalledDuringThePeriod_documentation_en-US" xlink:label="lab_agm_MediumTermNotesCalledDuringThePeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Medium Term Notes Called During the Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_MediumTermNotesCalledDuringThePeriod" xlink:href="agm-20240331.xsd#agm_MediumTermNotesCalledDuringThePeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_MediumTermNotesCalledDuringThePeriod" xlink:to="lab_agm_MediumTermNotesCalledDuringThePeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_6c31edae-d202-4aba-9954-00a1eb6997d7_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Operating Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_0e74b61e-5a10-4012-8fed-6e3b680f8dc8_terseLabel_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_label_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementClassOfStockAxis" xlink:to="lab_us-gaap_StatementClassOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitiesTable_c5bffc17-e11c-4c27-af84-fbf883a7a1e1_terseLabel_en-US" xlink:label="lab_dei_EntitiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entities [Table]</link:label>
    <link:label id="lab_dei_EntitiesTable_label_en-US" xlink:label="lab_dei_EntitiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entities [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitiesTable" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntitiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitiesTable" xlink:to="lab_dei_EntitiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DebtSecuritiesTradingMember_686cd6c6-b157-4f5b-9568-455d68c65a7b_terseLabel_en-US" xlink:label="lab_agm_DebtSecuritiesTradingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Securities</link:label>
    <link:label id="lab_agm_DebtSecuritiesTradingMember_label_en-US" xlink:label="lab_agm_DebtSecuritiesTradingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading [Member]</link:label>
    <link:label id="lab_agm_DebtSecuritiesTradingMember_documentation_en-US" xlink:label="lab_agm_DebtSecuritiesTradingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DebtSecuritiesTradingMember" xlink:href="agm-20240331.xsd#agm_DebtSecuritiesTradingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DebtSecuritiesTradingMember" xlink:to="lab_agm_DebtSecuritiesTradingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompRecoveryTable_terseLabel_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery</link:label>
    <link:label id="lab_ecd_ErrCompRecoveryTable_label_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompRecoveryTable" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_ErrCompRecoveryTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompRecoveryTable" xlink:to="lab_ecd_ErrCompRecoveryTable" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_HeldtoMaturitySecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield_f52b72e9-c5fc-4705-a890-0c700a6e0cc2_terseLabel_en-US" xlink:label="lab_agm_HeldtoMaturitySecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due within one year</link:label>
    <link:label id="lab_agm_HeldtoMaturitySecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield_label_en-US" xlink:label="lab_agm_HeldtoMaturitySecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Held-to-Maturity Securities, Debt Maturities, Next Twelve Months, Weighted-Average Yield</link:label>
    <link:label id="lab_agm_HeldtoMaturitySecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield_documentation_en-US" xlink:label="lab_agm_HeldtoMaturitySecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Held-to-Maturity Securities, Debt Maturities, Next Twelve Months, Weighted-Average Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_HeldtoMaturitySecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield" xlink:href="agm-20240331.xsd#agm_HeldtoMaturitySecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_HeldtoMaturitySecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield" xlink:to="lab_agm_HeldtoMaturitySecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_Security12gTitle_941a3172-42bd-42e9-bc8f-f3378d85c76a_terseLabel_en-US" xlink:label="lab_dei_Security12gTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(g) Security</link:label>
    <link:label id="lab_dei_Security12gTitle_label_en-US" xlink:label="lab_dei_Security12gTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title of 12(g) Security</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12gTitle" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_Security12gTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_Security12gTitle" xlink:to="lab_dei_Security12gTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodThreeMember_ef22967d-2305-4b47-bd40-3bba86c5ca2d_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodThreeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Three years</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodThreeMember_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodThreeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period Three [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodThreeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentRedemptionPeriodThreeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPeriodThreeMember" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPeriodThreeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgedAssetFairValueHedgeCumulativeIncreaseDecrease_f72a93ec-4b94-46f5-81d9-caca8c16ed20_terseLabel_en-US" xlink:label="lab_us-gaap_HedgedAssetFairValueHedgeCumulativeIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedged Asset</link:label>
    <link:label id="lab_us-gaap_HedgedAssetFairValueHedgeCumulativeIncreaseDecrease_label_en-US" xlink:label="lab_us-gaap_HedgedAssetFairValueHedgeCumulativeIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedged Asset, Fair Value Hedge, Cumulative Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgedAssetFairValueHedgeCumulativeIncreaseDecrease" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_HedgedAssetFairValueHedgeCumulativeIncreaseDecrease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgedAssetFairValueHedgeCumulativeIncreaseDecrease" xlink:to="lab_us-gaap_HedgedAssetFairValueHedgeCumulativeIncreaseDecrease" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeriesGPreferredStockMember_963acbf1-5114-42d5-8020-d7fd8a778db5_verboseLabel_en-US" xlink:label="lab_us-gaap_SeriesGPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">4.875% Non-Cumulative Preferred Stock, Series G</link:label>
    <link:label id="lab_us-gaap_SeriesGPreferredStockMember_94244b90-b357-47c3-910a-2d9d30591df3_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesGPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series G</link:label>
    <link:label id="lab_us-gaap_SeriesGPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesGPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series G Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesGPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SeriesGPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesGPreferredStockMember" xlink:to="lab_us-gaap_SeriesGPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AwardTmgHowMnpiCnsdrdTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:to="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MediumTermNotesMember_a6188a6a-90d3-4879-8cfe-501bcb305cee_verboseLabel_en-US" xlink:label="lab_us-gaap_MediumTermNotesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Medium-term notes</link:label>
    <link:label id="lab_us-gaap_MediumTermNotesMember_label_en-US" xlink:label="lab_us-gaap_MediumTermNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Medium-term Notes [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MediumTermNotesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MediumTermNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MediumTermNotesMember" xlink:to="lab_us-gaap_MediumTermNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInformationLineItems_c748bdf4-b846-4356-adde-49dd824bc15a_terseLabel_en-US" xlink:label="lab_dei_EntityInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Information [Line Items]</link:label>
    <link:label id="lab_dei_EntityInformationLineItems_label_en-US" xlink:label="lab_dei_EntityInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInformationLineItems" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInformationLineItems" xlink:to="lab_dei_EntityInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritiesPurchasedUnderAgreementsToResell_fcf51ee2-d96a-43e6-bb2b-55aa77904f79_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesPurchasedUnderAgreementsToResell" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial derivatives, net payable position</link:label>
    <link:label id="lab_us-gaap_SecuritiesPurchasedUnderAgreementsToResell_label_en-US" xlink:label="lab_us-gaap_SecuritiesPurchasedUnderAgreementsToResell" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Securities Purchased under Agreements to Resell</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesPurchasedUnderAgreementsToResell" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SecuritiesPurchasedUnderAgreementsToResell"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritiesPurchasedUnderAgreementsToResell" xlink:to="lab_us-gaap_SecuritiesPurchasedUnderAgreementsToResell" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsAxis_3e525925-d464-47d7-aab7-1ef05a45152e_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation Items [Axis]</link:label>
    <link:label id="lab_srt_ConsolidationItemsAxis_label_en-US" xlink:label="lab_srt_ConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation Items [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsAxis" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_ConsolidationItemsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidationItemsAxis" xlink:to="lab_srt_ConsolidationItemsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements_db20180e-6dc5-4741-8dc4-294ce5827ec0_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Settlements</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Settlements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInFinanceReceivables_1ef6527b-8ebb-4bab-bc78-df77c857c915_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInFinanceReceivables" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (decrease) in loan volume</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInFinanceReceivables_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInFinanceReceivables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Finance Receivables</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInFinanceReceivables" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInFinanceReceivables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInFinanceReceivables" xlink:to="lab_us-gaap_IncreaseDecreaseInFinanceReceivables" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember_2b7fa82f-d41f-49eb-95d4-06cb67ddb2f8_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AOCI, Cash Flow Hedge</link:label>
    <link:label id="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Gain (Loss), Net, Cash Flow Hedge, Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:to="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_ScheduleOfLongTermStandbyPurchaseCommitmentsTableTextBlock_e649df49-f1eb-4fe3-9633-b296d3633cf5_terseLabel_en-US" xlink:label="lab_agm_ScheduleOfLongTermStandbyPurchaseCommitmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Standby Purchase Commitments</link:label>
    <link:label id="lab_agm_ScheduleOfLongTermStandbyPurchaseCommitmentsTableTextBlock_label_en-US" xlink:label="lab_agm_ScheduleOfLongTermStandbyPurchaseCommitmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Standby Purchase Commitments [Table Text Block]</link:label>
    <link:label id="lab_agm_ScheduleOfLongTermStandbyPurchaseCommitmentsTableTextBlock_documentation_en-US" xlink:label="lab_agm_ScheduleOfLongTermStandbyPurchaseCommitmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Standby Purchase Commitments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_ScheduleOfLongTermStandbyPurchaseCommitmentsTableTextBlock" xlink:href="agm-20240331.xsd#agm_ScheduleOfLongTermStandbyPurchaseCommitmentsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_ScheduleOfLongTermStandbyPurchaseCommitmentsTableTextBlock" xlink:to="lab_agm_ScheduleOfLongTermStandbyPurchaseCommitmentsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_3e727fbf-1431-46bc-a5c1-2747e0523a67_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesIssued" xlink:to="lab_us-gaap_PreferredStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_59d7ce1b-5925-4e17-a336-5af863092b5b_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DerivativeLiabilityIncludingNotSubjectToMasterNettingArrangementAfterOffsetAndDeductionNetAmount_cc75cf6b-644f-451d-9b73-41d24931865a_negatedTotalLabel_en-US" xlink:label="lab_agm_DerivativeLiabilityIncludingNotSubjectToMasterNettingArrangementAfterOffsetAndDeductionNetAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Net amount</link:label>
    <link:label id="lab_agm_DerivativeLiabilityIncludingNotSubjectToMasterNettingArrangementAfterOffsetAndDeductionNetAmount_label_en-US" xlink:label="lab_agm_DerivativeLiabilityIncludingNotSubjectToMasterNettingArrangementAfterOffsetAndDeductionNetAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Including Not Subject To Master Netting Arrangement, After Offset And Deduction, Net Amount</link:label>
    <link:label id="lab_agm_DerivativeLiabilityIncludingNotSubjectToMasterNettingArrangementAfterOffsetAndDeductionNetAmount_documentation_en-US" xlink:label="lab_agm_DerivativeLiabilityIncludingNotSubjectToMasterNettingArrangementAfterOffsetAndDeductionNetAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Liability, Including Not Subject To Master Netting Arrangement, After Offset And Deduction, Net Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DerivativeLiabilityIncludingNotSubjectToMasterNettingArrangementAfterOffsetAndDeductionNetAmount" xlink:href="agm-20240331.xsd#agm_DerivativeLiabilityIncludingNotSubjectToMasterNettingArrangementAfterOffsetAndDeductionNetAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DerivativeLiabilityIncludingNotSubjectToMasterNettingArrangementAfterOffsetAndDeductionNetAmount" xlink:to="lab_agm_DerivativeLiabilityIncludingNotSubjectToMasterNettingArrangementAfterOffsetAndDeductionNetAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FixedInterestRateMember_a4aa6f99-1f37-41e8-93ba-ce47f95ef4d5_terseLabel_en-US" xlink:label="lab_agm_FixedInterestRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed Interest Rate</link:label>
    <link:label id="lab_agm_FixedInterestRateMember_label_en-US" xlink:label="lab_agm_FixedInterestRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Interest Rate [Member]</link:label>
    <link:label id="lab_agm_FixedInterestRateMember_documentation_en-US" xlink:label="lab_agm_FixedInterestRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Interest Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FixedInterestRateMember" xlink:href="agm-20240331.xsd#agm_FixedInterestRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FixedInterestRateMember" xlink:to="lab_agm_FixedInterestRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansHeldForSaleFairValueDisclosure_1b36f0cb-806f-4538-b774-62d5c490c737_terseLabel_en-US" xlink:label="lab_us-gaap_LoansHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans held for sale, at lower of cost or fair value</link:label>
    <link:label id="lab_us-gaap_LoansHeldForSaleFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LoansHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan, Held-for-Sale, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansHeldForSaleFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LoansHeldForSaleFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansHeldForSaleFairValueDisclosure" xlink:to="lab_us-gaap_LoansHeldForSaleFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure, Table</link:label>
    <link:label id="lab_ecd_PvpTableTextBlock_label_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_PvpTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTableTextBlock" xlink:to="lab_ecd_PvpTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_990b3170-1703-4fed-b763-668d6136262c_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetGainLossIncludingPortionAttributableToNoncontrollingInterestMember_2d3ce701-f681-4b30-8173-deb68ffca623_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetGainLossIncludingPortionAttributableToNoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Securities</link:label>
    <link:label id="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetGainLossIncludingPortionAttributableToNoncontrollingInterestMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetGainLossIncludingPortionAttributableToNoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Defined Benefit Plans Adjustment, Net Gain (Loss) Including Portion Attributable to Noncontrolling Interest [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetGainLossIncludingPortionAttributableToNoncontrollingInterestMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetGainLossIncludingPortionAttributableToNoncontrollingInterestMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetGainLossIncludingPortionAttributableToNoncontrollingInterestMember" xlink:to="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetGainLossIncludingPortionAttributableToNoncontrollingInterestMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndTitle_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title</link:label>
    <link:label id="lab_ecd_TrdArrIndTitle_label_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Title</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndTitle" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_TrdArrIndTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndTitle" xlink:to="lab_ecd_TrdArrIndTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss_8275c21c-9899-44df-8019-9f885e26b1fc_totalLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net interest income after release of/(provision for) losses</link:label>
    <link:label id="lab_us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss_label_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income (Expense), after Provision for Loan Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" xlink:to="lab_us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsWeightedAverageYield_422aa9b5-2872-45d4-937f-df0e96f08e0f_terseLabel_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after five years through ten years</link:label>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsWeightedAverageYield_label_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Held-To-Maturity Securities, Debt Maturities, After Five Through Ten Years, Weighted Average Yield</link:label>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsWeightedAverageYield_documentation_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Held-To-Maturity Securities, Debt Maturities, After Five Through Ten Years, Weighted Average Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsWeightedAverageYield" xlink:href="agm-20240331.xsd#agm_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsWeightedAverageYield"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsWeightedAverageYield" xlink:to="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsWeightedAverageYield" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockMember_b5af65fa-78c3-4d4d-8452-a9aea1908954_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockMember" xlink:to="lab_us-gaap_CommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_IndividualAxis_terseLabel_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individual:</link:label>
    <link:label id="lab_ecd_IndividualAxis_label_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Individual [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_IndividualAxis" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_IndividualAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_IndividualAxis" xlink:to="lab_ecd_IndividualAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressPostalZipCode_97c9d356-991e-4cd6-8299-72fe29694173_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressPostalZipCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressPostalZipCode" xlink:to="lab_dei_EntityAddressPostalZipCode" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearThree_5a9177e1-390c-48b9-be4a-1ae39d6e12f4_terseLabel_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearThree_label_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, Year Three</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearThree_documentation_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearThree" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LongTermDebtWithInterestRateResetMaturityYearThree" xlink:href="agm-20240331.xsd#agm_LongTermDebtWithInterestRateResetMaturityYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LongTermDebtWithInterestRateResetMaturityYearThree" xlink:to="lab_agm_LongTermDebtWithInterestRateResetMaturityYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_ClearedSwapsMember_d6dba0a8-e0bf-4bb5-90d9-0af450b1dd35_terseLabel_en-US" xlink:label="lab_agm_ClearedSwapsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cleared Swaps</link:label>
    <link:label id="lab_agm_ClearedSwapsMember_label_en-US" xlink:label="lab_agm_ClearedSwapsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cleared Swaps [Member]</link:label>
    <link:label id="lab_agm_ClearedSwapsMember_documentation_en-US" xlink:label="lab_agm_ClearedSwapsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cleared Swaps</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_ClearedSwapsMember" xlink:href="agm-20240331.xsd#agm_ClearedSwapsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_ClearedSwapsMember" xlink:to="lab_agm_ClearedSwapsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementLocationDomain_d39896a2-0b31-4e24-a533-00f2d4d0fc23_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Statement Location [Domain]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementLocationDomain_label_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement Location [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementLocationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncomeStatementLocationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementLocationDomain" xlink:to="lab_us-gaap_IncomeStatementLocationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract_eff9558a-38d6-40b6-a805-ddd1cfeac585_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair&#160;Value</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Maturity, Allocated and Single Maturity Date, Fair Value [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet_ff859394-950d-4e1b-b8c0-1030c90922e6_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Unamortized Premium/(Discount)</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet_d7785e53-9407-4da5-9a2b-08f9d6f1e975_negatedLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Unamortized Premium/(Discount)</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Unamortized Discount (Premium), Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet" xlink:to="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember_6518b4e9-bb67-4874-a129-35d9be3c4d40_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discounted cash flow</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Technique, Discounted Cash Flow [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ValuationTechniqueDiscountedCashFlowMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:to="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateYearOne_3e969395-d72f-41b3-b766-64ec9a4c4534_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateYearOne" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due within one year</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateYearOne_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateYearOne" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Amortized Cost Excluding Accrued Interest, after Allowance for Credit Loss, Maturity, Allocated and Single Maturity Date, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateYearOne" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateYearOne"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateYearOne" xlink:to="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateYearOne" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock_a1bf2416-3dbd-4b26-9423-08162087c100_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value Measurements</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurements, Recurring and Nonrecurring [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtWeightedAverageInterestRate_a3190dd1-b9be-452f-9934-bcb98a2b6830_terseLabel_en-US" xlink:label="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total weighted - average rate</link:label>
    <link:label id="lab_us-gaap_DebtWeightedAverageInterestRate_label_en-US" xlink:label="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Weighted Average Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtWeightedAverageInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtWeightedAverageInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtWeightedAverageInterestRate" xlink:to="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetFairValueGrossAssetIncludingNotSubjectToMasterNettingArrangement_54156553-11f6-4f3e-b047-634ef5600986_totalLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueGrossAssetIncludingNotSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Amount Presented in the Consolidated Balance Sheet</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetFairValueGrossAssetIncludingNotSubjectToMasterNettingArrangement_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueGrossAssetIncludingNotSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Fair Value, Gross Asset Including Not Subject to Master Netting Arrangement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetFairValueGrossAssetIncludingNotSubjectToMasterNettingArrangement" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeAssetFairValueGrossAssetIncludingNotSubjectToMasterNettingArrangement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetFairValueGrossAssetIncludingNotSubjectToMasterNettingArrangement" xlink:to="lab_us-gaap_DerivativeAssetFairValueGrossAssetIncludingNotSubjectToMasterNettingArrangement" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilities_f84da19b-246e-409f-8c5d-4f5f0946e859_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable and accrued expenses</link:label>
    <link:label id="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilities_label_en-US" xlink:label="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable and Other Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableAndOtherAccruedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccountsPayableAndOtherAccruedLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableAndOtherAccruedLiabilities" xlink:to="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityTransferInUnrealizedGainLoss_868c1c83-b7e3-40ce-90c3-e9230f7f947e_negatedTerseLabel_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityTransferInUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Held-to-maturity, transfer in, unrealized loss</link:label>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityTransferInUnrealizedGainLoss_label_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityTransferInUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Transfer In, Unrealized Gain (Loss)</link:label>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityTransferInUnrealizedGainLoss_documentation_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityTransferInUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale Transfer To Held-to-Maturity, Unrealized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DebtSecuritiesHeldToMaturityTransferInUnrealizedGainLoss" xlink:href="agm-20240331.xsd#agm_DebtSecuritiesHeldToMaturityTransferInUnrealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DebtSecuritiesHeldToMaturityTransferInUnrealizedGainLoss" xlink:to="lab_agm_DebtSecuritiesHeldToMaturityTransferInUnrealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FarmerMacGuaranteedSecuritiesMember_66da8daf-f3d1-4487-af85-776abf31a145_terseLabel_en-US" xlink:label="lab_agm_FarmerMacGuaranteedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Farmer Mac Guaranteed USDA Securities</link:label>
    <link:label id="lab_agm_FarmerMacGuaranteedSecuritiesMember_label_en-US" xlink:label="lab_agm_FarmerMacGuaranteedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Farmer Mac Guaranteed Securities [Member]</link:label>
    <link:label id="lab_agm_FarmerMacGuaranteedSecuritiesMember_documentation_en-US" xlink:label="lab_agm_FarmerMacGuaranteedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Farmer Mac Guaranteed Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FarmerMacGuaranteedSecuritiesMember" xlink:href="agm-20240331.xsd#agm_FarmerMacGuaranteedSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FarmerMacGuaranteedSecuritiesMember" xlink:to="lab_agm_FarmerMacGuaranteedSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MinimumMember_2ee67ef1-6d85-40b0-90a7-48286a1d8974_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum</link:label>
    <link:label id="lab_srt_MinimumMember_label_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Minimum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_MinimumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MinimumMember" xlink:to="lab_srt_MinimumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoninterestIncomeOtherOperatingIncome_71e4829c-b1cb-4b3c-9f78-638861b78b63_terseLabel_en-US" xlink:label="lab_us-gaap_NoninterestIncomeOtherOperatingIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income</link:label>
    <link:label id="lab_us-gaap_NoninterestIncomeOtherOperatingIncome_label_en-US" xlink:label="lab_us-gaap_NoninterestIncomeOtherOperatingIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Income, Other Operating Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoninterestIncomeOtherOperatingIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NoninterestIncomeOtherOperatingIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoninterestIncomeOtherOperatingIncome" xlink:to="lab_us-gaap_NoninterestIncomeOtherOperatingIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareCashPaid_77bcd301-ad9e-4759-a7fb-485095de55fe_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Quarterly dividend on all classes of common stock (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareCashPaid_label_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Dividends, Per Share, Cash Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockDividendsPerShareCashPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:to="lab_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax_e98e693f-a6da-4076-a41d-c0f3795f1090_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income/(loss) net of tax</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax_7d1f9849-1ee7-48e7-808a-6792891738ee_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income (loss) net of tax</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_2b6c5d8a-0479-4ce4-ae91-0b799f8889dd_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:to="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsAbstract_b3cc5159-172e-489e-bc03-48d2e2373bf1_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets:</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="lab_us-gaap_AssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AwardTmgMnpiDiscTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:to="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue_e3a3a1f5-a182-410e-b5ba-0e384068e2c5_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after ten years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, after Year 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GuarantyAssets_5b1e96c1-1a6b-49f2-b499-281587dc466f_terseLabel_en-US" xlink:label="lab_us-gaap_GuarantyAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantee and commitment fees receivable</link:label>
    <link:label id="lab_us-gaap_GuarantyAssets_19eba260-86de-4b34-9960-f8d6f5684677_verboseLabel_en-US" xlink:label="lab_us-gaap_GuarantyAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Guarantee and commitment fees receivable</link:label>
    <link:label id="lab_us-gaap_GuarantyAssets_label_en-US" xlink:label="lab_us-gaap_GuarantyAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guaranty Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GuarantyAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GuarantyAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GuarantyAssets" xlink:to="lab_us-gaap_GuarantyAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_2457a442-424c-4751-9b8b-77aae06e20f4_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Tax payments related to share-based awards</link:label>
    <link:label id="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment, Tax Withholding, Share-Based Payment Arrangement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:to="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_4072c834-5771-4d99-9a98-0fe5cb552dd3_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities:</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAbstract" xlink:to="lab_us-gaap_LiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_StockAppreciationRightsAndRestrictedStockMember_3e3c65cc-eb78-4c36-90a3-96e8564362f9_terseLabel_en-US" xlink:label="lab_agm_StockAppreciationRightsAndRestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights and Restricted Stock</link:label>
    <link:label id="lab_agm_StockAppreciationRightsAndRestrictedStockMember_label_en-US" xlink:label="lab_agm_StockAppreciationRightsAndRestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights and Restricted Stock [Member]</link:label>
    <link:label id="lab_agm_StockAppreciationRightsAndRestrictedStockMember_documentation_en-US" xlink:label="lab_agm_StockAppreciationRightsAndRestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights and Restricted Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_StockAppreciationRightsAndRestrictedStockMember" xlink:href="agm-20240331.xsd#agm_StockAppreciationRightsAndRestrictedStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_StockAppreciationRightsAndRestrictedStockMember" xlink:to="lab_agm_StockAppreciationRightsAndRestrictedStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_USTreasurySecuritiesMember_5dd65e99-36a6-440a-9130-454a21b0ba70_terseLabel_en-US" xlink:label="lab_us-gaap_USTreasurySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">US Treasuries</link:label>
    <link:label id="lab_us-gaap_USTreasurySecuritiesMember_label_en-US" xlink:label="lab_us-gaap_USTreasurySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Treasury Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USTreasurySecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_USTreasurySecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_USTreasurySecuritiesMember" xlink:to="lab_us-gaap_USTreasurySecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_ef5cc79a-8128-4a12-afca-d46a7515af93_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by financing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Financing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxAssetsNet_34004cb5-8cad-42ca-b3d1-c2ba4743b3c7_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxAssetsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax asset, net</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxAssetsNet_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxAssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Assets, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxAssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DeferredIncomeTaxAssetsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxAssetsNet" xlink:to="lab_us-gaap_DeferredIncomeTaxAssetsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_15cf581e-4a79-4d22-b70e-9d4c0a99105c_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">GUARANTEES AND COMMITMENTS</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommitmentsAndContingenciesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsMember_40c6a932-424e-41df-8b02-c604737a695f_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retained Earnings</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsMember_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RetainedEarningsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsMember" xlink:to="lab_us-gaap_RetainedEarningsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtCurrent_d7886949-4d6e-446d-a627-b2d7e2c74ab4_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding, Amount</link:label>
    <link:label id="lab_us-gaap_LongTermDebtCurrent_label_en-US" xlink:label="lab_us-gaap_LongTermDebtCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Current Maturities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongTermDebtCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtCurrent" xlink:to="lab_us-gaap_LongTermDebtCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote</link:label>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AdjToNonPeoNeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:to="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_1b8f59d3-6ca7-4070-8fd1-e64d171b4ce2_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic earnings per common share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_3764d367-897d-404c-a3d3-a233bd7503dc_verboseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net income attributable to common stockholders (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EarningsPerShareBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasic" xlink:to="lab_us-gaap_EarningsPerShareBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_ad14f272-0d4d-4812-bfc7-bf88837d1064_terseLabel_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_label_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountingPoliciesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccountingPoliciesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountingPoliciesAbstract" xlink:to="lab_us-gaap_AccountingPoliciesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireLoansHeldForInvestment_d276702c-6920-4976-8648-14c1c91493f9_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireLoansHeldForInvestment" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Purchases of loans held for investment</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireLoansHeldForInvestment_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireLoansHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment for Acquisition, Loan, Held-for-Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireLoansHeldForInvestment" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PaymentsToAcquireLoansHeldForInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireLoansHeldForInvestment" xlink:to="lab_us-gaap_PaymentsToAcquireLoansHeldForInvestment" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis</link:label>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_label_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompAnalysisTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_ErrCompAnalysisTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompAnalysisTextBlock" xlink:to="lab_ecd_ErrCompAnalysisTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProvisionForLoanLeaseAndOtherLosses_72fe80c1-2f61-40e7-bf34-9ffca4c6fb4a_terseLabel_en-US" xlink:label="lab_us-gaap_ProvisionForLoanLeaseAndOtherLosses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total provision for/(release of) allowance for losses</link:label>
    <link:label id="lab_us-gaap_ProvisionForLoanLeaseAndOtherLosses_label_en-US" xlink:label="lab_us-gaap_ProvisionForLoanLeaseAndOtherLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Provision for Loan, Lease, and Other Losses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProvisionForLoanLeaseAndOtherLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProvisionForLoanLeaseAndOtherLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProvisionForLoanLeaseAndOtherLosses" xlink:to="lab_us-gaap_ProvisionForLoanLeaseAndOtherLosses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueTableTextBlock_290150be-ea7e-4679-95d8-84cb66979c99_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Unrealized Losses on Available-for-Sale Investment Securities</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueTableTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Unrealized Loss Position, Fair Value [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueTableTextBlock" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsMember_63d56f38-74eb-43a2-8ac8-887a57a72931_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gains on financial derivatives</link:label>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsMember_label_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Derivative Instruments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnDerivativeInstrumentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GainLossOnDerivativeInstrumentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnDerivativeInstrumentsMember" xlink:to="lab_us-gaap_GainLossOnDerivativeInstrumentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtCurrentAndNoncurrentAbstract_dabdd784-a55f-468d-bdf1-1dfa32db1eb4_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtCurrentAndNoncurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after one year:</link:label>
    <link:label id="lab_us-gaap_LongtermDebtCurrentAndNoncurrentAbstract_label_en-US" xlink:label="lab_us-gaap_LongtermDebtCurrentAndNoncurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Current and Noncurrent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtCurrentAndNoncurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongtermDebtCurrentAndNoncurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtCurrentAndNoncurrentAbstract" xlink:to="lab_us-gaap_LongtermDebtCurrentAndNoncurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_b77cd00d-5f1c-4ba7-9092-6b2a1ab4b701_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principles of Consolidation</link:label>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ConsolidationPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:to="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_NetEffectiveSpread_c008d040-de99-4f6b-9626-fe5c90b23c2f_totalLabel_en-US" xlink:label="lab_agm_NetEffectiveSpread" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net effective spread</link:label>
    <link:label id="lab_agm_NetEffectiveSpread_label_en-US" xlink:label="lab_agm_NetEffectiveSpread" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Effective Spread</link:label>
    <link:label id="lab_agm_NetEffectiveSpread_documentation_en-US" xlink:label="lab_agm_NetEffectiveSpread" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Effective Spread</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_NetEffectiveSpread" xlink:href="agm-20240331.xsd#agm_NetEffectiveSpread"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_NetEffectiveSpread" xlink:to="lab_agm_NetEffectiveSpread" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentTransitionReport_79314137-3994-4b9c-8908-30baa36478e7_terseLabel_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:label id="lab_dei_DocumentTransitionReport_label_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentTransitionReport" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentTransitionReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentTransitionReport" xlink:to="lab_dei_DocumentTransitionReport" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined</link:label>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_label_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgPredtrmndFlag" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AwardTmgPredtrmndFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgPredtrmndFlag" xlink:to="lab_ecd_AwardTmgPredtrmndFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss_3a1ce269-e177-41a1-8c59-baee9b072eb7_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair&#160;Value</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss_f27e579b-8b0c-4568-9a2f-2525229fdac5_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total, Fair Value</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Excluding Accrued Interest, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:to="lab_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseMember_b1a730bc-b262-4d4e-84c3-8cb68273341e_verboseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total Interest Expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseMember_label_en-US" xlink:label="lab_us-gaap_InterestExpenseMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestExpenseMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseMember" xlink:to="lab_us-gaap_InterestExpenseMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_RegulatoryFees_f98f1160-5506-4a8b-908f-209b15429f39_terseLabel_en-US" xlink:label="lab_agm_RegulatoryFees" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Regulatory fees</link:label>
    <link:label id="lab_agm_RegulatoryFees_label_en-US" xlink:label="lab_agm_RegulatoryFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Regulatory Fees</link:label>
    <link:label id="lab_agm_RegulatoryFees_documentation_en-US" xlink:label="lab_agm_RegulatoryFees" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Regulatory Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_RegulatoryFees" xlink:href="agm-20240331.xsd#agm_RegulatoryFees"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_RegulatoryFees" xlink:to="lab_agm_RegulatoryFees" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_GuaranteeobligationsissuedafterJanuary12003Member_0b8035b3-c298-4a02-8135-b2cd90c2373e_terseLabel_en-US" xlink:label="lab_agm_GuaranteeobligationsissuedafterJanuary12003Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantee and commitment obligation</link:label>
    <link:label id="lab_agm_GuaranteeobligationsissuedafterJanuary12003Member_label_en-US" xlink:label="lab_agm_GuaranteeobligationsissuedafterJanuary12003Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guarantee obligations issued after January 1, 2003 [Member]</link:label>
    <link:label id="lab_agm_GuaranteeobligationsissuedafterJanuary12003Member_documentation_en-US" xlink:label="lab_agm_GuaranteeobligationsissuedafterJanuary12003Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Guarantee obligations issued after January 1, 2003 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_GuaranteeobligationsissuedafterJanuary12003Member" xlink:href="agm-20240331.xsd#agm_GuaranteeobligationsissuedafterJanuary12003Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_GuaranteeobligationsissuedafterJanuary12003Member" xlink:to="lab_agm_GuaranteeobligationsissuedafterJanuary12003Member" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLosses_c99170ca-ad9e-48af-a983-9dd2067836b2_totalLabel_en-US" xlink:label="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLosses" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Operating expenses</link:label>
    <link:label id="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLosses_bd52f82d-c795-44b6-a4b9-41e0260dd46e_negatedTerseLabel_en-US" xlink:label="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLosses" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Operating expenses</link:label>
    <link:label id="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLosses_label_en-US" xlink:label="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Expense, Excluding Loan, Lease and Other Losses</link:label>
    <link:label id="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLosses_documentation_en-US" xlink:label="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLosses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Noninterest Expense, Excluding Loan, Lease and Other Losses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLosses" xlink:href="agm-20240331.xsd#agm_NoninterestExpenseExcludingLoanLeaseAndOtherLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLosses" xlink:to="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLosses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear_5c7f1c4b-d364-47c3-b074-256a5292523c_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Five, Originated, Four Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_InConsolidatedTrustsMember_42ec933b-761a-4e34-a3ba-8bafb4ada41d_terseLabel_en-US" xlink:label="lab_agm_InConsolidatedTrustsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">In Consolidated Trusts</link:label>
    <link:label id="lab_agm_InConsolidatedTrustsMember_label_en-US" xlink:label="lab_agm_InConsolidatedTrustsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">In Consolidated Trusts [Member]</link:label>
    <link:label id="lab_agm_InConsolidatedTrustsMember_documentation_en-US" xlink:label="lab_agm_InConsolidatedTrustsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">In Consolidated Trusts [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_InConsolidatedTrustsMember" xlink:href="agm-20240331.xsd#agm_InConsolidatedTrustsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_InConsolidatedTrustsMember" xlink:to="lab_agm_InConsolidatedTrustsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableforSaleUnrealizedLossPositionAbstract_3229a1e2-2d2d-4436-98da-6cbfb57b32df_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableforSaleUnrealizedLossPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized&#160;loss&#160;position for less&#160;than&#160;12&#160;months</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableforSaleUnrealizedLossPositionAbstract_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableforSaleUnrealizedLossPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Unrealized Loss Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableforSaleUnrealizedLossPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesAvailableforSaleUnrealizedLossPositionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableforSaleUnrealizedLossPositionAbstract" xlink:to="lab_us-gaap_DebtSecuritiesAvailableforSaleUnrealizedLossPositionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_1b664a60-cc92-45e1-93e1-ad23195d8f77_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield_132025e4-7a48-4e52-9a0e-465a9d867872_terseLabel_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after ten years</link:label>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield_label_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Available-for-sale Securities, Debt Maturities, after Ten Years, Weighted-Average Yield</link:label>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield_documentation_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Available-for-sale Securities, Debt Maturities, after Ten Years, Weighted-Average Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:href="agm-20240331.xsd#agm_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:to="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_3625d03d-fa85-4d44-862d-be7a137d7cd2_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative, by Nature [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeInstrumentRiskAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:to="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DebtSecuritiesTradingAccruedInterest_1f014f05-9ace-4568-a3ac-42d5f6974a7b_terseLabel_en-US" xlink:label="lab_agm_DebtSecuritiesTradingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading securities, accrued interest excluded</link:label>
    <link:label id="lab_agm_DebtSecuritiesTradingAccruedInterest_label_en-US" xlink:label="lab_agm_DebtSecuritiesTradingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, Accrued Interest</link:label>
    <link:label id="lab_agm_DebtSecuritiesTradingAccruedInterest_documentation_en-US" xlink:label="lab_agm_DebtSecuritiesTradingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, Accrued Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DebtSecuritiesTradingAccruedInterest" xlink:href="agm-20240331.xsd#agm_DebtSecuritiesTradingAccruedInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DebtSecuritiesTradingAccruedInterest" xlink:to="lab_agm_DebtSecuritiesTradingAccruedInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllTradingArrangementsMember_terseLabel_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Trading Arrangements</link:label>
    <link:label id="lab_ecd_AllTradingArrangementsMember_label_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Trading Arrangements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllTradingArrangementsMember" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AllTradingArrangementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllTradingArrangementsMember" xlink:to="lab_ecd_AllTradingArrangementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubstandardMember_c512d863-1548-4a5b-8acf-fd0a848ac091_terseLabel_en-US" xlink:label="lab_us-gaap_SubstandardMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Substandard</link:label>
    <link:label id="lab_us-gaap_SubstandardMember_label_en-US" xlink:label="lab_us-gaap_SubstandardMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Substandard [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubstandardMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubstandardMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubstandardMember" xlink:to="lab_us-gaap_SubstandardMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost_be81aa6b-f64f-4faa-9965-af0475a5bb27_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due within one year</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllAdjToCompMember_terseLabel_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation</link:label>
    <link:label id="lab_ecd_AllAdjToCompMember_label_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllAdjToCompMember" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AllAdjToCompMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllAdjToCompMember" xlink:to="lab_ecd_AllAdjToCompMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_OutstandingRecoveryCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryCompAmt" xlink:to="lab_ecd_OutstandingRecoveryCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssets_5ab6b533-8521-42fe-8003-a4be52bd8eaf_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Financial derivatives, at fair value</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_2dad1883-21a8-4ea3-918b-508d0ef6e7fa_netLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Fair value, asset</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_02a30ff4-363f-4d5d-a102-5dee28d99e0c_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial derivatives</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_label_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssets" xlink:to="lab_us-gaap_DerivativeAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefit_091cdeec-488f-4908-9c17-3e294ac8f1a1_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred income taxes</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_223e8ab0-a2b9-4f1e-bf43-1fbb50a67b67_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Comprehensive Income [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Comprehensive Income [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:to="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotesReceivableNetAbstract_484cded1-2e1b-4a8e-b2df-34eaccd9ded9_terseLabel_en-US" xlink:label="lab_us-gaap_NotesReceivableNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans:</link:label>
    <link:label id="lab_us-gaap_NotesReceivableNetAbstract_label_en-US" xlink:label="lab_us-gaap_NotesReceivableNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, after Allowance for Credit Loss [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesReceivableNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NotesReceivableNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotesReceivableNetAbstract" xlink:to="lab_us-gaap_NotesReceivableNetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock_b30d5cd5-3e80-4fb1-8edb-c6bfd7675bf9_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Net Income/(Expense) Recognized</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Derivatives Instruments Statements of Financial Performance and Financial Position, Location [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherReceivables_9185096d-c6cc-4b7f-93fa-88e37a338efd_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherReceivables" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Guarantee and commitment fees receivable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherReceivables_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherReceivables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Receivables</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherReceivables" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInOtherReceivables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherReceivables" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherReceivables" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAverageRemainingMaturity1_63b2ab53-8848-4948-bac3-f81f184f6c36_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAverageRemainingMaturity1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted- Average Remaining Term (in&#160;years)</link:label>
    <link:label id="lab_us-gaap_DerivativeAverageRemainingMaturity1_label_en-US" xlink:label="lab_us-gaap_DerivativeAverageRemainingMaturity1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Average Remaining Maturity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAverageRemainingMaturity1" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeAverageRemainingMaturity1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAverageRemainingMaturity1" xlink:to="lab_us-gaap_DerivativeAverageRemainingMaturity1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList_22454ff6-7d1c-49f4-920e-800893263249_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accrued Interest, after Allowance for Credit Loss, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accrued Interest, after Allowance for Credit Loss, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_d486182b-d85b-42f3-af08-74ff58b0809d_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2025</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_fe2c1d46-af9b-4f05-bbe8-00b6d9f1d14a_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_ExcessTaxBenefitsFromShareBasedCompensation_fa73edd2-7ab7-41af-a85a-d67f4acb386f_terseLabel_en-US" xlink:label="lab_agm_ExcessTaxBenefitsFromShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Excess tax benefits related to stock-based awards</link:label>
    <link:label id="lab_agm_ExcessTaxBenefitsFromShareBasedCompensation_label_en-US" xlink:label="lab_agm_ExcessTaxBenefitsFromShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Excess Tax Benefits From Share-Based Compensation</link:label>
    <link:label id="lab_agm_ExcessTaxBenefitsFromShareBasedCompensation_documentation_en-US" xlink:label="lab_agm_ExcessTaxBenefitsFromShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Excess Tax Benefits From Share-Based Compensation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_ExcessTaxBenefitsFromShareBasedCompensation" xlink:href="agm-20240331.xsd#agm_ExcessTaxBenefitsFromShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_ExcessTaxBenefitsFromShareBasedCompensation" xlink:to="lab_agm_ExcessTaxBenefitsFromShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtWeightedAverageInterestRate_90177a23-cc6c-4611-9d9b-db9642328e61_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted - average rate</link:label>
    <link:label id="lab_us-gaap_LongtermDebtWeightedAverageInterestRate_a409bb8e-f659-4618-a08a-ac37bce1496b_verboseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Weighted-Average Rate</link:label>
    <link:label id="lab_us-gaap_LongtermDebtWeightedAverageInterestRate_label_en-US" xlink:label="lab_us-gaap_LongtermDebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Weighted Average Interest Rate, at Point in Time</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtWeightedAverageInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongtermDebtWeightedAverageInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtWeightedAverageInterestRate" xlink:to="lab_us-gaap_LongtermDebtWeightedAverageInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements_f5f98763-1787-48a9-bb38-60656600ea06_terseLabel_en-US" xlink:label="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SARs and restricted stock units (in shares)</link:label>
    <link:label id="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements_label_en-US" xlink:label="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Incremental Common Shares Attributable to Dilutive Effect of Share-Based Payment Arrangements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:to="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfGuaranteeObligationsTable_ba959523-140a-42f8-b620-9c2226ca9213_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfGuaranteeObligationsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Guarantor Obligations [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfGuaranteeObligationsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfGuaranteeObligationsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Guarantor Obligations [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfGuaranteeObligationsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfGuaranteeObligationsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfGuaranteeObligationsTable" xlink:to="lab_us-gaap_ScheduleOfGuaranteeObligationsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentPeriodEndDate_5814c13b-74a3-41fe-a9e8-caf4ee699d43_terseLabel_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:label id="lab_dei_DocumentPeriodEndDate_label_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentPeriodEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentPeriodEndDate" xlink:to="lab_dei_DocumentPeriodEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrAdoptionDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adoption Date</link:label>
    <link:label id="lab_ecd_TrdArrAdoptionDate_label_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Adoption Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrAdoptionDate" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_TrdArrAdoptionDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrAdoptionDate" xlink:to="lab_ecd_TrdArrAdoptionDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_635477a9-ec26-4569-ae2a-323f59730325_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting Information [Line Items]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_label_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SegmentReportingInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems" xlink:to="lab_us-gaap_SegmentReportingInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearAbstract_5ddf744b-b99b-473f-a2f0-276441577ed8_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year Three</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearAbstract_label_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated Two Years before Latest Fiscal Year [Abstract]</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearAbstract_documentation_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated Two Years before Latest Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearAbstract" xlink:href="agm-20240331.xsd#agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearAbstract" xlink:to="lab_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_8db3dcbf-2234-4eff-850b-ee54b94611cd_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income tax expense</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_db3ec0b0-da8d-459f-a4d2-41472e68b8bd_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Income tax (expense)/benefit</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_OnAndOffBalanceSheetProgramAssetsAtPrincipalBalance_b6b8e3bb-cd7e-49e2-ad63-335679454c6d_terseLabel_en-US" xlink:label="lab_agm_OnAndOffBalanceSheetProgramAssetsAtPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total on- and off-balance sheet program assets at principal balance</link:label>
    <link:label id="lab_agm_OnAndOffBalanceSheetProgramAssetsAtPrincipalBalance_label_en-US" xlink:label="lab_agm_OnAndOffBalanceSheetProgramAssetsAtPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">On And Off Balance Sheet Program Assets, At Principal Balance</link:label>
    <link:label id="lab_agm_OnAndOffBalanceSheetProgramAssetsAtPrincipalBalance_documentation_en-US" xlink:label="lab_agm_OnAndOffBalanceSheetProgramAssetsAtPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">On And Off Balance Sheet Program Assets, At Principal Balance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_OnAndOffBalanceSheetProgramAssetsAtPrincipalBalance" xlink:href="agm-20240331.xsd#agm_OnAndOffBalanceSheetProgramAssetsAtPrincipalBalance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_OnAndOffBalanceSheetProgramAssetsAtPrincipalBalance" xlink:to="lab_agm_OnAndOffBalanceSheetProgramAssetsAtPrincipalBalance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DesignatedAsHedgingInstrumentMember_77064316-7516-4642-80e9-fcc6f8f901e3_verboseLabel_en-US" xlink:label="lab_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Designated as hedge</link:label>
    <link:label id="lab_us-gaap_DesignatedAsHedgingInstrumentMember_label_en-US" xlink:label="lab_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Designated as Hedging Instrument [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DesignatedAsHedgingInstrumentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:to="lab_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueDomain_6f39ec0f-349d-45c7-8c71-7fe4708f127b_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueDomain_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ValuationTechniqueDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueDomain" xlink:to="lab_us-gaap_ValuationTechniqueDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_240fc246-6047-4346-bafa-17a46f0eee12_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">FAIR VALUE DISCLOSURES</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:to="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_9ff21347-f898-4768-9bcc-9d784c4eefa1_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of operating segments</link:label>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Operating Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfOperatingSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NumberOfOperatingSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfOperatingSegments" xlink:to="lab_us-gaap_NumberOfOperatingSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax_b1beb452-06ea-462f-8f44-adf2a448c120_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Amounts reclassified from AOCI</link:label>
    <link:label id="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax_7070e5ff-126f-4f33-9d53-b4eb93619182_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Less reclassification adjustments, provision (benefit)</link:label>
    <link:label id="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax_label_en-US" xlink:label="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification from Accumulated Other Comprehensive Income, Current Period, Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax" xlink:to="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss_2c8d12e0-4a13-4769-b4db-effd91c68049_negatedLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Unrealized loss position for more than 12 months, Unrealized Loss</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Continuous Unrealized Loss Position, 12 Months or Longer, Accumulated Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityAbstract_b6eca42c-4c8b-4241-82dc-94b72eb1674c_terseLabel_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity [Abstract]</link:label>
    <link:label id="lab_us-gaap_EquityAbstract_label_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityAbstract" xlink:to="lab_us-gaap_EquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_e7a4fc55-ef81-46cc-840c-7598a58016c8_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-sale [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:to="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivables60To89DaysPastDueMember_b6f88473-56af-4870-b381-6ad23f6660b2_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivables60To89DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">60-89 Days</link:label>
    <link:label id="lab_us-gaap_FinancingReceivables60To89DaysPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancingReceivables60To89DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, 60 to 89 Days Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivables60To89DaysPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivables60To89DaysPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivables60To89DaysPastDueMember" xlink:to="lab_us-gaap_FinancingReceivables60To89DaysPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact_a46621b9-4a11-41ff-b0f4-47aafcc7b237_negatedLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Preferred stock dividends</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact_2e426c28-5547-4847-b58c-0bd99e396899_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock dividends</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact_label_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock Dividends, Income Statement Impact</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockDividendsIncomeStatementImpact"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:to="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss_5a422401-701b-4ed2-87ab-b6dc4ebe1894_negatedLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Unrealized loss position for less than 12 months, Unrealized Loss</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Continuous Unrealized Loss Position, Less than 12 Months, Accumulated Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_9b5999ff-53c1-4c00-a6c8-c25dd64d7290_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, at Carrying Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable_89426e48-115a-44f2-ab13-dae1179673c4_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Financing Receivable, Recorded Investment, Credit Quality Indicator [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Credit Quality Indicator [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:to="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock_cb4274e6-b5f3-420d-86ec-dcbad37fee27_terseLabel_en-US" xlink:label="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Past Due Financing Receivables</link:label>
    <link:label id="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PastDueFinancingReceivablesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:to="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityMember_15eee462-ef9d-44fd-9d6d-b8ae4cbd81e2_terseLabel_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Held-to-Maturity Securities</link:label>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityMember_label_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-To-Maturity [Member]</link:label>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityMember_documentation_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-To-Maturity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DebtSecuritiesHeldToMaturityMember" xlink:href="agm-20240331.xsd#agm_DebtSecuritiesHeldToMaturityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DebtSecuritiesHeldToMaturityMember" xlink:to="lab_agm_DebtSecuritiesHeldToMaturityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear5Through10_3ac4693b-dc80-4d5b-9b6f-6a426f758afd_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear5Through10" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after five years through ten years</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear5Through10_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear5Through10" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Amortized Cost Excluding Accrued Interest, after Allowance for Credit Loss, Maturity, Allocated and Single Maturity Date, after Year 5 through 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear5Through10" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear5Through10"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear5Through10" xlink:to="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear5Through10" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual_67da5d1d-b2ec-488a-b1ea-e8f736d6c8fc_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nonaccrual loans</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Nonaccrual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral_23024e58-0b65-4b61-afd4-bf2ac336787d_totalLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net amount</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Including Not Subject to Master Netting Arrangement, after Offset and Deduction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:to="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_CompActuallyPaidVsOtherMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_AgVantageMember_bd61430e-b34b-45ef-a639-a31bef137ea1_terseLabel_en-US" xlink:label="lab_agm_AgVantageMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AgVantage</link:label>
    <link:label id="lab_agm_AgVantageMember_label_en-US" xlink:label="lab_agm_AgVantageMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AgVantage [Member]</link:label>
    <link:label id="lab_agm_AgVantageMember_documentation_en-US" xlink:label="lab_agm_AgVantageMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AgVantage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_AgVantageMember" xlink:href="agm-20240331.xsd#agm_AgVantageMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_AgVantageMember" xlink:to="lab_agm_AgVantageMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperating_450f0b0a-462b-4a33-8f13-c61d3b50c519_totalLabel_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total interest income</link:label>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperating_label_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Dividend Income, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestAndDividendIncomeOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestAndDividendIncomeOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestAndDividendIncomeOperating" xlink:to="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear_cf66300c-8f6a-4825-be45-73e9edf1c5ec_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Three, Originated, Two Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesLineItems_e8bfff8e-bf1c-487e-a4ec-5ae1cf0b3219_terseLabel_en-US" xlink:label="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-sale and Trading Securities [Line Items]</link:label>
    <link:label id="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesLineItems_label_en-US" xlink:label="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-sale and Trading Securities [Line Items]</link:label>
    <link:label id="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesLineItems_documentation_en-US" xlink:label="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-sale and Trading Securities [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesLineItems" xlink:href="agm-20240331.xsd#agm_ScheduleOfAvailableForSaleAndTradingSecuritiesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesLineItems" xlink:to="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestIncomeMember_06870b05-1069-4c43-b4b6-dbd2030b181e_terseLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Income Farmer Mac Guaranteed Securities and USDA Securities</link:label>
    <link:label id="lab_us-gaap_InterestIncomeMember_label_en-US" xlink:label="lab_us-gaap_InterestIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestIncomeMember" xlink:to="lab_us-gaap_InterestIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_15b3b6e8-f12f-43f0-9aea-c62038440d5a_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:to="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax_d41c716f-89f7-4c03-bb0f-6587ba23f6a3_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net unrealized gains/(losses) on cash flow hedges</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), before Reclassification, after Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivables30To59DaysPastDueMember_19a72625-2e9a-45fe-ac02-d4a2d0eaa88e_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivables30To59DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">30-59 Days</link:label>
    <link:label id="lab_us-gaap_FinancingReceivables30To59DaysPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancingReceivables30To59DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, 30 to 59 Days Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivables30To59DaysPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivables30To59DaysPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivables30To59DaysPastDueMember" xlink:to="lab_us-gaap_FinancingReceivables30To59DaysPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BalanceSheetLocationAxis_b2f5b72a-76b1-4d7c-aba1-3a96053fba1e_terseLabel_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Balance Sheet Location [Axis]</link:label>
    <link:label id="lab_us-gaap_BalanceSheetLocationAxis_label_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Balance Sheet Location [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BalanceSheetLocationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_BalanceSheetLocationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BalanceSheetLocationAxis" xlink:to="lab_us-gaap_BalanceSheetLocationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalAssets_9c181e01-57ca-4f0c-ab6d-9a79f757aa13_terseLabel_en-US" xlink:label="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percent of level three fair value assets and liabilities</link:label>
    <link:label id="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalAssets_label_en-US" xlink:label="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Fair Value as Percent of Total Assets</link:label>
    <link:label id="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalAssets_documentation_en-US" xlink:label="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Fair Value as Percent of Total Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalAssets" xlink:href="agm-20240331.xsd#agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalAssets" xlink:to="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue_155764f2-980c-4506-a794-ed1333ae979f_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after ten years</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Fair Value, Maturity, Allocated and Single Maturity Date, after Year 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CoverAbstract_cd9b3f03-e4cc-47f6-a1ed-04e453a88a67_terseLabel_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cover page.</link:label>
    <link:label id="lab_dei_CoverAbstract_label_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_CoverAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CoverAbstract" xlink:to="lab_dei_CoverAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsRecurringMember_b10bdfc4-ba3b-43a4-b128-70e350124eaa_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recurring</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsRecurringMember_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsRecurringMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueMeasurementsRecurringMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsRecurringMember" xlink:to="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss_f9ac50bf-c794-49e9-867d-6dbc8b87a124_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized cost of available-for-sale investment securities</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss_819b0ebc-0e67-4f42-9aa3-361222745d48_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Amortized cost</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss_51b3fe8c-230b-4115-8735-0e175e8e176d_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Available-for-sale, amortized cost</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Excluding Accrued Interest, before Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems_b0bc0815-a588-487c-a246-d9e8ccc04f47_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfGuaranteeObligationsTextBlock_e5cc338e-7d0b-43e0-bb6c-6e06fa116727_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfGuaranteeObligationsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Guarantor Obligations</link:label>
    <link:label id="lab_us-gaap_ScheduleOfGuaranteeObligationsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfGuaranteeObligationsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Guarantor Obligations [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfGuaranteeObligationsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfGuaranteeObligationsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfGuaranteeObligationsTextBlock" xlink:to="lab_us-gaap_ScheduleOfGuaranteeObligationsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_SegmentCoreEarningsBeforePreferredStockDividendsAndAttributionOfIncomeToNonControllingInterestPreferredStockDividends_3a71bd2f-cdeb-4f03-97c4-8780943f9194_totalLabel_en-US" xlink:label="lab_agm_SegmentCoreEarningsBeforePreferredStockDividendsAndAttributionOfIncomeToNonControllingInterestPreferredStockDividends" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Core earnings before preferred stock dividends</link:label>
    <link:label id="lab_agm_SegmentCoreEarningsBeforePreferredStockDividendsAndAttributionOfIncomeToNonControllingInterestPreferredStockDividends_label_en-US" xlink:label="lab_agm_SegmentCoreEarningsBeforePreferredStockDividendsAndAttributionOfIncomeToNonControllingInterestPreferredStockDividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Core Earnings, Before Preferred Stock Dividends And Attribution Of Income To Non-controlling Interest, Preferred Stock Dividends</link:label>
    <link:label id="lab_agm_SegmentCoreEarningsBeforePreferredStockDividendsAndAttributionOfIncomeToNonControllingInterestPreferredStockDividends_documentation_en-US" xlink:label="lab_agm_SegmentCoreEarningsBeforePreferredStockDividendsAndAttributionOfIncomeToNonControllingInterestPreferredStockDividends" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Segment Core Earnings, Before Preferred Stock Dividends And Attribution Of Income To Non-controlling Interest, Preferred Stock Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_SegmentCoreEarningsBeforePreferredStockDividendsAndAttributionOfIncomeToNonControllingInterestPreferredStockDividends" xlink:href="agm-20240331.xsd#agm_SegmentCoreEarningsBeforePreferredStockDividendsAndAttributionOfIncomeToNonControllingInterestPreferredStockDividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_SegmentCoreEarningsBeforePreferredStockDividendsAndAttributionOfIncomeToNonControllingInterestPreferredStockDividends" xlink:to="lab_agm_SegmentCoreEarningsBeforePreferredStockDividendsAndAttributionOfIncomeToNonControllingInterestPreferredStockDividends" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermStandbyPurchaseCommitmentsAndGuaranteedSecuritiesMember_5be4732e-4246-4534-933e-4dd1b9b1347a_verboseLabel_en-US" xlink:label="lab_agm_LongTermStandbyPurchaseCommitmentsAndGuaranteedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Agricultural Finance</link:label>
    <link:label id="lab_agm_LongTermStandbyPurchaseCommitmentsAndGuaranteedSecuritiesMember_b473863c-a0df-4052-8bab-347f7b863bc4_terseLabel_en-US" xlink:label="lab_agm_LongTermStandbyPurchaseCommitmentsAndGuaranteedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rural Infrastructure Finance:</link:label>
    <link:label id="lab_agm_LongTermStandbyPurchaseCommitmentsAndGuaranteedSecuritiesMember_label_en-US" xlink:label="lab_agm_LongTermStandbyPurchaseCommitmentsAndGuaranteedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Standby Purchase Commitments and Guaranteed Securities [Member]</link:label>
    <link:label id="lab_agm_LongTermStandbyPurchaseCommitmentsAndGuaranteedSecuritiesMember_documentation_en-US" xlink:label="lab_agm_LongTermStandbyPurchaseCommitmentsAndGuaranteedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Standby Purchase Commitments and Guaranteed Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LongTermStandbyPurchaseCommitmentsAndGuaranteedSecuritiesMember" xlink:href="agm-20240331.xsd#agm_LongTermStandbyPurchaseCommitmentsAndGuaranteedSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LongTermStandbyPurchaseCommitmentsAndGuaranteedSecuritiesMember" xlink:to="lab_agm_LongTermStandbyPurchaseCommitmentsAndGuaranteedSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_OffBalanceSheetMember_74c866b4-88d6-42a3-883c-1cb98a2727e4_terseLabel_en-US" xlink:label="lab_agm_OffBalanceSheetMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Off-balance sheet</link:label>
    <link:label id="lab_agm_OffBalanceSheetMember_label_en-US" xlink:label="lab_agm_OffBalanceSheetMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Off-balance sheet [Member]</link:label>
    <link:label id="lab_agm_OffBalanceSheetMember_documentation_en-US" xlink:label="lab_agm_OffBalanceSheetMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Off-balance sheet [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_OffBalanceSheetMember" xlink:href="agm-20240331.xsd#agm_OffBalanceSheetMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_OffBalanceSheetMember" xlink:to="lab_agm_OffBalanceSheetMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_AOCIAccumulatedGainLossDebtSecuritiesParentMember_6eaa6eea-ecee-4c14-9235-2e7c8ae26108_terseLabel_en-US" xlink:label="lab_agm_AOCIAccumulatedGainLossDebtSecuritiesParentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AOCI, Securities</link:label>
    <link:label id="lab_agm_AOCIAccumulatedGainLossDebtSecuritiesParentMember_label_en-US" xlink:label="lab_agm_AOCIAccumulatedGainLossDebtSecuritiesParentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI, Accumulated Gain (Loss), Debt Securities, Parent [Member]</link:label>
    <link:label id="lab_agm_AOCIAccumulatedGainLossDebtSecuritiesParentMember_documentation_en-US" xlink:label="lab_agm_AOCIAccumulatedGainLossDebtSecuritiesParentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AOCI, Accumulated Gain (Loss), Debt Securities, Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_AOCIAccumulatedGainLossDebtSecuritiesParentMember" xlink:href="agm-20240331.xsd#agm_AOCIAccumulatedGainLossDebtSecuritiesParentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_AOCIAccumulatedGainLossDebtSecuritiesParentMember" xlink:to="lab_agm_AOCIAccumulatedGainLossDebtSecuritiesParentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases_ff996479-7a8a-48e0-83f6-a3497d90f612_verboseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Purchases</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Purchases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivablePercentOfPrincipalBalancePaidDown_2a581302-0198-4ab6-95a5-6ef6edd011c4_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivablePercentOfPrincipalBalancePaidDown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principal balance paydown</link:label>
    <link:label id="lab_agm_FinancingReceivablePercentOfPrincipalBalancePaidDown_label_en-US" xlink:label="lab_agm_FinancingReceivablePercentOfPrincipalBalancePaidDown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Percent Of Principal Balance Paid Down</link:label>
    <link:label id="lab_agm_FinancingReceivablePercentOfPrincipalBalancePaidDown_documentation_en-US" xlink:label="lab_agm_FinancingReceivablePercentOfPrincipalBalancePaidDown" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Percent Of Principal Balance Paid Down</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivablePercentOfPrincipalBalancePaidDown" xlink:href="agm-20240331.xsd#agm_FinancingReceivablePercentOfPrincipalBalancePaidDown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivablePercentOfPrincipalBalancePaidDown" xlink:to="lab_agm_FinancingReceivablePercentOfPrincipalBalancePaidDown" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashFlowHedgingMember_0158a16c-21cc-4bd9-9d76-a1fd15bf2eaf_terseLabel_en-US" xlink:label="lab_us-gaap_CashFlowHedgingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flow hedges:</link:label>
    <link:label id="lab_us-gaap_CashFlowHedgingMember_label_en-US" xlink:label="lab_us-gaap_CashFlowHedgingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Flow Hedging [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashFlowHedgingMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CashFlowHedgingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashFlowHedgingMember" xlink:to="lab_us-gaap_CashFlowHedgingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_5620150a-1276-4459-9ed3-4f5b76d768d8_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BUSINESS SEGMENT REPORTING</link:label>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SegmentReportingDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:to="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_ReserveForLosses_4b1ac3c2-21b9-41a9-b4e8-0f1c3f69e214_terseLabel_en-US" xlink:label="lab_agm_ReserveForLosses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reserve for losses</link:label>
    <link:label id="lab_agm_ReserveForLosses_f8d79150-bbba-4255-8e72-dffabba1880f_periodStartLabel_en-US" xlink:label="lab_agm_ReserveForLosses" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_agm_ReserveForLosses_fbcb25fa-ebdf-4fba-92c3-b6aa663715e3_periodEndLabel_en-US" xlink:label="lab_agm_ReserveForLosses" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_agm_ReserveForLosses_label_en-US" xlink:label="lab_agm_ReserveForLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reserve for losses</link:label>
    <link:label id="lab_agm_ReserveForLosses_documentation_en-US" xlink:label="lab_agm_ReserveForLosses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The reserve for guarantee losses is a liability account in the consolidated balance sheets that reflects an estimate of incurred credit losses related to the guaranty of unconsolidated trusts and other credit guarantees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_ReserveForLosses" xlink:href="agm-20240331.xsd#agm_ReserveForLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_ReserveForLosses" xlink:to="lab_agm_ReserveForLosses" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_f3097839-2fbb-4287-acf3-99a6d9ee7f95_negatedTerseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Current period charge-offs</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_ef0c385b-3d24-488d-9955-4b3d70e118cb_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current period charge-offs</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_label_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated In Current Fiscal Year, Excluding Accrued Interest, Allowance for Credit Loss, Write-Off</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_documentation_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated In Current Fiscal Year, Excluding Accrued Interest, Allowance for Credit Loss, Write-Off</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableOriginatedInCurrentFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:href="agm-20240331.xsd#agm_FinancingReceivableOriginatedInCurrentFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivableOriginatedInCurrentFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:to="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_7e763e45-04d3-479c-aa13-72f81d6cc66d_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net change in cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Period Increase (Decrease), Including Exchange Rate Effect</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgedLiabilityFairValueHedgeCumulativeIncreaseDecrease_4629dca5-cdc5-4af1-a6dd-6a31df3464dd_terseLabel_en-US" xlink:label="lab_us-gaap_HedgedLiabilityFairValueHedgeCumulativeIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedged Liability</link:label>
    <link:label id="lab_us-gaap_HedgedLiabilityFairValueHedgeCumulativeIncreaseDecrease_label_en-US" xlink:label="lab_us-gaap_HedgedLiabilityFairValueHedgeCumulativeIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedged Liability, Fair Value Hedge, Cumulative Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgedLiabilityFairValueHedgeCumulativeIncreaseDecrease" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_HedgedLiabilityFairValueHedgeCumulativeIncreaseDecrease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgedLiabilityFairValueHedgeCumulativeIncreaseDecrease" xlink:to="lab_us-gaap_HedgedLiabilityFairValueHedgeCumulativeIncreaseDecrease" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAverageVariableInterestRate_182787f4-3233-4c1f-b66d-0767d011e076_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAverageVariableInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted- Average Receive Rate</link:label>
    <link:label id="lab_us-gaap_DerivativeAverageVariableInterestRate_label_en-US" xlink:label="lab_us-gaap_DerivativeAverageVariableInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Average Variable Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAverageVariableInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeAverageVariableInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAverageVariableInterestRate" xlink:to="lab_us-gaap_DerivativeAverageVariableInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityComponentDomain_b379f0c6-48ce-45d4-8d6a-3d295e8e2c46_terseLabel_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:label id="lab_us-gaap_EquityComponentDomain_label_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EquityComponentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityComponentDomain" xlink:to="lab_us-gaap_EquityComponentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DueYearThreeMember_f3d46d0d-5819-47b5-9c78-034da912fd3a_terseLabel_en-US" xlink:label="lab_agm_DueYearThreeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year three</link:label>
    <link:label id="lab_agm_DueYearThreeMember_label_en-US" xlink:label="lab_agm_DueYearThreeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Due year three [Member]</link:label>
    <link:label id="lab_agm_DueYearThreeMember_documentation_en-US" xlink:label="lab_agm_DueYearThreeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Due year three [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DueYearThreeMember" xlink:href="agm-20240331.xsd#agm_DueYearThreeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DueYearThreeMember" xlink:to="lab_agm_DueYearThreeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingAssetsTableTextBlock_38a8336a-f0af-4d02-acbc-561f2866446b_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Offsetting Assets</link:label>
    <link:label id="lab_us-gaap_OffsettingAssetsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_OffsettingAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Assets [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingAssetsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OffsettingAssetsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingAssetsTableTextBlock" xlink:to="lab_us-gaap_OffsettingAssetsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_ScheduleOfCashFlowsRelatedToTransferOfSecuritizationsTableTextBlock_79257962-14cb-46d9-affc-5f17e1d19a6c_terseLabel_en-US" xlink:label="lab_agm_ScheduleOfCashFlowsRelatedToTransferOfSecuritizationsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Cash Flows Related To Transfer of Securitizations</link:label>
    <link:label id="lab_agm_ScheduleOfCashFlowsRelatedToTransferOfSecuritizationsTableTextBlock_label_en-US" xlink:label="lab_agm_ScheduleOfCashFlowsRelatedToTransferOfSecuritizationsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Cash Flows Related To Transfer of Securitizations [Table Text Block]</link:label>
    <link:label id="lab_agm_ScheduleOfCashFlowsRelatedToTransferOfSecuritizationsTableTextBlock_documentation_en-US" xlink:label="lab_agm_ScheduleOfCashFlowsRelatedToTransferOfSecuritizationsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Cash Flows Related To Transfer of Securitizations [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_ScheduleOfCashFlowsRelatedToTransferOfSecuritizationsTableTextBlock" xlink:href="agm-20240331.xsd#agm_ScheduleOfCashFlowsRelatedToTransferOfSecuritizationsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_ScheduleOfCashFlowsRelatedToTransferOfSecuritizationsTableTextBlock" xlink:to="lab_agm_ScheduleOfCashFlowsRelatedToTransferOfSecuritizationsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description</link:label>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_label_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_NonGaapMeasureDescriptionTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:to="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCurrentReportingStatus_de39ad0f-9261-4237-b4cb-8d7c79d58caf_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:label id="lab_dei_EntityCurrentReportingStatus_label_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCurrentReportingStatus" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityCurrentReportingStatus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCurrentReportingStatus" xlink:to="lab_dei_EntityCurrentReportingStatus" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_ScheduleOfReserveForLossesTableTextBlock_31f4da65-4081-4b16-8378-38c32fb74bf2_terseLabel_en-US" xlink:label="lab_agm_ScheduleOfReserveForLossesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Reserve for Losses</link:label>
    <link:label id="lab_agm_ScheduleOfReserveForLossesTableTextBlock_label_en-US" xlink:label="lab_agm_ScheduleOfReserveForLossesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Reserve for Losses [Table Text Block]</link:label>
    <link:label id="lab_agm_ScheduleOfReserveForLossesTableTextBlock_documentation_en-US" xlink:label="lab_agm_ScheduleOfReserveForLossesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Reserve for Losses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_ScheduleOfReserveForLossesTableTextBlock" xlink:href="agm-20240331.xsd#agm_ScheduleOfReserveForLossesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_ScheduleOfReserveForLossesTableTextBlock" xlink:to="lab_agm_ScheduleOfReserveForLossesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidatedEntitiesDomain_1bf58ea1-d33e-4485-a125-b6cee24acd62_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesDomain_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesDomain" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_ConsolidatedEntitiesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidatedEntitiesDomain" xlink:to="lab_srt_ConsolidatedEntitiesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeriesCPreferredStockMember_c7c9f5ef-cccf-49e2-a828-210b8d519062_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesCPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">6.000% Fixed-to-Floating Rate Non-Cumulative Preferred Stock, Series C</link:label>
    <link:label id="lab_us-gaap_SeriesCPreferredStockMember_af22147b-e11b-480e-a640-66a97aa572b0_verboseLabel_en-US" xlink:label="lab_us-gaap_SeriesCPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Series C</link:label>
    <link:label id="lab_us-gaap_SeriesCPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesCPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series C Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesCPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SeriesCPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesCPreferredStockMember" xlink:to="lab_us-gaap_SeriesCPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearTwo_22d55c06-7876-4246-a5e1-9e36d1331495_terseLabel_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearTwo_label_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, Year Two</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearTwo_documentation_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearTwo" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LongTermDebtWithInterestRateResetMaturityYearTwo" xlink:href="agm-20240331.xsd#agm_LongTermDebtWithInterestRateResetMaturityYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LongTermDebtWithInterestRateResetMaturityYearTwo" xlink:to="lab_agm_LongTermDebtWithInterestRateResetMaturityYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal_681fb2b7-baab-4b24-a5a3-64e782bf6477_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision for/(release of) losses</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Credit Loss Expense (Reversal)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrepaidExpenseAndOtherAssets_da15dd00-5539-48b9-ab79-ec50e03659be_terseLabel_en-US" xlink:label="lab_us-gaap_PrepaidExpenseAndOtherAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepaid expenses and other assets</link:label>
    <link:label id="lab_us-gaap_PrepaidExpenseAndOtherAssets_label_en-US" xlink:label="lab_us-gaap_PrepaidExpenseAndOtherAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepaid Expense and Other Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidExpenseAndOtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PrepaidExpenseAndOtherAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrepaidExpenseAndOtherAssets" xlink:to="lab_us-gaap_PrepaidExpenseAndOtherAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_22c7c725-a128-4c05-944f-d0a6631bfaa6_terseLabel_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:to="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_81a2c283-6b36-4f4b-bfe8-449adf7bff19_terseLabel_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair&#160;Value</link:label>
    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Estimate of Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EstimateOfFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract_17f5c399-c173-495c-9eeb-e2a89696115d_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">After Tax</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalFinancialInstrumentsMeasuredAtFairValue_904be542-2b8c-48b5-bf40-e70faa21ea7e_terseLabel_en-US" xlink:label="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalFinancialInstrumentsMeasuredAtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial instruments level three percent</link:label>
    <link:label id="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalFinancialInstrumentsMeasuredAtFairValue_label_en-US" xlink:label="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalFinancialInstrumentsMeasuredAtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities, Fair Value as Percent of Total Financial Instruments Measured at Fair Value</link:label>
    <link:label id="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalFinancialInstrumentsMeasuredAtFairValue_documentation_en-US" xlink:label="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalFinancialInstrumentsMeasuredAtFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities, Fair Value as Percent of Total Financial Instruments Measured at Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalFinancialInstrumentsMeasuredAtFairValue" xlink:href="agm-20240331.xsd#agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalFinancialInstrumentsMeasuredAtFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalFinancialInstrumentsMeasuredAtFairValue" xlink:to="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalFinancialInstrumentsMeasuredAtFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgageBackedSecuritiesMember_46a55be0-c771-46c8-a2be-1c1e13216ede_terseLabel_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guaranteed mortgage-backed securities</link:label>
    <link:label id="lab_us-gaap_MortgageBackedSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateralized Mortgage-Backed Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageBackedSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MortgageBackedSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgageBackedSecuritiesMember" xlink:to="lab_us-gaap_MortgageBackedSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AwardsCloseToMnpiDiscTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossFeeAndLoanInProcess_7c025c39-294d-4b78-811f-fdb252b01b50_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossFeeAndLoanInProcess" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total loans</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossFeeAndLoanInProcess_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossFeeAndLoanInProcess" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, before Allowance for Credit Loss, Fee, and Loan in Process</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossFeeAndLoanInProcess" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossFeeAndLoanInProcess"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossFeeAndLoanInProcess" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossFeeAndLoanInProcess" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GuaranteeObligationsCurrentCarryingValue_250a9d4b-9871-425f-8f3d-4f1cfba90452_terseLabel_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsCurrentCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantee and commitment obligation</link:label>
    <link:label id="lab_us-gaap_GuaranteeObligationsCurrentCarryingValue_label_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsCurrentCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guarantor Obligations, Current Carrying Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GuaranteeObligationsCurrentCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GuaranteeObligationsCurrentCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GuaranteeObligationsCurrentCarryingValue" xlink:to="lab_us-gaap_GuaranteeObligationsCurrentCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_TreasurySegmentMember_e09c8b4c-3276-4a90-911d-e6f02e9d16a9_terseLabel_en-US" xlink:label="lab_agm_TreasurySegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury</link:label>
    <link:label id="lab_agm_TreasurySegmentMember_label_en-US" xlink:label="lab_agm_TreasurySegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Segment [Member]</link:label>
    <link:label id="lab_agm_TreasurySegmentMember_documentation_en-US" xlink:label="lab_agm_TreasurySegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Treasury Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_TreasurySegmentMember" xlink:href="agm-20240331.xsd#agm_TreasurySegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_TreasurySegmentMember" xlink:to="lab_agm_TreasurySegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_c56c8087-64a4-4152-86e0-7487e25b1905_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity:</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Including Portion Attributable to Noncontrolling Interest [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:to="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving_731eb56a-c276-43ad-892a-cfd2c9df9416_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Revolving</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestRevolving"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_3625b4a0-1b8c-408e-8976-7e3cfb86ce8c_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesAxis" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_ConsolidatedEntitiesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidatedEntitiesAxis" xlink:to="lab_srt_ConsolidatedEntitiesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PayVsPerformanceDisclosureLineItems_label_en-US" xlink:label="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_PayVsPerformanceDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:to="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeMember_b14106bf-857f-4260-bbbc-f671aad86f5f_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Range [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_RangeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeMember" xlink:to="lab_srt_RangeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_terseLabel_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change</link:label>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_label_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_UndrlygSecurityMktPriceChngPct"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:to="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_bc5a4dc9-dc8a-454e-acea-d4e80fd7e065_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NOTES PAYABLE</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureTextBlock" xlink:to="lab_us-gaap_DebtDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_179f89ed-9d08-485c-8a2c-9e17ebdd9502_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TradingSecurities_31551390-e85b-49e0-afed-1ffb8f491489_terseLabel_en-US" xlink:label="lab_us-gaap_TradingSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading, at fair value</link:label>
    <link:label id="lab_us-gaap_TradingSecurities_58405e80-c459-41e8-99ce-c45cc0b51946_verboseLabel_en-US" xlink:label="lab_us-gaap_TradingSecurities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair&#160;Value</link:label>
    <link:label id="lab_us-gaap_TradingSecurities_label_en-US" xlink:label="lab_us-gaap_TradingSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, and Equity Securities, FV-NI</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradingSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TradingSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TradingSecurities" xlink:to="lab_us-gaap_TradingSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_b2c9ee03-ffe4-4f47-8b65-a16a833e9bac_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments, Debt and Equity Securities [Abstract]</link:label>
    <link:label id="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_label_en-US" xlink:label="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Debt and Equity Securities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:to="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_5e829179-0914-4c59-a1db-531e0bcf5b68_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated VIE</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Primary Beneficiary [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_VariableInterestEntityPrimaryBeneficiaryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:to="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_terseLabel_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value</link:label>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_label_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_MnpiDiscTimedForCompValFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:to="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PerformanceSharesMember_31b1d7dd-89af-4525-a6ec-bb94d6128302_terseLabel_en-US" xlink:label="lab_us-gaap_PerformanceSharesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Performance Shares</link:label>
    <link:label id="lab_us-gaap_PerformanceSharesMember_label_en-US" xlink:label="lab_us-gaap_PerformanceSharesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Performance Shares [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PerformanceSharesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PerformanceSharesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PerformanceSharesMember" xlink:to="lab_us-gaap_PerformanceSharesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingAbstract_070418ed-55ff-45d4-b2af-59ffc3849829_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingAbstract_label_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SegmentReportingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingAbstract" xlink:to="lab_us-gaap_SegmentReportingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDateAxis_terseLabel_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date:</link:label>
    <link:label id="lab_ecd_RestatementDateAxis_label_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDateAxis" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_RestatementDateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDateAxis" xlink:to="lab_ecd_RestatementDateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_c697e79c-7c62-41a3-aff2-ef5bccf5883c_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies (Note 6)</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingencies" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommitmentsAndContingencies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingencies" xlink:to="lab_us-gaap_CommitmentsAndContingencies" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAmountOfHedgedItem_cfc3ff84-ccec-436f-aadf-77d54626fa7a_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAmountOfHedgedItem" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying Amount of Hedged Assets/(Liabilities)</link:label>
    <link:label id="lab_us-gaap_DerivativeAmountOfHedgedItem_label_en-US" xlink:label="lab_us-gaap_DerivativeAmountOfHedgedItem" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Amount of Hedged Item</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAmountOfHedgedItem" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeAmountOfHedgedItem"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAmountOfHedgedItem" xlink:to="lab_us-gaap_DerivativeAmountOfHedgedItem" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableUnamortizedLoanCommitmentOriginationFeeAndPremiumDiscount_12bfcfc0-c338-4d84-aa0e-c169e5528ebe_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableUnamortizedLoanCommitmentOriginationFeeAndPremiumDiscount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unamortized premiums, discounts, fair value hedge basis adjustment, and other cost basis adjustments</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableUnamortizedLoanCommitmentOriginationFeeAndPremiumDiscount_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableUnamortizedLoanCommitmentOriginationFeeAndPremiumDiscount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Unamortized Loan Cost (Fee) and Purchase Premium (Discount)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableUnamortizedLoanCommitmentOriginationFeeAndPremiumDiscount" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableUnamortizedLoanCommitmentOriginationFeeAndPremiumDiscount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableUnamortizedLoanCommitmentOriginationFeeAndPremiumDiscount" xlink:to="lab_us-gaap_FinancingReceivableUnamortizedLoanCommitmentOriginationFeeAndPremiumDiscount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeriesEPreferredStockMember_fc855a5c-964b-490c-9c89-6cf1efc72436_verboseLabel_en-US" xlink:label="lab_us-gaap_SeriesEPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">5.750% Non-Cumulative Preferred Stock, Series E</link:label>
    <link:label id="lab_us-gaap_SeriesEPreferredStockMember_04f6e46a-c960-460c-9907-28562b112d82_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesEPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series E</link:label>
    <link:label id="lab_us-gaap_SeriesEPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesEPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series E Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesEPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SeriesEPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesEPreferredStockMember" xlink:to="lab_us-gaap_SeriesEPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_b7d11f7a-aa32-4623-9dcd-29b23815e3cc_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from common stock issuance</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromIssuanceOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilityNotSubjectToMasterNettingArrangement_f4862da5-a3a6-408b-82f6-28cbce91b6d1_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityNotSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative liability, not subject to master netting arrangement</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityNotSubjectToMasterNettingArrangement_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityNotSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Not Subject to Master Netting Arrangement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityNotSubjectToMasterNettingArrangement" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeLiabilityNotSubjectToMasterNettingArrangement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityNotSubjectToMasterNettingArrangement" xlink:to="lab_us-gaap_DerivativeLiabilityNotSubjectToMasterNettingArrangement" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability_e440c667-c385-4550-a8fa-b4309bcd40f8_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Custodial deposit liability</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Contract with Customer, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInContractWithCustomerLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:to="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FutureMember_b1e18160-87bd-498f-9871-bf70a91b4d18_terseLabel_en-US" xlink:label="lab_us-gaap_FutureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury futures</link:label>
    <link:label id="lab_us-gaap_FutureMember_label_en-US" xlink:label="lab_us-gaap_FutureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Future [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FutureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FutureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FutureMember" xlink:to="lab_us-gaap_FutureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CapitalRequiredForCapitalAdequacy_f17abfb0-8fa8-41ff-8dc5-335ad0be2c74_terseLabel_en-US" xlink:label="lab_us-gaap_CapitalRequiredForCapitalAdequacy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital required for capital adequacy</link:label>
    <link:label id="lab_us-gaap_CapitalRequiredForCapitalAdequacy_label_en-US" xlink:label="lab_us-gaap_CapitalRequiredForCapitalAdequacy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Total Risk-Based Capital, Capital Adequacy, Minimum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalRequiredForCapitalAdequacy" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CapitalRequiredForCapitalAdequacy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CapitalRequiredForCapitalAdequacy" xlink:to="lab_us-gaap_CapitalRequiredForCapitalAdequacy" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearAbstract_d2324cd0-df9a-4050-a564-7c98845db666_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year Two</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearAbstract_label_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated in Fiscal Year before Latest Fiscal Year [Abstract]</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearAbstract_documentation_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated in Fiscal Year before Latest Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearAbstract" xlink:href="agm-20240331.xsd#agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearAbstract" xlink:to="lab_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GuaranteeObligationsByNatureAxis_514bc1c7-a551-4e2e-a5eb-1ab91167c5db_verboseLabel_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsByNatureAxis" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Guarantor Obligations, Nature [Axis]</link:label>
    <link:label id="lab_us-gaap_GuaranteeObligationsByNatureAxis_0084bc0d-a183-482d-addb-bff93decff3f_terseLabel_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsByNatureAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantor Obligations, Nature [Axis]</link:label>
    <link:label id="lab_us-gaap_GuaranteeObligationsByNatureAxis_label_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsByNatureAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guarantor Obligations, Nature [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GuaranteeObligationsByNatureAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GuaranteeObligationsByNatureAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GuaranteeObligationsByNatureAxis" xlink:to="lab_us-gaap_GuaranteeObligationsByNatureAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_849c59cb-70fb-48d5-b2ea-2825f2bfb57e_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_4003c2ab-575f-4e02-a401-e3570a8903e6_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurements, Recurring and Nonrecurring [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_91c626e1-a931-4024-90ee-3878f4dd189e_negatedTerseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Current period charge-offs</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_5750e30a-eba0-4d64-a4f2-f7eb813ed29b_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current period charge-offs</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_label_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated Three Years Before Latest Fiscal Year, Excluding Accrued Interest, Allowance For Credit Loss, Write Off</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_documentation_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated Three Years Before Latest Fiscal Year, Excluding Accrued Interest, Allowance For Credit Loss, Write Off</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:href="agm-20240331.xsd#agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:to="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_149bee39-5adc-4b8f-a761-be7b9a544a2a_totalLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total loans, net of allowance</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiability_37bccb71-1540-4ebe-a04c-4f1a8942efed_negatedLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Gross Amount Recognized</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiability_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, before Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeFairValueOfDerivativeLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:to="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoTotalCompAmt_label_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_PeoTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoTotalCompAmt" xlink:to="lab_ecd_PeoTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis_f682aa66-f78a-458b-a584-62d0b2f5f907_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging Relationship [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Relationship [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis" xlink:to="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FloatingInterestRateMember_9858fd87-38aa-492e-82b5-9d7e9e24bedf_terseLabel_en-US" xlink:label="lab_agm_FloatingInterestRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Floating interest rate</link:label>
    <link:label id="lab_agm_FloatingInterestRateMember_label_en-US" xlink:label="lab_agm_FloatingInterestRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Floating Interest Rate [Member]</link:label>
    <link:label id="lab_agm_FloatingInterestRateMember_documentation_en-US" xlink:label="lab_agm_FloatingInterestRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Floating Interest Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FloatingInterestRateMember" xlink:href="agm-20240331.xsd#agm_FloatingInterestRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FloatingInterestRateMember" xlink:to="lab_agm_FloatingInterestRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_AgricultureFinanceFarmAndRanchSegmentMember_a95b9f5d-799c-4964-a412-484a763b98d0_terseLabel_en-US" xlink:label="lab_agm_AgricultureFinanceFarmAndRanchSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Farm &amp; Ranch</link:label>
    <link:label id="lab_agm_AgricultureFinanceFarmAndRanchSegmentMember_label_en-US" xlink:label="lab_agm_AgricultureFinanceFarmAndRanchSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Agriculture Finance, Farm And Ranch Segment [Member]</link:label>
    <link:label id="lab_agm_AgricultureFinanceFarmAndRanchSegmentMember_documentation_en-US" xlink:label="lab_agm_AgricultureFinanceFarmAndRanchSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Farm &amp; Ranch [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_AgricultureFinanceFarmAndRanchSegmentMember" xlink:href="agm-20240331.xsd#agm_AgricultureFinanceFarmAndRanchSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_AgricultureFinanceFarmAndRanchSegmentMember" xlink:to="lab_agm_AgricultureFinanceFarmAndRanchSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TradingArrByIndTable_terseLabel_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual</link:label>
    <link:label id="lab_ecd_TradingArrByIndTable_label_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrByIndTable" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_TradingArrByIndTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrByIndTable" xlink:to="lab_ecd_TradingArrByIndTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_8a36eac9-00b0-4eca-97e1-ff2316ae479a_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 3</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 3 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel3Member" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueInputsLevel3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel3Member" xlink:to="lab_us-gaap_FairValueInputsLevel3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet_75b08945-6209-4513-8f8c-2ed071bc4bc5_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Interest receivable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accrued Interest Receivable, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet" xlink:to="lab_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_2f2a2915-015f-4b7a-9889-1bf944b40591_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Available-for-sale, at fair value</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_a1f9cd87-1d51-48ca-9ec9-33fcbb86b257_netLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Carrying value</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_dc7bf27d-7ae5-42fa-8cc5-d7deede93dc8_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair&#160;Value</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_9e82161b-52ec-4d73-94ab-4656986da007_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total fair value</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Excluding Accrued Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost_70a05d8d-8b38-4f8f-8d65-435508e4be3d_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after five years through ten years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, after Year 5 Through 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperatingAbstract_e898f6af-87e0-4c86-86d9-a3f8e57d49cb_terseLabel_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperatingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest income:</link:label>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperatingAbstract_label_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperatingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Dividend Income, Operating [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestAndDividendIncomeOperatingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestAndDividendIncomeOperatingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestAndDividendIncomeOperatingAbstract" xlink:to="lab_us-gaap_InterestAndDividendIncomeOperatingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_NonPeoNeoAvgCompActuallyPaidAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:to="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock_b8fc3877-4e60-4173-b400-126d50a9a027_terseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule Allowance for Losses</link:label>
    <link:label id="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:to="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossTax_81b44219-3b2a-4e56-a353-760054147f34_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Income tax (expense)/benefit related to other comprehensive income/(loss)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossTax_761a9fb7-49fa-4f19-a88c-1afe99887046_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income/(loss), Provision (Benefit)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherComprehensiveIncomeLossTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_2edd0607-fe19-4ac2-9282-02922c8f1e7d_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_5a30225e-8293-4b0a-af6e-d7531d5f0315_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Income</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnDiscontinuationOfInterestRateCashFlowHedgeDueToForecastedTransactionProbableOfNotOccurringNet_eb3299ee-a7d5-41ac-986e-da8d02594f56_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnDiscontinuationOfInterestRateCashFlowHedgeDueToForecastedTransactionProbableOfNotOccurringNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain (loss) from interest rate swaps designated as cash flow hedges reclassified to earnings</link:label>
    <link:label id="lab_us-gaap_GainLossOnDiscontinuationOfInterestRateCashFlowHedgeDueToForecastedTransactionProbableOfNotOccurringNet_label_en-US" xlink:label="lab_us-gaap_GainLossOnDiscontinuationOfInterestRateCashFlowHedgeDueToForecastedTransactionProbableOfNotOccurringNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Discontinuation of Interest Rate Cash Flow Hedge Due to Forecasted Transaction Probable of Not Occurring, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnDiscontinuationOfInterestRateCashFlowHedgeDueToForecastedTransactionProbableOfNotOccurringNet" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GainLossOnDiscontinuationOfInterestRateCashFlowHedgeDueToForecastedTransactionProbableOfNotOccurringNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnDiscontinuationOfInterestRateCashFlowHedgeDueToForecastedTransactionProbableOfNotOccurringNet" xlink:to="lab_us-gaap_GainLossOnDiscontinuationOfInterestRateCashFlowHedgeDueToForecastedTransactionProbableOfNotOccurringNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_9a631fa3-5006-4922-8b6d-d5cb75d12a4d_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_label_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeContractTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeContractTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeContractTypeDomain" xlink:to="lab_us-gaap_DerivativeContractTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_NumberOfSubsidiaries_14b6c358-50b0-423b-a25c-4b1309f66d98_terseLabel_en-US" xlink:label="lab_agm_NumberOfSubsidiaries" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of subsidiaries</link:label>
    <link:label id="lab_agm_NumberOfSubsidiaries_label_en-US" xlink:label="lab_agm_NumberOfSubsidiaries" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Subsidiaries</link:label>
    <link:label id="lab_agm_NumberOfSubsidiaries_documentation_en-US" xlink:label="lab_agm_NumberOfSubsidiaries" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number Of Subsidiaries</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_NumberOfSubsidiaries" xlink:href="agm-20240331.xsd#agm_NumberOfSubsidiaries"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_NumberOfSubsidiaries" xlink:to="lab_agm_NumberOfSubsidiaries" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember_102e7be9-ab6c-476d-adbc-f33386fb5465_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">90 Days and Greater</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Equal to or Greater than 90 Days Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:to="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote</link:label>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_label_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_ChangedPeerGroupFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:to="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureName_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureName_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureName" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_CoSelectedMeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureName" xlink:to="lab_ecd_CoSelectedMeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_03fe6705-5a5d-4db6-b665-d7ba63cde2b9_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after one year through five years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, after Year One Through Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GuarantyLiabilities_cde66cf4-ea55-4bc2-85fe-f7b43e761153_terseLabel_en-US" xlink:label="lab_us-gaap_GuarantyLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantee and commitment obligation</link:label>
    <link:label id="lab_us-gaap_GuarantyLiabilities_label_en-US" xlink:label="lab_us-gaap_GuarantyLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guaranty Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GuarantyLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GuarantyLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GuarantyLiabilities" xlink:to="lab_us-gaap_GuarantyLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_15a92578-f00e-4dbb-b3c2-41a111c92c3d_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities and Equity:</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodValue_3547b6d3-2894-4733-bd97-f460af79151e_terseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares repurchased</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodValue_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased During Period, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedDuringPeriodValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockRepurchasedDuringPeriodValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchasedDuringPeriodValue" xlink:to="lab_us-gaap_StockRepurchasedDuringPeriodValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodAxis_900c6e63-0148-45d9-9275-3b08d0353d15_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period [Axis]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentRedemptionPeriodAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPeriodAxis" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPeriodAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable_1cdbd81c-3836-4bff-913d-0eb765abf850_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Table]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable" xlink:to="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax_fdf4575f-4674-4d71-a7b8-5c7294ce9bb0_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Unrealized Losses</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accumulated Gross Unrealized Loss, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:to="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_HedgedItemNetInterestSettlements_ff9909db-b46e-4ec0-8f1b-f42c97387017_terseLabel_en-US" xlink:label="lab_agm_HedgedItemNetInterestSettlements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recognized on hedged items</link:label>
    <link:label id="lab_agm_HedgedItemNetInterestSettlements_label_en-US" xlink:label="lab_agm_HedgedItemNetInterestSettlements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedged Item Net Interest Settlements</link:label>
    <link:label id="lab_agm_HedgedItemNetInterestSettlements_documentation_en-US" xlink:label="lab_agm_HedgedItemNetInterestSettlements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Hedged Item Net Interest Settlements (Interest Accruals)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_HedgedItemNetInterestSettlements" xlink:href="agm-20240331.xsd#agm_HedgedItemNetInterestSettlements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_HedgedItemNetInterestSettlements" xlink:to="lab_agm_HedgedItemNetInterestSettlements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock_0bb69deb-233a-4625-9376-0e1a3758c715_terseLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Comprehensive Income</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ComprehensiveIncomePolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:to="lab_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonClassBMember_1286bfe0-7be9-4577-96ee-a1ea91db3dd3_terseLabel_en-US" xlink:label="lab_us-gaap_CommonClassBMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class B voting common stock</link:label>
    <link:label id="lab_us-gaap_CommonClassBMember_label_en-US" xlink:label="lab_us-gaap_CommonClassBMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Class B [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassBMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonClassBMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonClassBMember" xlink:to="lab_us-gaap_CommonClassBMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DerivativeNetInterestSettlements_aa720ba6-5985-4dcd-84d1-9f95d57dd601_terseLabel_en-US" xlink:label="lab_agm_DerivativeNetInterestSettlements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recognized on derivatives</link:label>
    <link:label id="lab_agm_DerivativeNetInterestSettlements_label_en-US" xlink:label="lab_agm_DerivativeNetInterestSettlements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Net Interest Settlements</link:label>
    <link:label id="lab_agm_DerivativeNetInterestSettlements_documentation_en-US" xlink:label="lab_agm_DerivativeNetInterestSettlements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Net Interest Settlements (Interest Accruals)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DerivativeNetInterestSettlements" xlink:href="agm-20240331.xsd#agm_DerivativeNetInterestSettlements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DerivativeNetInterestSettlements" xlink:to="lab_agm_DerivativeNetInterestSettlements" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DerivativeAssetSubjectToMasterNettingArrangementCollateralObligationToReturnSecurityNotOffsetNet_a8b80d8e-d194-467d-93b7-9588bd536f9d_negatedTerseLabel_en-US" xlink:label="lab_agm_DerivativeAssetSubjectToMasterNettingArrangementCollateralObligationToReturnSecurityNotOffsetNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Financial instruments pledged</link:label>
    <link:label id="lab_agm_DerivativeAssetSubjectToMasterNettingArrangementCollateralObligationToReturnSecurityNotOffsetNet_label_en-US" xlink:label="lab_agm_DerivativeAssetSubjectToMasterNettingArrangementCollateralObligationToReturnSecurityNotOffsetNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject To Master Netting Arrangement, Collateral, Obligation To Return Security Not Offset, Net</link:label>
    <link:label id="lab_agm_DerivativeAssetSubjectToMasterNettingArrangementCollateralObligationToReturnSecurityNotOffsetNet_documentation_en-US" xlink:label="lab_agm_DerivativeAssetSubjectToMasterNettingArrangementCollateralObligationToReturnSecurityNotOffsetNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject To Master Netting Arrangement, Collateral, Obligation To Return Security Not Offset, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DerivativeAssetSubjectToMasterNettingArrangementCollateralObligationToReturnSecurityNotOffsetNet" xlink:href="agm-20240331.xsd#agm_DerivativeAssetSubjectToMasterNettingArrangementCollateralObligationToReturnSecurityNotOffsetNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DerivativeAssetSubjectToMasterNettingArrangementCollateralObligationToReturnSecurityNotOffsetNet" xlink:to="lab_agm_DerivativeAssetSubjectToMasterNettingArrangementCollateralObligationToReturnSecurityNotOffsetNet" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_WeightedAverageRemainingMaturityLoansUnderlyingGuaranteesNotHeldByTransferor_8a842aa2-69b8-4a41-b812-a03a0fc43af7_terseLabel_en-US" xlink:label="lab_agm_WeightedAverageRemainingMaturityLoansUnderlyingGuaranteesNotHeldByTransferor" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average remaining maturity</link:label>
    <link:label id="lab_agm_WeightedAverageRemainingMaturityLoansUnderlyingGuaranteesNotHeldByTransferor_label_en-US" xlink:label="lab_agm_WeightedAverageRemainingMaturityLoansUnderlyingGuaranteesNotHeldByTransferor" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted average remaining maturity, Loans underlying guarantees not held by transferor</link:label>
    <link:label id="lab_agm_WeightedAverageRemainingMaturityLoansUnderlyingGuaranteesNotHeldByTransferor_documentation_en-US" xlink:label="lab_agm_WeightedAverageRemainingMaturityLoansUnderlyingGuaranteesNotHeldByTransferor" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Weighted average remaining maturity, Loans underlying guarantees not held by transferor</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_WeightedAverageRemainingMaturityLoansUnderlyingGuaranteesNotHeldByTransferor" xlink:href="agm-20240331.xsd#agm_WeightedAverageRemainingMaturityLoansUnderlyingGuaranteesNotHeldByTransferor"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_WeightedAverageRemainingMaturityLoansUnderlyingGuaranteesNotHeldByTransferor" xlink:to="lab_agm_WeightedAverageRemainingMaturityLoansUnderlyingGuaranteesNotHeldByTransferor" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureName_terseLabel_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_MeasureName_label_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureName" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_MeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureName" xlink:to="lab_ecd_MeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_ForgoneRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryIndName" xlink:to="lab_ecd_ForgoneRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_81ed2bea-7abb-432f-a885-9039036a3a1f_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueByMeasurementBasisAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:to="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_terseLabel_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Securities</link:label>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_label_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Underlying Securities Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AwardUndrlygSecuritiesAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:to="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansAndFinanceReceivablesMember_b8a754ef-1888-4030-a9c5-8ff8e2343473_terseLabel_en-US" xlink:label="lab_us-gaap_LoansAndFinanceReceivablesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Income Loans</link:label>
    <link:label id="lab_us-gaap_LoansAndFinanceReceivablesMember_label_en-US" xlink:label="lab_us-gaap_LoansAndFinanceReceivablesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans and Finance Receivables [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansAndFinanceReceivablesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LoansAndFinanceReceivablesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansAndFinanceReceivablesMember" xlink:to="lab_us-gaap_LoansAndFinanceReceivablesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_2b462391-3782-4cd4-987b-c84ba389f24d_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueDisclosureItemAmountsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:to="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThanTwelveMonthsFairValue_88b504b7-260c-491c-bb98-b5a6f5438a8e_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThanTwelveMonthsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair&#160;Value</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThanTwelveMonthsFairValue_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThanTwelveMonthsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Continuous Unrealized Loss Position, Less than 12 Months, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThanTwelveMonthsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThanTwelveMonthsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThanTwelveMonthsFairValue" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThanTwelveMonthsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfTrustPreferredSecurities_21ddc4b7-f2f7-453b-a48a-d765547001c1_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfTrustPreferredSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from issuance of debt securities of consolidated trusts</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfTrustPreferredSecurities_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfTrustPreferredSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Trust Preferred Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfTrustPreferredSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromIssuanceOfTrustPreferredSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfTrustPreferredSecurities" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfTrustPreferredSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransactionDomain_6acb2c17-51d2-44b8-a9eb-b1895d0614c2_terseLabel_en-US" xlink:label="lab_us-gaap_TransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transaction [Domain]</link:label>
    <link:label id="lab_us-gaap_TransactionDomain_label_en-US" xlink:label="lab_us-gaap_TransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transaction [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TransactionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransactionDomain" xlink:to="lab_us-gaap_TransactionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CollateralAxis_8aabc257-bb4a-489b-97bf-218b226d7eb1_terseLabel_en-US" xlink:label="lab_us-gaap_CollateralAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral [Axis]</link:label>
    <link:label id="lab_us-gaap_CollateralAxis_label_en-US" xlink:label="lab_us-gaap_CollateralAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateral Held [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CollateralAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CollateralAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CollateralAxis" xlink:to="lab_us-gaap_CollateralAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_83f43289-2a7e-49a8-9f60-2500fda29e51_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock dividends per common share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_label_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Dividends, Per Share, Declared</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockDividendsPerShareDeclared" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockDividendsPerShareDeclared"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockDividendsPerShareDeclared" xlink:to="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock_7424dc70-1cd3-4daf-9533-99f8c2fe24dd_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-Sale Securities Maturities</link:label>
    <link:label id="lab_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock_16d41c4b-1ae4-4e01-97aa-2cf7d360b9e5_verboseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-Sale and Held-to-Maturity Securities Maturities</link:label>
    <link:label id="lab_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments Classified by Contractual Maturity Date [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock" xlink:to="lab_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTerm_6ca8f131-7a1c-4f51-ab2a-496d0c9229ef_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maturities of notes</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTerm_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTerm" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTerm" xlink:to="lab_us-gaap_DebtInstrumentTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable_95984e9f-2011-43a2-bded-716133556ace_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_12529cb0-0c08-4e19-8d01-1fc5dc878ea6_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentNameDomain" xlink:to="lab_us-gaap_DebtInstrumentNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodBeforeTax_8e2d46c7-e04b-45df-9314-00d155c3e7ef_negatedLabel_en-US" xlink:label="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodBeforeTax" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Less reclassification adjustments, before tax</link:label>
    <link:label id="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodBeforeTax_aa98d1e3-3f0c-49df-ac75-4c4210652798_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest settlements reclassified from AOCI into net income on derivatives</link:label>
    <link:label id="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodBeforeTax_label_en-US" xlink:label="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification from Accumulated Other Comprehensive Income, Current Period, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodBeforeTax" xlink:to="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtWithInterestRateReset_140ec527-bedb-4fcc-99cc-4f49b73fdce3_totalLabel_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateReset" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total principal net of discounts</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateReset_label_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateReset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateReset_documentation_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateReset" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LongTermDebtWithInterestRateReset" xlink:href="agm-20240331.xsd#agm_LongTermDebtWithInterestRateReset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LongTermDebtWithInterestRateReset" xlink:to="lab_agm_LongTermDebtWithInterestRateReset" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_IncomeExpenseInterestSettlementsFairValueHedges_02c45313-a956-413f-a863-882307fd1f58_totalLabel_en-US" xlink:label="lab_agm_IncomeExpenseInterestSettlementsFairValueHedges" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income/(expense) related to interest settlements on fair value hedging relationships</link:label>
    <link:label id="lab_agm_IncomeExpenseInterestSettlementsFairValueHedges_label_en-US" xlink:label="lab_agm_IncomeExpenseInterestSettlementsFairValueHedges" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Expense, Interest Settlements, Fair Value Hedges</link:label>
    <link:label id="lab_agm_IncomeExpenseInterestSettlementsFairValueHedges_documentation_en-US" xlink:label="lab_agm_IncomeExpenseInterestSettlementsFairValueHedges" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Income Expense, Interest Settlements, Fair Value Hedges</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_IncomeExpenseInterestSettlementsFairValueHedges" xlink:href="agm-20240331.xsd#agm_IncomeExpenseInterestSettlementsFairValueHedges"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_IncomeExpenseInterestSettlementsFairValueHedges" xlink:to="lab_agm_IncomeExpenseInterestSettlementsFairValueHedges" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract_783b7b46-30f8-448d-b02a-df51c6367559_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial assets:</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments, Financial Assets, Balance Sheet Groupings [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:to="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementLocationAxis_30b6165d-d410-49f2-a10f-13cd8eb0d14e_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Statement Location [Axis]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementLocationAxis_label_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement Location [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementLocationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncomeStatementLocationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementLocationAxis" xlink:to="lab_us-gaap_IncomeStatementLocationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinanceReceivableAccruedInterestPayable_a88c435f-2dfa-40e0-82d8-9f257a7e2584_terseLabel_en-US" xlink:label="lab_agm_FinanceReceivableAccruedInterestPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest payable</link:label>
    <link:label id="lab_agm_FinanceReceivableAccruedInterestPayable_label_en-US" xlink:label="lab_agm_FinanceReceivableAccruedInterestPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Receivable, Accrued Interest Payable</link:label>
    <link:label id="lab_agm_FinanceReceivableAccruedInterestPayable_documentation_en-US" xlink:label="lab_agm_FinanceReceivableAccruedInterestPayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Finance Receivable, Accrued Interest Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinanceReceivableAccruedInterestPayable" xlink:href="agm-20240331.xsd#agm_FinanceReceivableAccruedInterestPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinanceReceivableAccruedInterestPayable" xlink:to="lab_agm_FinanceReceivableAccruedInterestPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionFairValueAbstract_3e9f7964-8cf7-43f5-bc80-97caeadadeed_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionFairValueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized&#160;loss&#160;position for less&#160;than&#160;12&#160;months</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionFairValueAbstract_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionFairValueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Unrealized Loss Position, Fair Value [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionFairValueAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionFairValueAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionFairValueAbstract" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionFairValueAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_95803921-02ac-4510-937e-f26c4e8562ad_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after five years through ten years</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Fair Value, Maturity, Allocated and Single Maturity Date, after Year 5 Through 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DebtSecurityInvestmentCategoryAxis_a74cf29d-6a55-4fef-97cb-760dc7e39849_terseLabel_en-US" xlink:label="lab_agm_DebtSecurityInvestmentCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Security Investment Category [Axis]</link:label>
    <link:label id="lab_agm_DebtSecurityInvestmentCategoryAxis_label_en-US" xlink:label="lab_agm_DebtSecurityInvestmentCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Security Investment Category [Axis]</link:label>
    <link:label id="lab_agm_DebtSecurityInvestmentCategoryAxis_documentation_en-US" xlink:label="lab_agm_DebtSecurityInvestmentCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Security Investment Category</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DebtSecurityInvestmentCategoryAxis" xlink:href="agm-20240331.xsd#agm_DebtSecurityInvestmentCategoryAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DebtSecurityInvestmentCategoryAxis" xlink:to="lab_agm_DebtSecurityInvestmentCategoryAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_ScheduleofHeldtoMaturityAvailableforsaleandTradingSecuritiesTable_0f2e9a58-2b61-4d25-a5db-e41dca385662_terseLabel_en-US" xlink:label="lab_agm_ScheduleofHeldtoMaturityAvailableforsaleandTradingSecuritiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Held-to-Maturity, Available-for-sale, and Trading Securities [Table]</link:label>
    <link:label id="lab_agm_ScheduleofHeldtoMaturityAvailableforsaleandTradingSecuritiesTable_label_en-US" xlink:label="lab_agm_ScheduleofHeldtoMaturityAvailableforsaleandTradingSecuritiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Held-to-Maturity, Available-for-sale, and Trading Securities [Table]</link:label>
    <link:label id="lab_agm_ScheduleofHeldtoMaturityAvailableforsaleandTradingSecuritiesTable_documentation_en-US" xlink:label="lab_agm_ScheduleofHeldtoMaturityAvailableforsaleandTradingSecuritiesTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of held to maturity, available for sale, and trading securities which includes, but is not limited to changes in the cost basis and fair value, fair value and gross unrealized gain (loss), fair values by type of security, contractual maturity and classification, amortized cost basis and other related disclosures</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_ScheduleofHeldtoMaturityAvailableforsaleandTradingSecuritiesTable" xlink:href="agm-20240331.xsd#agm_ScheduleofHeldtoMaturityAvailableforsaleandTradingSecuritiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_ScheduleofHeldtoMaturityAvailableforsaleandTradingSecuritiesTable" xlink:to="lab_agm_ScheduleofHeldtoMaturityAvailableforsaleandTradingSecuritiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_b077fbcd-d3cb-4ac8-a487-e8c79b5c80f7_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value, by Balance Sheet Grouping</link:label>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueByBalanceSheetGroupingTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:to="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductsAndServicesDomain_57bdf4ea-3af5-4e34-9498-d71a26367b4f_terseLabel_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:label id="lab_srt_ProductsAndServicesDomain_label_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_ProductsAndServicesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductsAndServicesDomain" xlink:to="lab_srt_ProductsAndServicesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_label_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OtherPerfMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_OtherPerfMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OtherPerfMeasureAmt" xlink:to="lab_ecd_OtherPerfMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeCollateralRightToReclaimCash_9d0a8b2c-2d8c-4050-9ed2-10954f154444_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash collateral</link:label>
    <link:label id="lab_us-gaap_DerivativeCollateralRightToReclaimCash_label_en-US" xlink:label="lab_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, Collateral, Right to Reclaim Cash Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeCollateralRightToReclaimCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:to="lab_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_4cd7687b-eefe-40ea-b608-e29681d8596c_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from investing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Investing Activities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract_3ce1724b-ef03-43c5-9972-73b30310b1d8_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:to="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_MarketableSecuritiesFairValueDisclosure_20e3f14d-f2af-4598-8736-6e5ec94d6ad8_verboseLabel_en-US" xlink:label="lab_agm_MarketableSecuritiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Marketable securities</link:label>
    <link:label id="lab_agm_MarketableSecuritiesFairValueDisclosure_label_en-US" xlink:label="lab_agm_MarketableSecuritiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketable Securities, Fair Value Disclosure</link:label>
    <link:label id="lab_agm_MarketableSecuritiesFairValueDisclosure_documentation_en-US" xlink:label="lab_agm_MarketableSecuritiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Marketable Securities, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_MarketableSecuritiesFairValueDisclosure" xlink:href="agm-20240331.xsd#agm_MarketableSecuritiesFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_MarketableSecuritiesFairValueDisclosure" xlink:to="lab_agm_MarketableSecuritiesFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialAssetPastDueMember_706baab7-fedf-4a7d-8b38-9395fb1df3b8_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialAssetPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Past Due</link:label>
    <link:label id="lab_us-gaap_FinancialAssetPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancialAssetPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialAssetPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialAssetPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialAssetPastDueMember" xlink:to="lab_us-gaap_FinancialAssetPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpense_646b51c3-a85a-4bd5-9bb0-047d721bc641_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpense_369f4cab-aa97-4a67-8af1-9bd7e8eb8db9_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_InterestExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Total interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpense_label_en-US" xlink:label="lab_us-gaap_InterestExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpense" xlink:to="lab_us-gaap_InterestExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList_1e0e3a13-859f-4c9d-879d-961c84f9b543_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Accrued Interest, after Allowance for Credit Loss, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Accrued Interest, after Allowance for Credit Loss, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TradingArrAxis_terseLabel_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangement:</link:label>
    <link:label id="lab_ecd_TradingArrAxis_label_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrAxis" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_TradingArrAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrAxis" xlink:to="lab_ecd_TradingArrAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList_576eaf08-c760-46bc-ab62-f4d41711a2f3_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Asset, Recurring Basis, Unobservable Input Reconciliation, Gain (Loss), Statement of Income or Comprehensive Income [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList_label_en-US" xlink:label="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Asset, Recurring Basis, Unobservable Input Reconciliation, Gain (Loss), Statement of Income or Comprehensive Income [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList" xlink:to="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesAxis_389add43-ceb0-41b9-bdba-2d015258d229_terseLabel_en-US" xlink:label="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecorded maximum potential exposure on guarantees [Axis]</link:label>
    <link:label id="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesAxis_label_en-US" xlink:label="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecorded maximum potential exposure on guarantees [Axis]</link:label>
    <link:label id="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesAxis_documentation_en-US" xlink:label="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unrecorded maximum potential exposure on guarantees, pertinent information about guarantee obligations issued [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_UnrecordedMaximumPotentialExposureOnGuaranteesAxis" xlink:href="agm-20240331.xsd#agm_UnrecordedMaximumPotentialExposureOnGuaranteesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_UnrecordedMaximumPotentialExposureOnGuaranteesAxis" xlink:to="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_3efd1b31-941c-4737-8a70-cf2c4aa450a8_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeDomain" xlink:to="lab_us-gaap_LongtermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesAbstract_e55ef5fd-4b02-4fb8-9cfb-b7c3d6d9a338_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Available-for-sale:</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesAbstract_3cbdcde5-441a-4ebb-865a-e5d13dcbddd6_verboseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Available-for-Sale Securities</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesAbstract_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AvailableForSaleSecuritiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFileNumber_4a78b00f-b207-4f4f-a4cc-988d374d2294_terseLabel_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:label id="lab_dei_EntityFileNumber_label_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityFileNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFileNumber" xlink:to="lab_dei_EntityFileNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityTransferIn_5e996a75-e4ce-4759-a3ec-60115fbf604e_terseLabel_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityTransferIn" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Held-to-maturity, transfer in</link:label>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityTransferIn_label_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityTransferIn" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Transfer In</link:label>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityTransferIn_documentation_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityTransferIn" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Transfer In</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DebtSecuritiesHeldToMaturityTransferIn" xlink:href="agm-20240331.xsd#agm_DebtSecuritiesHeldToMaturityTransferIn"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DebtSecuritiesHeldToMaturityTransferIn" xlink:to="lab_agm_DebtSecuritiesHeldToMaturityTransferIn" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentUnamortizedDiscount_9d8b45e4-9680-4efc-9bf2-0c8016c87a5a_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnamortizedDiscount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unamortized discount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentUnamortizedDiscount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnamortizedDiscount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Unamortized Discount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentUnamortizedDiscount" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentUnamortizedDiscount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentUnamortizedDiscount" xlink:to="lab_us-gaap_DebtInstrumentUnamortizedDiscount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputDiscountRateMember_db8ba0db-870b-4e5e-bc7b-b2f0d7a81af7_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discount rate</link:label>
    <link:label id="lab_us-gaap_MeasurementInputDiscountRateMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Discount Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputDiscountRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MeasurementInputDiscountRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputDiscountRateMember" xlink:to="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_88fd6879-05d3-46d6-b8ec-a2749861386e_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Three years</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_80166abe-91a4-4f7b-bcf4-c539237eac55_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DueAfterFourYearsMember_32cbf227-fd60-4bfd-bc6b-6e5960207cf9_terseLabel_en-US" xlink:label="lab_agm_DueAfterFourYearsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_agm_DueAfterFourYearsMember_label_en-US" xlink:label="lab_agm_DueAfterFourYearsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Due after four years [Member]</link:label>
    <link:label id="lab_agm_DueAfterFourYearsMember_documentation_en-US" xlink:label="lab_agm_DueAfterFourYearsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Due after four years</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DueAfterFourYearsMember" xlink:href="agm-20240331.xsd#agm_DueAfterFourYearsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DueAfterFourYearsMember" xlink:to="lab_agm_DueAfterFourYearsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearAbstract_3922f9c8-e38c-41cd-95c4-e274ec8783c9_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year One</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearAbstract_label_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated in Current Fiscal Year [Abstract]</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearAbstract_documentation_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated in Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableOriginatedInCurrentFiscalYearAbstract" xlink:href="agm-20240331.xsd#agm_FinancingReceivableOriginatedInCurrentFiscalYearAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivableOriginatedInCurrentFiscalYearAbstract" xlink:to="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityShellCompany_94b60a62-45bb-48ea-a32e-88c5c46f2fc4_terseLabel_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:label id="lab_dei_EntityShellCompany_label_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityShellCompany" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityShellCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityShellCompany" xlink:to="lab_dei_EntityShellCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeriesDPreferredStockMember_8791bcf0-b37d-4283-a06d-e3676f3118a0_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesDPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">5.700% Non-Cumulative Preferred Stock, Series D</link:label>
    <link:label id="lab_us-gaap_SeriesDPreferredStockMember_be139a53-db88-46bf-bb93-903e364fe469_verboseLabel_en-US" xlink:label="lab_us-gaap_SeriesDPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Series D</link:label>
    <link:label id="lab_us-gaap_SeriesDPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesDPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series D Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesDPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SeriesDPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesDPreferredStockMember" xlink:to="lab_us-gaap_SeriesDPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDeterminationDate_terseLabel_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:label id="lab_ecd_RestatementDeterminationDate_label_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDeterminationDate" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_RestatementDeterminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDeterminationDate" xlink:to="lab_ecd_RestatementDeterminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable_228235f1-c838-4f0c-b73e-4c126b991e23_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Financing Receivable, Allowance for Credit Losses [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable" xlink:to="lab_us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_06db4a5e-a3de-419a-9e7f-87f4ec1d49a5_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInOtherOperatingLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_Rule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:to="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityTransferInAccumulatedLoss_25cbb999-33e1-48a1-9931-c1d2d5f7624c_terseLabel_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityTransferInAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Held-to-maturity, transfer in, accumulated unrealized loss</link:label>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityTransferInAccumulatedLoss_label_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityTransferInAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Transfer In, Accumulated Loss</link:label>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityTransferInAccumulatedLoss_documentation_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityTransferInAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Transfer In, Accumulated Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DebtSecuritiesHeldToMaturityTransferInAccumulatedLoss" xlink:href="agm-20240331.xsd#agm_DebtSecuritiesHeldToMaturityTransferInAccumulatedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DebtSecuritiesHeldToMaturityTransferInAccumulatedLoss" xlink:to="lab_agm_DebtSecuritiesHeldToMaturityTransferInAccumulatedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_6492f556-e44c-43c7-8801-480767ae9395_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents at beginning of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_dc60812e-7704-4154-8ccf-2a9233acea4c_periodEndLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents at end of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByAssetClassAxis_3d802939-8fe4-451a-b13e-7372a6ebe6f5_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByAssetClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByAssetClassAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByAssetClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByAssetClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueByAssetClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByAssetClassAxis" xlink:to="lab_us-gaap_FairValueByAssetClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_AgriculturalFinanceMember_1649fc62-59d3-4187-b23d-6b9170ab4e87_terseLabel_en-US" xlink:label="lab_agm_AgriculturalFinanceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Agricultural Finance</link:label>
    <link:label id="lab_agm_AgriculturalFinanceMember_label_en-US" xlink:label="lab_agm_AgriculturalFinanceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Agricultural Finance [Member]</link:label>
    <link:label id="lab_agm_AgriculturalFinanceMember_documentation_en-US" xlink:label="lab_agm_AgriculturalFinanceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Agricultural Finance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_AgriculturalFinanceMember" xlink:href="agm-20240331.xsd#agm_AgriculturalFinanceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_AgriculturalFinanceMember" xlink:to="lab_agm_AgriculturalFinanceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger_4488b04e-c00b-442a-a6ca-c1026dc2215a_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized loss position for more than 12 months, Fair Value</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Continuous Unrealized Loss Position, 12 Months or Longer</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss_91df80aa-57e3-4066-85a3-94a1a6a9441d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Unrealized Losses</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Accumulated Unrecognized Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_012dcff3-4aff-419e-a903-43f553c02fb9_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Assets at fair value</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosure" xlink:to="lab_us-gaap_AssetsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebt_0bc19069-0987-407a-a143-82e9508a84d2_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Debt securities of consolidated trusts held by third parties</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_2aad3133-32cc-4c6b-b5e0-0c9f2b5c7d81_totalLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total principal net of discounts</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_label_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebt" xlink:to="lab_us-gaap_LongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_0442ef9f-d5ba-485f-8813-7995c1c28258_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Four years</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_d53c55e9-2b13-4565-8803-e0895bcec60d_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAverageFixedInterestRate_3adb3723-354f-4007-9351-55fbb806f536_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAverageFixedInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted- Average Pay Rate</link:label>
    <link:label id="lab_us-gaap_DerivativeAverageFixedInterestRate_label_en-US" xlink:label="lab_us-gaap_DerivativeAverageFixedInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Average Fixed Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAverageFixedInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeAverageFixedInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAverageFixedInterestRate" xlink:to="lab_us-gaap_DerivativeAverageFixedInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_PaymentsToThirdPartiesOnDebtSecuritiesOfConsolidatedTrusts_97babcf3-53e2-46a3-b92a-d8101fea180d_negatedTerseLabel_en-US" xlink:label="lab_agm_PaymentsToThirdPartiesOnDebtSecuritiesOfConsolidatedTrusts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payments to third parties on debt securities of consolidated trusts</link:label>
    <link:label id="lab_agm_PaymentsToThirdPartiesOnDebtSecuritiesOfConsolidatedTrusts_label_en-US" xlink:label="lab_agm_PaymentsToThirdPartiesOnDebtSecuritiesOfConsolidatedTrusts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments To Third Parties On Debt Securities Of Consolidated Trusts</link:label>
    <link:label id="lab_agm_PaymentsToThirdPartiesOnDebtSecuritiesOfConsolidatedTrusts_documentation_en-US" xlink:label="lab_agm_PaymentsToThirdPartiesOnDebtSecuritiesOfConsolidatedTrusts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The cash outflows associated with consolidated trusts where Farmer Mac is determined to be the primary beneficiary but trusts are owned by third parties.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_PaymentsToThirdPartiesOnDebtSecuritiesOfConsolidatedTrusts" xlink:href="agm-20240331.xsd#agm_PaymentsToThirdPartiesOnDebtSecuritiesOfConsolidatedTrusts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_PaymentsToThirdPartiesOnDebtSecuritiesOfConsolidatedTrusts" xlink:to="lab_agm_PaymentsToThirdPartiesOnDebtSecuritiesOfConsolidatedTrusts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentBeforeTax_6ea93ed6-0c8f-4d6b-921a-1cbfbbc1a4e4_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net unrealized gains on available-for-sale securities</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentBeforeTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OCI, Debt Securities, Available-for-Sale, Gain (Loss), after Adjustment, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentBeforeTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfOrdinaryDividends_4bfa4c80-5dbc-43f4-9723-119d653a578b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfOrdinaryDividends" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Dividends paid on common and preferred stock</link:label>
    <link:label id="lab_us-gaap_PaymentsOfOrdinaryDividends_label_en-US" xlink:label="lab_us-gaap_PaymentsOfOrdinaryDividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Ordinary Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfOrdinaryDividends" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PaymentsOfOrdinaryDividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfOrdinaryDividends" xlink:to="lab_us-gaap_PaymentsOfOrdinaryDividends" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonClassAMember_97d51f81-76db-4d05-aaae-f342442872d0_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonClassAMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Class A voting common stock</link:label>
    <link:label id="lab_us-gaap_CommonClassAMember_label_en-US" xlink:label="lab_us-gaap_CommonClassAMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Class A [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassAMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonClassAMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonClassAMember" xlink:to="lab_us-gaap_CommonClassAMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesTradingAndAvailableForSaleAbstract_c1816990-200f-47f2-8311-bf7e03bb966e_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesTradingAndAvailableForSaleAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading:</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesTradingAndAvailableForSaleAbstract_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesTradingAndAvailableForSaleAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading and Available-for-Sale [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesTradingAndAvailableForSaleAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesTradingAndAvailableForSaleAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesTradingAndAvailableForSaleAbstract" xlink:to="lab_us-gaap_DebtSecuritiesTradingAndAvailableForSaleAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_f69b66f0-3043-4388-aee9-3cd879623764_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Comprehensive income</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ComprehensiveIncomeNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeriesFPreferredStockMember_aad84e91-b749-4536-8eed-8709be5e1d95_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesFPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">5.250% Non-Cumulative Preferred Stock, Series F</link:label>
    <link:label id="lab_us-gaap_SeriesFPreferredStockMember_022345c2-e96e-45a4-ada3-73ff5ca321ed_verboseLabel_en-US" xlink:label="lab_us-gaap_SeriesFPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Series F</link:label>
    <link:label id="lab_us-gaap_SeriesFPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesFPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series F Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesFPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SeriesFPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesFPreferredStockMember" xlink:to="lab_us-gaap_SeriesFPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotesPayableToBanksMember_57af3811-a1c7-4043-9e08-c185e1c9fe56_verboseLabel_en-US" xlink:label="lab_us-gaap_NotesPayableToBanksMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Discount notes</link:label>
    <link:label id="lab_us-gaap_NotesPayableToBanksMember_label_en-US" xlink:label="lab_us-gaap_NotesPayableToBanksMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Payable to Banks [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesPayableToBanksMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NotesPayableToBanksMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotesPayableToBanksMember" xlink:to="lab_us-gaap_NotesPayableToBanksMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_66438b57-53c6-496f-92d5-039a7674a07e_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressAddressLine1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine2_f76f8f69-8018-4064-80b4-76f25dd53b98_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line Two</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine2_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine2" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine2" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressAddressLine2"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine2" xlink:to="lab_dei_EntityAddressAddressLine2" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract_fcf9bf9d-f1c1-4110-bdeb-e43e130b187b_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial liabilities:</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments, Financial Liabilities, Balance Sheet Groupings [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract" xlink:to="lab_us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansMember_14c7f729-6451-416d-aceb-6dd742cd3027_terseLabel_en-US" xlink:label="lab_us-gaap_LoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans</link:label>
    <link:label id="lab_us-gaap_LoansMember_label_en-US" xlink:label="lab_us-gaap_LoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansMember" xlink:to="lab_us-gaap_LoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossAndLoansHeldForSaleFairValueDisclosure_fe918f8e-9d06-470d-a6d6-8ddfd5e295f0_totalLabel_en-US" xlink:label="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossAndLoansHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total loans</link:label>
    <link:label id="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossAndLoansHeldForSaleFairValueDisclosure_label_en-US" xlink:label="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossAndLoansHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Before Allowance for Credit Loss And Loans Held-For-Sale Fair Value Disclosure</link:label>
    <link:label id="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossAndLoansHeldForSaleFairValueDisclosure_documentation_en-US" xlink:label="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossAndLoansHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Before Allowance for Credit Loss And Loans Held-For-Sale Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossAndLoansHeldForSaleFairValueDisclosure" xlink:href="agm-20240331.xsd#agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossAndLoansHeldForSaleFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossAndLoansHeldForSaleFairValueDisclosure" xlink:to="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossAndLoansHeldForSaleFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_2725ee9c-6d97-44cf-bc6f-5dbf94dfc553_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:to="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Capital_9f9f962b-d864-4763-b435-f32413f40391_terseLabel_en-US" xlink:label="lab_us-gaap_Capital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital</link:label>
    <link:label id="lab_us-gaap_Capital_label_en-US" xlink:label="lab_us-gaap_Capital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Total Capital, Actual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Capital" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_Capital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Capital" xlink:to="lab_us-gaap_Capital" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_InterestRevenueExpenseNetMember_637df612-1733-477e-aa14-ca93e1846174_terseLabel_en-US" xlink:label="lab_agm_InterestRevenueExpenseNetMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Income Investments and Cash Equivalents</link:label>
    <link:label id="lab_agm_InterestRevenueExpenseNetMember_label_en-US" xlink:label="lab_agm_InterestRevenueExpenseNetMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Revenue (Expense), Net [Member]</link:label>
    <link:label id="lab_agm_InterestRevenueExpenseNetMember_documentation_en-US" xlink:label="lab_agm_InterestRevenueExpenseNetMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Revenue (Expense), Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_InterestRevenueExpenseNetMember" xlink:href="agm-20240331.xsd#agm_InterestRevenueExpenseNetMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_InterestRevenueExpenseNetMember" xlink:to="lab_agm_InterestRevenueExpenseNetMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockNumberOfSharesParValueAndOtherDisclosuresAbstract_fe15b2b1-fb45-4451-a096-a4ddfba536b8_verboseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockNumberOfSharesParValueAndOtherDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock:</link:label>
    <link:label id="lab_us-gaap_PreferredStockNumberOfSharesParValueAndOtherDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_PreferredStockNumberOfSharesParValueAndOtherDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Number of Shares, Par Value and Other Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockNumberOfSharesParValueAndOtherDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockNumberOfSharesParValueAndOtherDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockNumberOfSharesParValueAndOtherDisclosuresAbstract" xlink:to="lab_us-gaap_PreferredStockNumberOfSharesParValueAndOtherDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionTwelveMonthsOrLongerFairValue_fd74e004-a5c0-4f97-bdce-0b600798631f_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionTwelveMonthsOrLongerFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair&#160;Value</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionTwelveMonthsOrLongerFairValue_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionTwelveMonthsOrLongerFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Continuous Unrealized Loss Position, 12 Months or Longer, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionTwelveMonthsOrLongerFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionTwelveMonthsOrLongerFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionTwelveMonthsOrLongerFairValue" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionTwelveMonthsOrLongerFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_8d093176-4da1-4ac3-add0-ab3336f560ce_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncomeStatementAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementAbstract" xlink:to="lab_us-gaap_IncomeStatementAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_4b9c020b-0e63-4738-92c7-73655720c806_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of Class C Common Stock (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_6a32c59d-c1f3-4cec-9af2-1cea1279e498_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ValuationTechniqueAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueAxis" xlink:to="lab_us-gaap_ValuationTechniqueAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_InsiderTrdPoliciesProcAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:to="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure_7bddce34-829a-4672-8d91-9e54d85be948_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CashAndCashEquivalentsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:to="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems_6c89beaa-c8e0-44e3-ae04-956d79b61191_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Recorded Investment [Line Items]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Credit Quality Indicator [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableRecordedInvestmentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:to="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsTax_257189fd-7c65-41a4-be59-b7ec36a9ee68_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized gains/(losses), provision (benefit)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss) before Reclassifications, Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsTax" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_ProceedsFromMaturitiesPrepaymentsAndCallsOfDebtSecuritiesAvailableForSaleAndHeldToMaturity_9d602fc5-f84c-488a-85fb-99debbf1fd0b_terseLabel_en-US" xlink:label="lab_agm_ProceedsFromMaturitiesPrepaymentsAndCallsOfDebtSecuritiesAvailableForSaleAndHeldToMaturity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from repayment of available-for-sale and held-to-maturity investment securities</link:label>
    <link:label id="lab_agm_ProceedsFromMaturitiesPrepaymentsAndCallsOfDebtSecuritiesAvailableForSaleAndHeldToMaturity_label_en-US" xlink:label="lab_agm_ProceedsFromMaturitiesPrepaymentsAndCallsOfDebtSecuritiesAvailableForSaleAndHeldToMaturity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From Maturities, Prepayments And Calls Of Debt Securities, Available-For-Sale And Held-To-Maturity</link:label>
    <link:label id="lab_agm_ProceedsFromMaturitiesPrepaymentsAndCallsOfDebtSecuritiesAvailableForSaleAndHeldToMaturity_documentation_en-US" xlink:label="lab_agm_ProceedsFromMaturitiesPrepaymentsAndCallsOfDebtSecuritiesAvailableForSaleAndHeldToMaturity" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds From Maturities, Prepayments And Calls Of Debt Securities, Available-For-Sale And Held-To-Maturity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_ProceedsFromMaturitiesPrepaymentsAndCallsOfDebtSecuritiesAvailableForSaleAndHeldToMaturity" xlink:href="agm-20240331.xsd#agm_ProceedsFromMaturitiesPrepaymentsAndCallsOfDebtSecuritiesAvailableForSaleAndHeldToMaturity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_ProceedsFromMaturitiesPrepaymentsAndCallsOfDebtSecuritiesAvailableForSaleAndHeldToMaturity" xlink:to="lab_agm_ProceedsFromMaturitiesPrepaymentsAndCallsOfDebtSecuritiesAvailableForSaleAndHeldToMaturity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilities_76e9410d-038d-4ec4-a338-9bf8056fa6fc_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Financial derivatives, at fair value</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_bda91c9c-13e9-4271-b09e-b3fd34c5bde0_negatedLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Fair value, liability</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_d301c1e1-fba8-4731-b4e5-3655fb5cbc18_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial derivatives</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilities" xlink:to="lab_us-gaap_DerivativeLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_ReconcilingAdjustmentsFromNetInterestIncomeToNetEffectiveSpreadNet_e09ddc2d-d607-4ff8-ace9-90ca317aad28_negatedTerseLabel_en-US" xlink:label="lab_agm_ReconcilingAdjustmentsFromNetInterestIncomeToNetEffectiveSpreadNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: reconciling adjustments</link:label>
    <link:label id="lab_agm_ReconcilingAdjustmentsFromNetInterestIncomeToNetEffectiveSpreadNet_label_en-US" xlink:label="lab_agm_ReconcilingAdjustmentsFromNetInterestIncomeToNetEffectiveSpreadNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reconciling Adjustments From Net Interest Income To Net Effective Spread, Net</link:label>
    <link:label id="lab_agm_ReconcilingAdjustmentsFromNetInterestIncomeToNetEffectiveSpreadNet_documentation_en-US" xlink:label="lab_agm_ReconcilingAdjustmentsFromNetInterestIncomeToNetEffectiveSpreadNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reconciling Adjustments From Net Interest Income To Net Effective Spread, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_ReconcilingAdjustmentsFromNetInterestIncomeToNetEffectiveSpreadNet" xlink:href="agm-20240331.xsd#agm_ReconcilingAdjustmentsFromNetInterestIncomeToNetEffectiveSpreadNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_ReconcilingAdjustmentsFromNetInterestIncomeToNetEffectiveSpreadNet" xlink:to="lab_agm_ReconcilingAdjustmentsFromNetInterestIncomeToNetEffectiveSpreadNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_6ebeb125-104d-4d24-8d00-a2dae06b1b51_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_label_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfStockLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockLineItems" xlink:to="lab_us-gaap_ClassOfStockLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ExchangeClearedMember_fbc20b63-dd7b-4f0e-b4ab-56b60f6d00a5_terseLabel_en-US" xlink:label="lab_us-gaap_ExchangeClearedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exchange Cleared</link:label>
    <link:label id="lab_us-gaap_ExchangeClearedMember_label_en-US" xlink:label="lab_us-gaap_ExchangeClearedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Exchange Cleared [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ExchangeClearedMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ExchangeClearedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ExchangeClearedMember" xlink:to="lab_us-gaap_ExchangeClearedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareDilutedAbstract_fd299056-af47-4aeb-9906-fa3926e2c550_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDilutedAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effect of dilutive securities</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDilutedAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDilutedAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDilutedAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EarningsPerShareDilutedAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareDilutedAbstract" xlink:to="lab_us-gaap_EarningsPerShareDilutedAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MaturitiesOfLongTermDebtAbstract_26133a6c-4f52-48f6-a73e-2b6d9f2dd32a_terseLabel_en-US" xlink:label="lab_us-gaap_MaturitiesOfLongTermDebtAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Medium-term notes due in:</link:label>
    <link:label id="lab_us-gaap_MaturitiesOfLongTermDebtAbstract_label_en-US" xlink:label="lab_us-gaap_MaturitiesOfLongTermDebtAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maturities of Long-Term Debt [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MaturitiesOfLongTermDebtAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MaturitiesOfLongTermDebtAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MaturitiesOfLongTermDebtAbstract" xlink:to="lab_us-gaap_MaturitiesOfLongTermDebtAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossTaxAbstract_aeeea502-d239-4ced-a8a0-adafca6eaa53_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossTaxAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision (Benefit)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossTaxAbstract_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossTaxAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Tax [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossTaxAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherComprehensiveIncomeLossTaxAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossTaxAbstract" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossTaxAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FarmerMacAndUsdaGuaranteedSecuritiesMember_3dc6c260-9771-4df7-8373-272c14e84951_terseLabel_en-US" xlink:label="lab_agm_FarmerMacAndUsdaGuaranteedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Farmer Mac Guaranteed Securities and USDA Securities</link:label>
    <link:label id="lab_agm_FarmerMacAndUsdaGuaranteedSecuritiesMember_label_en-US" xlink:label="lab_agm_FarmerMacAndUsdaGuaranteedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Farmer Mac and USDA Guaranteed Securities [Member]</link:label>
    <link:label id="lab_agm_FarmerMacAndUsdaGuaranteedSecuritiesMember_documentation_en-US" xlink:label="lab_agm_FarmerMacAndUsdaGuaranteedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Farmer Mac and USDA Guaranteed Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FarmerMacAndUsdaGuaranteedSecuritiesMember" xlink:href="agm-20240331.xsd#agm_FarmerMacAndUsdaGuaranteedSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FarmerMacAndUsdaGuaranteedSecuritiesMember" xlink:to="lab_agm_FarmerMacAndUsdaGuaranteedSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_adb99480-0550-429a-9727-4b53f8f5cd47_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentAxis" xlink:to="lab_us-gaap_FinancialInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestReceivable_c7ac7bce-e32c-40c7-8236-2d59c387b238_terseLabel_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest receivable (includes $9,963 and $16,764, respectively, related to consolidated trusts)</link:label>
    <link:label id="lab_us-gaap_InterestReceivable_d916d731-73b7-4555-9c40-e937f1c5d3d5_verboseLabel_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Interest receivable</link:label>
    <link:label id="lab_us-gaap_InterestReceivable_label_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestReceivable" xlink:to="lab_us-gaap_InterestReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_TotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnAmt" xlink:to="lab_ecd_TotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_e29aa18c-2206-4a69-acb0-20a08beb64fa_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCommonStockSharesOutstanding" xlink:to="lab_dei_EntityCommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote</link:label>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToPeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AdjToPeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToPeoCompFnTextBlock" xlink:to="lab_ecd_AdjToPeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentDomain_bdeaecf1-6709-47ec-b41d-6c3df55f4234_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:label id="lab_us-gaap_SegmentDomain_label_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SegmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentDomain" xlink:to="lab_us-gaap_SegmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember_d2d3c225-f11e-440d-96ad-436696ec27ee_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unconsolidated VIE</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Not Primary Beneficiary [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:to="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_58765419-9a46-49c5-8816-51f13a5b85fc_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsDomain_52fd8674-99b2-4341-98d7-ddb6ea85023d_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:label id="lab_srt_ConsolidationItemsDomain_label_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsDomain" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_ConsolidationItemsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidationItemsDomain" xlink:to="lab_srt_ConsolidationItemsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_07127e71-579a-4698-9e14-5f78365e0563_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retained earnings</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CollateralDomain_f65ea188-cc1d-41df-9abd-5dd483a4c95b_terseLabel_en-US" xlink:label="lab_us-gaap_CollateralDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral [Domain]</link:label>
    <link:label id="lab_us-gaap_CollateralDomain_label_en-US" xlink:label="lab_us-gaap_CollateralDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateral Held [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CollateralDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CollateralDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CollateralDomain" xlink:to="lab_us-gaap_CollateralDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_2b81ea38-4c22-4de7-b3a6-5cb4db75c8ff_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressStateOrProvince"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesDomain_4d3bd1be-53b2-4acb-95dc-d4e71547844f_terseLabel_en-US" xlink:label="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecorded maximum potential exposure on guarantees [Domain]</link:label>
    <link:label id="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesDomain_label_en-US" xlink:label="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecorded maximum potential exposure on guarantees [Domain]</link:label>
    <link:label id="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesDomain_documentation_en-US" xlink:label="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">[Domain] for Unrecorded maximum potential exposure on guarantees, pertinent information about guarantee obligations issued [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_UnrecordedMaximumPotentialExposureOnGuaranteesDomain" xlink:href="agm-20240331.xsd#agm_UnrecordedMaximumPotentialExposureOnGuaranteesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_UnrecordedMaximumPotentialExposureOnGuaranteesDomain" xlink:to="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_64f61d15-0f34-48e8-b379-99885ec8e0c0_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from operating activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Operating Activities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GuaranteeObligationsLineItems_875d6a5d-eb88-41d3-8270-f9913a6ad134_terseLabel_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantor Obligations [Line Items]</link:label>
    <link:label id="lab_us-gaap_GuaranteeObligationsLineItems_label_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guarantor Obligations [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GuaranteeObligationsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GuaranteeObligationsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GuaranteeObligationsLineItems" xlink:to="lab_us-gaap_GuaranteeObligationsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_RuralInfrastructureRenewableEnergySegmentMember_23e34158-61e6-480e-b9df-b0108a63c6a9_terseLabel_en-US" xlink:label="lab_agm_RuralInfrastructureRenewableEnergySegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Renewable Energy</link:label>
    <link:label id="lab_agm_RuralInfrastructureRenewableEnergySegmentMember_label_en-US" xlink:label="lab_agm_RuralInfrastructureRenewableEnergySegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rural Infrastructure, Renewable Energy Segment [Member]</link:label>
    <link:label id="lab_agm_RuralInfrastructureRenewableEnergySegmentMember_documentation_en-US" xlink:label="lab_agm_RuralInfrastructureRenewableEnergySegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Rural Infrastructure, Renewable Energy Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_RuralInfrastructureRenewableEnergySegmentMember" xlink:href="agm-20240331.xsd#agm_RuralInfrastructureRenewableEnergySegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_RuralInfrastructureRenewableEnergySegmentMember" xlink:to="lab_agm_RuralInfrastructureRenewableEnergySegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities_7ced7210-dc2b-4d40-8faa-c2d5b7f589eb_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from repayment of Farmer Mac Guaranteed Securities and USDA Securities</link:label>
    <link:label id="lab_us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities_label_en-US" xlink:label="lab_us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Maturities, Prepayments and Calls of Debt Securities, Available-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities" xlink:to="lab_us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasicAbstract_7fa86fec-da20-42ce-a7d2-673b46748d2c_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic EPS</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasicAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasicAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EarningsPerShareBasicAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasicAbstract" xlink:to="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoninterestIncomeAbstract_07d42d90-1f9e-46b6-9e75-c4b031c23a63_terseLabel_en-US" xlink:label="lab_us-gaap_NoninterestIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-interest income/(expense):</link:label>
    <link:label id="lab_us-gaap_NoninterestIncomeAbstract_label_en-US" xlink:label="lab_us-gaap_NoninterestIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Income [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoninterestIncomeAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NoninterestIncomeAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoninterestIncomeAbstract" xlink:to="lab_us-gaap_NoninterestIncomeAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DiscountNotesMember_b3fcb122-71f1-49b5-8f6e-ce2a381671ea_terseLabel_en-US" xlink:label="lab_agm_DiscountNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discount Notes</link:label>
    <link:label id="lab_agm_DiscountNotesMember_label_en-US" xlink:label="lab_agm_DiscountNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Discount Notes [Member]</link:label>
    <link:label id="lab_agm_DiscountNotesMember_documentation_en-US" xlink:label="lab_agm_DiscountNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Discount Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DiscountNotesMember" xlink:href="agm-20240331.xsd#agm_DiscountNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DiscountNotesMember" xlink:to="lab_agm_DiscountNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromShortTermDebt_8c46b4d8-219e-4fa1-bc43-890aced8afe8_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromShortTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from issuance of discount notes</link:label>
    <link:label id="lab_us-gaap_ProceedsFromShortTermDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromShortTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Short-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromShortTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromShortTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromShortTermDebt" xlink:to="lab_us-gaap_ProceedsFromShortTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_85adb07b-9b8e-4d1f-b483-c3538368bbd9_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Line Items]</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityFairValueNetOfAllowance_5659a04b-ebb1-4ea9-959e-860672fc65f7_terseLabel_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityFairValueNetOfAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair&#160;Value</link:label>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityFairValueNetOfAllowance_label_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityFairValueNetOfAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-maturity, Fair Value, Net of Allowance</link:label>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityFairValueNetOfAllowance_documentation_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityFairValueNetOfAllowance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-maturity, Fair Value, Net of Allowance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DebtSecuritiesHeldToMaturityFairValueNetOfAllowance" xlink:href="agm-20240331.xsd#agm_DebtSecuritiesHeldToMaturityFairValueNetOfAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DebtSecuritiesHeldToMaturityFairValueNetOfAllowance" xlink:to="lab_agm_DebtSecuritiesHeldToMaturityFairValueNetOfAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_ea8f6078-671f-4e2f-86a1-b09caeb35477_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Class [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAsset_df4f6fa9-7bd7-44a6-8e7f-f2c0fd9170ae_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Amount Recognized</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAsset_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, before Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeFairValueOfDerivativeAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:to="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_AvailableForSaleSecuritiesInLossPositionForMoreThan12MonthsQualitativeDisclosurePercentOfAmortizedCost_362f27d8-771b-4e6f-9a75-f2f3a6260d88_terseLabel_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesInLossPositionForMoreThan12MonthsQualitativeDisclosurePercentOfAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Average percent of amortized cost for securities in unrealized loss positions for more than 12 months</link:label>
    <link:label id="lab_agm_AvailableForSaleSecuritiesInLossPositionForMoreThan12MonthsQualitativeDisclosurePercentOfAmortizedCost_label_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesInLossPositionForMoreThan12MonthsQualitativeDisclosurePercentOfAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Available-for-sale securities in a loss position for more than 12 months, qualitative disclosure, percent of amortized cost</link:label>
    <link:label id="lab_agm_AvailableForSaleSecuritiesInLossPositionForMoreThan12MonthsQualitativeDisclosurePercentOfAmortizedCost_documentation_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesInLossPositionForMoreThan12MonthsQualitativeDisclosurePercentOfAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Available-for-sale securities in a loss position for more than 12 months, qualitative disclosure, percent of amortized cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_AvailableForSaleSecuritiesInLossPositionForMoreThan12MonthsQualitativeDisclosurePercentOfAmortizedCost" xlink:href="agm-20240331.xsd#agm_AvailableForSaleSecuritiesInLossPositionForMoreThan12MonthsQualitativeDisclosurePercentOfAmortizedCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_AvailableForSaleSecuritiesInLossPositionForMoreThan12MonthsQualitativeDisclosurePercentOfAmortizedCost" xlink:to="lab_agm_AvailableForSaleSecuritiesInLossPositionForMoreThan12MonthsQualitativeDisclosurePercentOfAmortizedCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableNonaccrualInterestIncome_c516256d-717e-40e8-96b0-f779c02895a8_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableNonaccrualInterestIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest received on nonaccrual loans</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableNonaccrualInterestIncome_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableNonaccrualInterestIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Nonaccrual, Interest Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableNonaccrualInterestIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableNonaccrualInterestIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableNonaccrualInterestIncome" xlink:to="lab_us-gaap_FinancingReceivableNonaccrualInterestIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfHeldToMaturitySecuritiesLineItems_a0b25fc8-e0f6-4520-8773-99a3425e61fe_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfHeldToMaturitySecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Held-to-maturity Securities [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfHeldToMaturitySecuritiesLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfHeldToMaturitySecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Held-to-Maturity Securities [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfHeldToMaturitySecuritiesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfHeldToMaturitySecuritiesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfHeldToMaturitySecuritiesLineItems" xlink:to="lab_us-gaap_ScheduleOfHeldToMaturitySecuritiesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockDomain_674d18bc-feec-4aa5-ab4b-eeb95d181ea6_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfStockDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockDomain" xlink:to="lab_us-gaap_ClassOfStockDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock_4e8cba26-fa68-415b-8d0b-7146d3bb7f85_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Reclassification out of Accumulated Other Comprehensive Income</link:label>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock" xlink:to="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_2ef0afad-62e3-46ae-a5f9-bae22c9dfd24_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income attributable to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_94d8995c-53a0-4578-8823-0c453a48c690_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income attributable to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_EarningsPerShareOnIncrementalCommonSharesAttributableToShareBasedPaymentArrangements_66d09514-849d-4272-8a1e-57feea8e9cbe_terseLabel_en-US" xlink:label="lab_agm_EarningsPerShareOnIncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SARs and restricted stock units (in dollars per share)</link:label>
    <link:label id="lab_agm_EarningsPerShareOnIncrementalCommonSharesAttributableToShareBasedPaymentArrangements_label_en-US" xlink:label="lab_agm_EarningsPerShareOnIncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, On Incremental Common Shares Attributable to Share-based Payment Arrangements</link:label>
    <link:label id="lab_agm_EarningsPerShareOnIncrementalCommonSharesAttributableToShareBasedPaymentArrangements_documentation_en-US" xlink:label="lab_agm_EarningsPerShareOnIncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Earnings Per Share, On Incremental Common Shares Attributable to Share-based Payment Arrangements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_EarningsPerShareOnIncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:href="agm-20240331.xsd#agm_EarningsPerShareOnIncrementalCommonSharesAttributableToShareBasedPaymentArrangements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_EarningsPerShareOnIncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:to="lab_agm_EarningsPerShareOnIncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_TotalShareholderRtnVsPeerGroupTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:to="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_46aaca0c-b293-4aff-9a0c-7a621a961f01_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss)</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_AggtErrCompAmt_label_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompAmt" xlink:to="lab_ecd_AggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_terseLabel_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Executive Categories</link:label>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_label_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Executive Categories [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllExecutiveCategoriesMember" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AllExecutiveCategoriesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllExecutiveCategoriesMember" xlink:to="lab_ecd_AllExecutiveCategoriesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AuctionRateSecuritiesMember_0fd48649-a706-4907-b065-831ef85bce7d_terseLabel_en-US" xlink:label="lab_us-gaap_AuctionRateSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Floating rate auction-rate certificates backed by Government guaranteed student loans</link:label>
    <link:label id="lab_us-gaap_AuctionRateSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_AuctionRateSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Auction Rate Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AuctionRateSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AuctionRateSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AuctionRateSecuritiesMember" xlink:to="lab_us-gaap_AuctionRateSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoninterestExpense_8fc029d2-dd26-48d5-941d-bc64b172a4d4_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_NoninterestExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Total non-interest expense</link:label>
    <link:label id="lab_us-gaap_NoninterestExpense_label_en-US" xlink:label="lab_us-gaap_NoninterestExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoninterestExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NoninterestExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoninterestExpense" xlink:to="lab_us-gaap_NoninterestExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_d2e83936-5775-4b98-be85-79abc8113845_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Table]</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_202ef930-989e-4a4d-aaea-2e716032c277_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureAbstract" xlink:to="lab_us-gaap_DebtDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLoss_db72698f-20ea-426d-b835-6424412b216c_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest on cleared swaps</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Accrued Interest, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLoss" xlink:to="lab_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_PaymentsToAcquireDebtSecuritiesAvailableForSaleAndHeldToMaturity_833922fe-d018-473b-b47a-c89804b948dc_negatedTerseLabel_en-US" xlink:label="lab_agm_PaymentsToAcquireDebtSecuritiesAvailableForSaleAndHeldToMaturity" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of available-for-sale and held-to-maturity investment securities</link:label>
    <link:label id="lab_agm_PaymentsToAcquireDebtSecuritiesAvailableForSaleAndHeldToMaturity_label_en-US" xlink:label="lab_agm_PaymentsToAcquireDebtSecuritiesAvailableForSaleAndHeldToMaturity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Debt Securities, Available-for-Sale And Held-to-Maturity</link:label>
    <link:label id="lab_agm_PaymentsToAcquireDebtSecuritiesAvailableForSaleAndHeldToMaturity_documentation_en-US" xlink:label="lab_agm_PaymentsToAcquireDebtSecuritiesAvailableForSaleAndHeldToMaturity" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments to Acquire Debt Securities, Available-for-Sale And Held-to-Maturity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_PaymentsToAcquireDebtSecuritiesAvailableForSaleAndHeldToMaturity" xlink:href="agm-20240331.xsd#agm_PaymentsToAcquireDebtSecuritiesAvailableForSaleAndHeldToMaturity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_PaymentsToAcquireDebtSecuritiesAvailableForSaleAndHeldToMaturity" xlink:to="lab_agm_PaymentsToAcquireDebtSecuritiesAvailableForSaleAndHeldToMaturity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_511de6a8-e249-4f01-81a3-11a99afd48c2_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings per common share:</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EarningsPerShareAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareAbstract" xlink:to="lab_us-gaap_EarningsPerShareAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_9533cc41-e0f9-408b-b410-801aee643769_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Consolidation of Variable Interest Entities</link:label>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Variable Interest Entities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:to="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ChangeInUnrealizedGainLossOnHedgedItemInFairValueHedge1_48337cc7-455d-4410-9d38-84d3f3fc25e1_terseLabel_en-US" xlink:label="lab_us-gaap_ChangeInUnrealizedGainLossOnHedgedItemInFairValueHedge1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recognized on hedged items</link:label>
    <link:label id="lab_us-gaap_ChangeInUnrealizedGainLossOnHedgedItemInFairValueHedge1_label_en-US" xlink:label="lab_us-gaap_ChangeInUnrealizedGainLossOnHedgedItemInFairValueHedge1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Unrealized Gain (Loss) on Hedged Item in Fair Value Hedge</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ChangeInUnrealizedGainLossOnHedgedItemInFairValueHedge1" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ChangeInUnrealizedGainLossOnHedgedItemInFairValueHedge1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ChangeInUnrealizedGainLossOnHedgedItemInFairValueHedge1" xlink:to="lab_us-gaap_ChangeInUnrealizedGainLossOnHedgedItemInFairValueHedge1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockValue_8e1481b7-3bfb-49fb-8d51-210dde9539ed_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockValue" xlink:to="lab_us-gaap_CommonStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommercialRealEstateMember_1c30aea8-07b9-4da8-a2de-11fd02c67615_terseLabel_en-US" xlink:label="lab_us-gaap_CommercialRealEstateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial Real Estate</link:label>
    <link:label id="lab_us-gaap_CommercialRealEstateMember_label_en-US" xlink:label="lab_us-gaap_CommercialRealEstateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Real Estate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommercialRealEstateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommercialRealEstateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommercialRealEstateMember" xlink:to="lab_us-gaap_CommercialRealEstateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_f010ddae-320b-4225-bdf3-f99c31948ca9_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after one year through five years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, after Year One Through Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAllowanceForCreditLossExcludingAccruedInterest_f5f56f30-d180-4101-86a4-d7de309059e1_negatedLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Allowance for losses</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAllowanceForCreditLossExcludingAccruedInterest_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Allowance for Credit Loss, Excluding Accrued Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAllowanceForCreditLossExcludingAccruedInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAllowanceForCreditLossExcludingAccruedInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAllowanceForCreditLossExcludingAccruedInterest" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAllowanceForCreditLossExcludingAccruedInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromPrincipalRepaymentsOnLoansAndLeasesHeldForInvestment_29502f56-e6f7-4f23-a22a-b15614d55c73_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromPrincipalRepaymentsOnLoansAndLeasesHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from repayment of loans purchased as held for investment</link:label>
    <link:label id="lab_us-gaap_ProceedsFromPrincipalRepaymentsOnLoansAndLeasesHeldForInvestment_label_en-US" xlink:label="lab_us-gaap_ProceedsFromPrincipalRepaymentsOnLoansAndLeasesHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Principal Repayment, Loan and Lease, Held-for-Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromPrincipalRepaymentsOnLoansAndLeasesHeldForInvestment" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromPrincipalRepaymentsOnLoansAndLeasesHeldForInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromPrincipalRepaymentsOnLoansAndLeasesHeldForInvestment" xlink:to="lab_us-gaap_ProceedsFromPrincipalRepaymentsOnLoansAndLeasesHeldForInvestment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfNewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock_aaf9e578-b993-4cf9-a296-00e3f59cc72d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfNewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Recently Adopted Accounting Guidance</link:label>
    <link:label id="lab_us-gaap_ScheduleOfNewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfNewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Standards Update and Change in Accounting Principle [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfNewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfNewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfNewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock" xlink:to="lab_us-gaap_ScheduleOfNewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_b024d7ff-5060-415d-b59c-c6cec5b136c2_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest payable (includes $6,338 and $9,407, respectively, related to consolidated trusts)</link:label>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_3f367fab-2790-47a1-88f0-a6c03d183d77_verboseLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest payable - consolidated trusts amount</link:label>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestPayableCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:to="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllIndividualsMember_terseLabel_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Individuals</link:label>
    <link:label id="lab_ecd_AllIndividualsMember_label_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Individuals [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllIndividualsMember" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AllIndividualsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="lab_ecd_AllIndividualsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFilerCategory_10cc0c83-1b70-41b9-8816-9503b67ab9ed_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:label id="lab_dei_EntityFilerCategory_label_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityFilerCategory"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFilerCategory" xlink:to="lab_dei_EntityFilerCategory" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss_52d6c3fa-c3c8-4c61-ad31-e7c8d78c03c9_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Unrealized Loss</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Continuous Unrealized Loss Position, 12 Months or Longer, Accumulated Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_NonPeoNeoAvgTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:to="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementTable_161d5e8d-2309-4f56-bf32-37695562e1bb_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementTable" xlink:to="lab_us-gaap_StatementTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_ff15622a-8d2d-4aae-9695-66227e6e7bf3_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date:</link:label>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_CurrentFiscalYearEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CurrentFiscalYearEndDate" xlink:to="lab_dei_CurrentFiscalYearEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1_0b7fdd44-0bff-4f8f-90ce-0bd5cbffa12c_terseLabel_en-US" xlink:label="lab_us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recognized on derivatives</link:label>
    <link:label id="lab_us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1_label_en-US" xlink:label="lab_us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Unrealized Gain (Loss) on Fair Value Hedging Instruments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1" xlink:to="lab_us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoName_terseLabel_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:label id="lab_ecd_PeoName_label_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoName" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_PeoName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoName" xlink:to="lab_ecd_PeoName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear_9a5fb378-cfc1-41b4-9b30-6fa8bcc1577a_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year One, Originated, Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PassMember_88951184-d4a3-4e02-af94-ac4a659fcc99_terseLabel_en-US" xlink:label="lab_us-gaap_PassMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acceptable</link:label>
    <link:label id="lab_us-gaap_PassMember_label_en-US" xlink:label="lab_us-gaap_PassMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pass [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PassMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PassMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PassMember" xlink:to="lab_us-gaap_PassMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTable_c653f3d3-4266-45f6-b79e-563657fce1fd_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTable_label_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueByBalanceSheetGroupingTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:to="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_df39e5de-bf5a-4804-848c-8b8471364727_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesAuthorized" xlink:to="lab_us-gaap_PreferredStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossHeldInTrust_86e1e625-9d04-438b-a2fa-b74767077ecb_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossHeldInTrust" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans held for investment in consolidated trusts, at amortized cost</link:label>
    <link:label id="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossHeldInTrust_label_en-US" xlink:label="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossHeldInTrust" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, before Allowance for Credit Loss, Held In Trust</link:label>
    <link:label id="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossHeldInTrust_documentation_en-US" xlink:label="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossHeldInTrust" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, before Allowance for Credit Loss, Held In Trust</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossHeldInTrust" xlink:href="agm-20240331.xsd#agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossHeldInTrust"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossHeldInTrust" xlink:to="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossHeldInTrust" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtHedgingAdjustments_a087311a-3b8d-4ec8-a6eb-feb414397626_terseLabel_en-US" xlink:label="lab_agm_LongTermDebtHedgingAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging adjustments</link:label>
    <link:label id="lab_agm_LongTermDebtHedgingAdjustments_label_en-US" xlink:label="lab_agm_LongTermDebtHedgingAdjustments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-term Debt, Hedging Adjustments</link:label>
    <link:label id="lab_agm_LongTermDebtHedgingAdjustments_documentation_en-US" xlink:label="lab_agm_LongTermDebtHedgingAdjustments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-term Debt, Hedging Adjustments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LongTermDebtHedgingAdjustments" xlink:href="agm-20240331.xsd#agm_LongTermDebtHedgingAdjustments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LongTermDebtHedgingAdjustments" xlink:to="lab_agm_LongTermDebtHedgingAdjustments" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_ClearedDerivativesMember_b571deb9-f078-4ea9-b596-f9ca42327273_terseLabel_en-US" xlink:label="lab_agm_ClearedDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cleared derivatives</link:label>
    <link:label id="lab_agm_ClearedDerivativesMember_label_en-US" xlink:label="lab_agm_ClearedDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cleared Derivatives [Member]</link:label>
    <link:label id="lab_agm_ClearedDerivativesMember_documentation_en-US" xlink:label="lab_agm_ClearedDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cleared Derivatives</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_ClearedDerivativesMember" xlink:href="agm-20240331.xsd#agm_ClearedDerivativesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_ClearedDerivativesMember" xlink:to="lab_agm_ClearedDerivativesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesTextBlock_cab35e38-639a-4855-a7e7-4c2d8767a630_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">LOANS</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesTextBlock_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivables [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivablesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesTextBlock" xlink:to="lab_us-gaap_FinancingReceivablesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_380e867b-9a45-4d40-8a2c-ec4f82a5a037_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesOutstanding" xlink:to="lab_us-gaap_PreferredStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShortTermBorrowingsAbstract_8f9e49e3-cec4-4ea4-9801-630ae582f2d0_terseLabel_en-US" xlink:label="lab_us-gaap_ShortTermBorrowingsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due&#160;within&#160;one&#160;year:</link:label>
    <link:label id="lab_us-gaap_ShortTermBorrowingsAbstract_label_en-US" xlink:label="lab_us-gaap_ShortTermBorrowingsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Debt [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermBorrowingsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShortTermBorrowingsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortTermBorrowingsAbstract" xlink:to="lab_us-gaap_ShortTermBorrowingsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems_15231214-6be9-4af7-9c95-6e61ef509716_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Losses [Line Items]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems" xlink:to="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherIncomeMember_7801a667-1e6d-4c4e-bd6d-22515d1e9174_terseLabel_en-US" xlink:label="lab_us-gaap_OtherIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income</link:label>
    <link:label id="lab_us-gaap_OtherIncomeMember_label_en-US" xlink:label="lab_us-gaap_OtherIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Income [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherIncomeMember" xlink:to="lab_us-gaap_OtherIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesTradingMeasurementInput_b76f037e-6ac0-4c23-8da8-9b2435c6176e_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesTradingMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">USDA securities, measurement input</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesTradingMeasurementInput_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesTradingMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesTradingMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesTradingMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesTradingMeasurementInput" xlink:to="lab_us-gaap_DebtSecuritiesTradingMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss_4fde8ba0-5ca3-4233-9dab-67692f0dcc8f_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized gains/(losses) included&#160;in Other Comprehensive Income</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Gain (Loss) Included in Other Comprehensive Income (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireOtherInvestments_1e2427e0-d18c-4194-942f-14ac9429750b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireOtherInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of other investment securities</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireOtherInvestments_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireOtherInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Other Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireOtherInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PaymentsToAcquireOtherInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireOtherInvestments" xlink:to="lab_us-gaap_PaymentsToAcquireOtherInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CorporateNonSegmentMember_d2940905-cb56-445b-955f-c486de3112a4_terseLabel_en-US" xlink:label="lab_us-gaap_CorporateNonSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Corporate, non-segment</link:label>
    <link:label id="lab_us-gaap_CorporateNonSegmentMember_label_en-US" xlink:label="lab_us-gaap_CorporateNonSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Corporate, Non-Segment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CorporateNonSegmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CorporateNonSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CorporateNonSegmentMember" xlink:to="lab_us-gaap_CorporateNonSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesTradingUnrealizedGain_717db26e-3e3e-4cf4-97c7-76f7dd9eebfc_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesTradingUnrealizedGain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized Gains</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesTradingUnrealizedGain_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesTradingUnrealizedGain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, Unrealized Gain</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesTradingUnrealizedGain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesTradingUnrealizedGain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesTradingUnrealizedGain" xlink:to="lab_us-gaap_DebtSecuritiesTradingUnrealizedGain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems_6595539a-e96f-49c7-82eb-0d7d6bf64d94_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts, Notes, Loans and Financing Receivable [Line Items]</link:label>
    <link:label id="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems_label_en-US" xlink:label="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts, Notes, Loans and Financing Receivable [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccountsNotesAndLoansReceivableLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:to="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearAbstract_2365f375-73c3-4fd1-87b5-9a1c37fb3843_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year Five</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearAbstract_label_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated Four Years before Latest Fiscal Year [Abstract]</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearAbstract_documentation_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated Four Years before Latest Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearAbstract" xlink:href="agm-20240331.xsd#agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearAbstract" xlink:to="lab_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_02601c02-8235-4250-8154-27def63c6757_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:to="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleMeasurementInput_b9a49b3f-871d-454c-9aa2-9f99e7da3a67_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment securities, measurement input</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleMeasurementInput_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesAvailableForSaleMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleMeasurementInput" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_1a805c26-7ce3-48f9-abd7-5d19a03ecd31_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_703835da-4f66-4294-99d0-2477e7e0fadf_periodStartLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_4e6c1a7a-460d-4b64-8844-35e249f58135_periodEndLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue_a7749db8-89d0-49e7-94bd-38d0e77b364c_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due within one year</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Fair Value, Maturity, Allocated and Single Maturity Date, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock_d83e9814-8064-4b13-9828-46d6c530a017_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value Inputs, Assets and Liabilities, Quantitative Information</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_ccd19f9b-66a1-459c-908e-24a53bc16c44_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Stock by Class [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Stock by Class [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfStockByClassTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfStockByClassTable" xlink:to="lab_us-gaap_ScheduleOfStockByClassTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_cd2037f1-dc77-4818-8504-8034f98ee361_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income before income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable_85df6872-49fa-42cf-93fe-a485ed7be0c7_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NondesignatedMember_256cae37-5a45-40bf-b0eb-4eacfd9de0bb_verboseLabel_en-US" xlink:label="lab_us-gaap_NondesignatedMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">No hedge designation</link:label>
    <link:label id="lab_us-gaap_NondesignatedMember_label_en-US" xlink:label="lab_us-gaap_NondesignatedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Not Designated as Hedging Instrument [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NondesignatedMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NondesignatedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NondesignatedMember" xlink:to="lab_us-gaap_NondesignatedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems_734b21d2-70a5-4803-88b2-a78219a63d27_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Recorded Investment, Past Due [Line Items]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems" xlink:to="lab_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgingDesignationDomain_f02b0609-2b11-4f38-99a6-4c65d669bc3b_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingDesignationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging Designation [Domain]</link:label>
    <link:label id="lab_us-gaap_HedgingDesignationDomain_label_en-US" xlink:label="lab_us-gaap_HedgingDesignationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Designation [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingDesignationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_HedgingDesignationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgingDesignationDomain" xlink:to="lab_us-gaap_HedgingDesignationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_151d50d4-d3da-4183-b0d3-968ca3828bec_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 2</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel2Member" xlink:to="lab_us-gaap_FairValueInputsLevel2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear_3d4084d7-2739-418e-9a2d-023aa15bf6bd_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Two, Originated, Fiscal Year before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesClassifiedAbstract_2abe74d3-e696-4097-8fe6-1c508b2c8bce_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesClassifiedAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Held-to-maturity:</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesClassifiedAbstract_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesClassifiedAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Amortized Cost, before Allowance for Credit Loss [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesClassifiedAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_HeldToMaturitySecuritiesClassifiedAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesClassifiedAbstract" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesClassifiedAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireProductiveAssets_81ddc5a9-808d-485e-93c8-7efb26c3ac01_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireProductiveAssets" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of equipment and leasehold improvements</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireProductiveAssets_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireProductiveAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Productive Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireProductiveAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PaymentsToAcquireProductiveAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireProductiveAssets" xlink:to="lab_us-gaap_PaymentsToAcquireProductiveAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield_a75df3cd-8be0-4def-911a-f456796824b0_terseLabel_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after one year through five years</link:label>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield_label_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Available-for-sale Securities, Debt Maturities, Year Two Through Five, Weighted-Average Yield</link:label>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield_documentation_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Available-for-sale Securities, Debt Maturities, Year Two Through Five, Weighted-Average Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_AvailableForSaleSecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield" xlink:href="agm-20240331.xsd#agm_AvailableForSaleSecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_AvailableForSaleSecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield" xlink:to="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_b906eca7-e819-4159-804a-f6d6f58b60b1_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote</link:label>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_label_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_NamedExecutiveOfficersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:to="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_0fb39c0a-daf0-458d-bf9f-fd44253209d8_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalPeriodFocus" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentFiscalPeriodFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalPeriodFocus" xlink:to="lab_dei_DocumentFiscalPeriodFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensation_5a8ecc7c-3b48-4f9d-853d-a6bb7db1fd8b_verboseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Stock-based compensation expense</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Noncash Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensation" xlink:to="lab_us-gaap_ShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_WeightedAverageMember_e4c89f58-03ec-4985-a19d-4cb5afd39ac9_terseLabel_en-US" xlink:label="lab_srt_WeightedAverageMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average</link:label>
    <link:label id="lab_srt_WeightedAverageMember_label_en-US" xlink:label="lab_srt_WeightedAverageMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_WeightedAverageMember" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_WeightedAverageMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_WeightedAverageMember" xlink:to="lab_srt_WeightedAverageMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodFiveMember_3d576173-9a6f-4c25-9251-0bfca7da02a3_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodFiveMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Five years</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodFiveMember_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodFiveMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period Five [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodFiveMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentRedemptionPeriodFiveMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPeriodFiveMember" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPeriodFiveMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CityAreaCode_3f78d077-4a17-409d-9b5f-8f6bf385ff2a_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_CityAreaCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CityAreaCode" xlink:to="lab_dei_CityAreaCode" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain_56b0f9a9-90c6-4e76-871d-2be89b62f322_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Asset, Period Past Due [Domain]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Aging [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivablesPeriodPastDueDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:to="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductOrServiceAxis_012c7af0-265b-48bb-9248-ffa6fda3aef1_terseLabel_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:label id="lab_srt_ProductOrServiceAxis_label_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductOrServiceAxis" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_ProductOrServiceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductOrServiceAxis" xlink:to="lab_srt_ProductOrServiceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleList_765398b8-d4c0-4513-bafb-7c12bcfbb48e_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Asset, Recurring Basis, Unobservable Input Reconciliation, Asset, Gain (Loss), Statement of Other Comprehensive Income or Comprehensive Income [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleList_label_en-US" xlink:label="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Asset, Recurring Basis, Unobservable Input Reconciliation, Asset, Gain (Loss), Statement of Other Comprehensive Income or Comprehensive Income [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleList" xlink:to="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_GuaranteeAndCommitmentObligationsMember_e7904803-ffe4-4723-baf6-91bdff861b0d_terseLabel_en-US" xlink:label="lab_agm_GuaranteeAndCommitmentObligationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantee and commitment obligations:</link:label>
    <link:label id="lab_agm_GuaranteeAndCommitmentObligationsMember_label_en-US" xlink:label="lab_agm_GuaranteeAndCommitmentObligationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guarantee And Commitment Obligations [Member]</link:label>
    <link:label id="lab_agm_GuaranteeAndCommitmentObligationsMember_documentation_en-US" xlink:label="lab_agm_GuaranteeAndCommitmentObligationsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Guarantee And Commitment Obligations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_GuaranteeAndCommitmentObligationsMember" xlink:href="agm-20240331.xsd#agm_GuaranteeAndCommitmentObligationsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_GuaranteeAndCommitmentObligationsMember" xlink:to="lab_agm_GuaranteeAndCommitmentObligationsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_136a23c5-1ad8-4ff1-bc3b-581f5bf2f165_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalYearFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentFiscalYearFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalYearFocus" xlink:to="lab_dei_DocumentFiscalYearFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_TradingSecuritiesUnpaidPrincipalBalance_3dafc998-1328-49e6-9274-46f3fd5a617c_terseLabel_en-US" xlink:label="lab_agm_TradingSecuritiesUnpaidPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unpaid Principal Balance</link:label>
    <link:label id="lab_agm_TradingSecuritiesUnpaidPrincipalBalance_label_en-US" xlink:label="lab_agm_TradingSecuritiesUnpaidPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Securities Unpaid Principal Balance</link:label>
    <link:label id="lab_agm_TradingSecuritiesUnpaidPrincipalBalance_documentation_en-US" xlink:label="lab_agm_TradingSecuritiesUnpaidPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Trading Securities Unpaid Principal Balance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_TradingSecuritiesUnpaidPrincipalBalance" xlink:href="agm-20240331.xsd#agm_TradingSecuritiesUnpaidPrincipalBalance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_TradingSecuritiesUnpaidPrincipalBalance" xlink:to="lab_agm_TradingSecuritiesUnpaidPrincipalBalance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnFairValueHedgesRecognizedInEarnings_9747d6df-3f4b-46a8-8041-c292abaa94d0_totalLabel_en-US" xlink:label="lab_us-gaap_GainLossOnFairValueHedgesRecognizedInEarnings" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Gains/(losses) on fair value hedging relationships</link:label>
    <link:label id="lab_us-gaap_GainLossOnFairValueHedgesRecognizedInEarnings_label_en-US" xlink:label="lab_us-gaap_GainLossOnFairValueHedgesRecognizedInEarnings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Fair Value Hedges Recognized in Earnings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnFairValueHedgesRecognizedInEarnings" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GainLossOnFairValueHedgesRecognizedInEarnings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnFairValueHedgesRecognizedInEarnings" xlink:to="lab_us-gaap_GainLossOnFairValueHedgesRecognizedInEarnings" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LiabilitiesHeldInTrust_d2e39895-598f-4f3e-b9ab-bfab30e07262_terseLabel_en-US" xlink:label="lab_agm_LiabilitiesHeldInTrust" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt securities of consolidated trusts held by third parties</link:label>
    <link:label id="lab_agm_LiabilitiesHeldInTrust_label_en-US" xlink:label="lab_agm_LiabilitiesHeldInTrust" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities Held in Trust</link:label>
    <link:label id="lab_agm_LiabilitiesHeldInTrust_documentation_en-US" xlink:label="lab_agm_LiabilitiesHeldInTrust" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Liabilities Held in Trust</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LiabilitiesHeldInTrust" xlink:href="agm-20240331.xsd#agm_LiabilitiesHeldInTrust"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LiabilitiesHeldInTrust" xlink:to="lab_agm_LiabilitiesHeldInTrust" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_OnBalanceSheetMember_9f1c0371-a9c0-45fa-9be1-36f8ba671e17_verboseLabel_en-US" xlink:label="lab_agm_OnBalanceSheetMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">On-balance sheet</link:label>
    <link:label id="lab_agm_OnBalanceSheetMember_label_en-US" xlink:label="lab_agm_OnBalanceSheetMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">On-balance sheet [Member]</link:label>
    <link:label id="lab_agm_OnBalanceSheetMember_documentation_en-US" xlink:label="lab_agm_OnBalanceSheetMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">On-balance sheet [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_OnBalanceSheetMember" xlink:href="agm-20240331.xsd#agm_OnBalanceSheetMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_OnBalanceSheetMember" xlink:to="lab_agm_OnBalanceSheetMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReceivablesAbstract_af978feb-d0b3-40e8-8f5b-682032ecf8ce_terseLabel_en-US" xlink:label="lab_us-gaap_ReceivablesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivables [Abstract]</link:label>
    <link:label id="lab_us-gaap_ReceivablesAbstract_label_en-US" xlink:label="lab_us-gaap_ReceivablesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivables [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivablesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ReceivablesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReceivablesAbstract" xlink:to="lab_us-gaap_ReceivablesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardExrcPrice_terseLabel_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise Price</link:label>
    <link:label id="lab_ecd_AwardExrcPrice_label_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardExrcPrice" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AwardExrcPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardExrcPrice" xlink:to="lab_ecd_AwardExrcPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityAfterYearFour_8edffe66-6abd-4239-908f-8d7709fa834f_terseLabel_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityAfterYearFour_label_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, After Year Four</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityAfterYearFour_documentation_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, After Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LongTermDebtWithInterestRateResetMaturityAfterYearFour" xlink:href="agm-20240331.xsd#agm_LongTermDebtWithInterestRateResetMaturityAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LongTermDebtWithInterestRateResetMaturityAfterYearFour" xlink:to="lab_agm_LongTermDebtWithInterestRateResetMaturityAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsCommonStockCash_c174787c-2a67-4900-b185-51b33dc0cf40_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DividendsCommonStockCash" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Cash dividends, common stock</link:label>
    <link:label id="lab_us-gaap_DividendsCommonStockCash_label_en-US" xlink:label="lab_us-gaap_DividendsCommonStockCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Common Stock, Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsCommonStockCash" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DividendsCommonStockCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsCommonStockCash" xlink:to="lab_us-gaap_DividendsCommonStockCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosure_cf2f4a74-5950-45d9-b4da-e06315580c8d_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Liabilities at fair value</link:label>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LiabilitiesFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesFairValueDisclosure" xlink:to="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DerivativeWeightedAverageForwardPrice_cc923049-19d5-44ed-8e4b-9542197124bb_terseLabel_en-US" xlink:label="lab_agm_DerivativeWeightedAverageForwardPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted- Average Forward Price (in dollars per share)</link:label>
    <link:label id="lab_agm_DerivativeWeightedAverageForwardPrice_label_en-US" xlink:label="lab_agm_DerivativeWeightedAverageForwardPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Weighted-Average Forward Price</link:label>
    <link:label id="lab_agm_DerivativeWeightedAverageForwardPrice_documentation_en-US" xlink:label="lab_agm_DerivativeWeightedAverageForwardPrice" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative, Weighted-Average Forward Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DerivativeWeightedAverageForwardPrice" xlink:href="agm-20240331.xsd#agm_DerivativeWeightedAverageForwardPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DerivativeWeightedAverageForwardPrice" xlink:to="lab_agm_DerivativeWeightedAverageForwardPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesAbstract_122035fc-323a-4497-9723-161697bba5e4_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">(Liability)</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeLiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilitiesAbstract" xlink:to="lab_us-gaap_DerivativeLiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProfitLoss_2a8eeebf-d095-48d8-b350-c6047cbf5195_terseLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_label_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProfitLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProfitLoss" xlink:to="lab_us-gaap_ProfitLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityUnrealizedLossPositionMoreThan12MonthsNumberOfPositions_b636832b-8c99-43da-9e9b-04e3b72b70aa_terseLabel_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityUnrealizedLossPositionMoreThan12MonthsNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt securities, held-to-maturity, unrealized loss position for more than 12 months, Number of securities in loss position</link:label>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityUnrealizedLossPositionMoreThan12MonthsNumberOfPositions_label_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityUnrealizedLossPositionMoreThan12MonthsNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-maturity, Unrealized Loss Position More Than 12 Months, Number of Positions</link:label>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityUnrealizedLossPositionMoreThan12MonthsNumberOfPositions_documentation_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityUnrealizedLossPositionMoreThan12MonthsNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-maturity, Unrealized Loss Position More Than 12 Months, Number of Positions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DebtSecuritiesHeldToMaturityUnrealizedLossPositionMoreThan12MonthsNumberOfPositions" xlink:href="agm-20240331.xsd#agm_DebtSecuritiesHeldToMaturityUnrealizedLossPositionMoreThan12MonthsNumberOfPositions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DebtSecuritiesHeldToMaturityUnrealizedLossPositionMoreThan12MonthsNumberOfPositions" xlink:to="lab_agm_DebtSecuritiesHeldToMaturityUnrealizedLossPositionMoreThan12MonthsNumberOfPositions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsNumberOfPositions_9ccbd6b7-f528-40b4-a4fa-9688b53c6a2a_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized loss position for less than 12 months, Number of securities in loss position</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsNumberOfPositions_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Continuous Unrealized Loss Position, Less than 12 Months, Number of Positions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsNumberOfPositions" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsNumberOfPositions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsNumberOfPositions" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsNumberOfPositions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments_20c0669f-9dc2-4c48-b3ec-f57d94074bae_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net amortization of deferred gains, premiums, and discounts on loans, investments, Farmer Mac Guaranteed Securities, and USDA Securities</link:label>
    <link:label id="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments_label_en-US" xlink:label="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accretion (Amortization) of Discounts and Premiums, Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:to="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_b36f9d1c-09bc-416a-9e63-7edc41915b13_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Liabilities and Equity</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_PeerGroupTotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:to="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearFour_43f69fd3-8e60-436f-b9c8-299fa31e82ec_terseLabel_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearFour_label_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, Year Four</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearFour_documentation_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LongTermDebtWithInterestRateResetMaturityYearFour" xlink:href="agm-20240331.xsd#agm_LongTermDebtWithInterestRateResetMaturityYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LongTermDebtWithInterestRateResetMaturityYearFour" xlink:to="lab_agm_LongTermDebtWithInterestRateResetMaturityYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_InterestRateSwapReceiveFixedNonCallableMember_1e18e3ab-33f3-4ea8-8ec6-07d9b8b80dca_terseLabel_en-US" xlink:label="lab_agm_InterestRateSwapReceiveFixedNonCallableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receive fixed non-callable</link:label>
    <link:label id="lab_agm_InterestRateSwapReceiveFixedNonCallableMember_label_en-US" xlink:label="lab_agm_InterestRateSwapReceiveFixedNonCallableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swap, Receive Fixed Non-Callable [Member]</link:label>
    <link:label id="lab_agm_InterestRateSwapReceiveFixedNonCallableMember_documentation_en-US" xlink:label="lab_agm_InterestRateSwapReceiveFixedNonCallableMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Rate Swap, Receive Fixed Non-Callable [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_InterestRateSwapReceiveFixedNonCallableMember" xlink:href="agm-20240331.xsd#agm_InterestRateSwapReceiveFixedNonCallableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_InterestRateSwapReceiveFixedNonCallableMember" xlink:to="lab_agm_InterestRateSwapReceiveFixedNonCallableMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTable_7d315a01-9020-49a4-be89-5f61ee5493ba_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-term Debt Instruments [Table]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTable_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTable" xlink:to="lab_us-gaap_DebtInstrumentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote</link:label>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_label_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_EquityValuationAssumptionDifferenceFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:to="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CollateralPledgedMember_7ca2afcb-d200-455a-885d-e82ce9cc5d4d_terseLabel_en-US" xlink:label="lab_us-gaap_CollateralPledgedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral Pledged</link:label>
    <link:label id="lab_us-gaap_CollateralPledgedMember_label_en-US" xlink:label="lab_us-gaap_CollateralPledgedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateral Pledged [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CollateralPledgedMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CollateralPledgedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CollateralPledgedMember" xlink:to="lab_us-gaap_CollateralPledgedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_ce66fa15-6785-46e4-9826-a08cfa3814d1_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income, diluted EPS</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrDuration_terseLabel_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arrangement Duration</link:label>
    <link:label id="lab_ecd_TrdArrDuration_label_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Duration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrDuration" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_TrdArrDuration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrDuration" xlink:to="lab_ecd_TrdArrDuration" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_SegmentCoreEarningsBeforeIncomeTaxes_5940a006-2bda-4fdc-911e-1167b868304e_totalLabel_en-US" xlink:label="lab_agm_SegmentCoreEarningsBeforeIncomeTaxes" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Core earnings before income taxes</link:label>
    <link:label id="lab_agm_SegmentCoreEarningsBeforeIncomeTaxes_label_en-US" xlink:label="lab_agm_SegmentCoreEarningsBeforeIncomeTaxes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Core Earnings Before Income Taxes</link:label>
    <link:label id="lab_agm_SegmentCoreEarningsBeforeIncomeTaxes_documentation_en-US" xlink:label="lab_agm_SegmentCoreEarningsBeforeIncomeTaxes" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Segment core earnings before income taxes adjusted for reconciling items for segment reporting</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_SegmentCoreEarningsBeforeIncomeTaxes" xlink:href="agm-20240331.xsd#agm_SegmentCoreEarningsBeforeIncomeTaxes"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_SegmentCoreEarningsBeforeIncomeTaxes" xlink:to="lab_agm_SegmentCoreEarningsBeforeIncomeTaxes" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_1898548d-a655-46ea-a587-ae298fc619c8_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AwardTmgMnpiCnsdrdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:to="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_b7b13f13-90e1-4063-960b-edb5cbb0d87b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_OtherComprehensiveIncomeLossHeldToMaturitySecuritiesBeforeTax_f57f1125-16df-449d-a095-3e662b349c00_terseLabel_en-US" xlink:label="lab_agm_OtherComprehensiveIncomeLossHeldToMaturitySecuritiesBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net changes in held-to-maturity securities</link:label>
    <link:label id="lab_agm_OtherComprehensiveIncomeLossHeldToMaturitySecuritiesBeforeTax_label_en-US" xlink:label="lab_agm_OtherComprehensiveIncomeLossHeldToMaturitySecuritiesBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Held-To-Maturity Securities, Before Tax</link:label>
    <link:label id="lab_agm_OtherComprehensiveIncomeLossHeldToMaturitySecuritiesBeforeTax_documentation_en-US" xlink:label="lab_agm_OtherComprehensiveIncomeLossHeldToMaturitySecuritiesBeforeTax" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Held-To-Maturity Securities, Before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_OtherComprehensiveIncomeLossHeldToMaturitySecuritiesBeforeTax" xlink:href="agm-20240331.xsd#agm_OtherComprehensiveIncomeLossHeldToMaturitySecuritiesBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_OtherComprehensiveIncomeLossHeldToMaturitySecuritiesBeforeTax" xlink:to="lab_agm_OtherComprehensiveIncomeLossHeldToMaturitySecuritiesBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonClassCMember_0f20111d-62d0-4278-b12c-10078298548e_terseLabel_en-US" xlink:label="lab_us-gaap_CommonClassCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class C non-voting common stock</link:label>
    <link:label id="lab_us-gaap_CommonClassCMember_label_en-US" xlink:label="lab_us-gaap_CommonClassCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Class C [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassCMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonClassCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonClassCMember" xlink:to="lab_us-gaap_CommonClassCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear10_d7939aa1-5431-4e65-8e9d-4a3f116f8c8c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear10" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after ten years</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear10_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear10" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Amortized Cost Excluding Accrued Interest, after Allowance for Credit Loss, Maturity, Allocated and Single Maturity Date, after Year 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear10" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear10"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear10" xlink:to="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear10" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1_36961e5f-b2da-429d-a840-333af9233228_terseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining authorized amount for repurchase</link:label>
    <link:label id="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1_label_en-US" xlink:label="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchase Program, Remaining Authorized Repurchase Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:to="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrTerminationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Termination Date</link:label>
    <link:label id="lab_ecd_TrdArrTerminationDate_label_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Termination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrTerminationDate" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_TrdArrTerminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrTerminationDate" xlink:to="lab_ecd_TrdArrTerminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable_8bd0274b-2b07-41b0-a97a-5756b08b1772_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Financing Receivables Past Due [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfFinancingReceivablesPastDueTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:to="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateLoanMember_2cc5ccfb-50d7-4cad-9cdd-c06f63a7ff69_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateLoanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Loan</link:label>
    <link:label id="lab_us-gaap_RealEstateLoanMember_label_en-US" xlink:label="lab_us-gaap_RealEstateLoanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Loan [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateLoanMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RealEstateLoanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateLoanMember" xlink:to="lab_us-gaap_RealEstateLoanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis_3a7680bd-4985-49cf-ba07-fd66ba2a3dc3_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Asset, Period Past Due [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Aging [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivablesPeriodPastDueAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:to="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_2a4c4b6f-1362-4346-879b-d38caecd2308_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized Gains</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accumulated Gross Unrealized Gain, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:to="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShorttermDebtMaximumMonthendOutstandingAmount_f3e7890f-c636-4153-bafc-f288d6e96b9d_terseLabel_en-US" xlink:label="lab_us-gaap_ShorttermDebtMaximumMonthendOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum amount of discount notes outstanding at any month end</link:label>
    <link:label id="lab_us-gaap_ShorttermDebtMaximumMonthendOutstandingAmount_label_en-US" xlink:label="lab_us-gaap_ShorttermDebtMaximumMonthendOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Debt, Maximum Month-end Outstanding Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShorttermDebtMaximumMonthendOutstandingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShorttermDebtMaximumMonthendOutstandingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShorttermDebtMaximumMonthendOutstandingAmount" xlink:to="lab_us-gaap_ShorttermDebtMaximumMonthendOutstandingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_eb71017c-a3bb-404c-994b-d66c2fb35ddc_negatedTerseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Current period charge-offs</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_b7071c28-4ba7-4e12-b966-5b9342a1c0a2_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current period charge-offs</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_label_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated Four Years Before Latest Fiscal Year, Excluding Accrued Interest, Allowance for Credit Loss, Write-Off</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff_documentation_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated Four Years Before Latest Fiscal Year, Excluding Accrued Interest, Allowance for Credit Loss, Write-Off</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:href="agm-20240331.xsd#agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:to="lab_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAbstract_945805d5-a56c-43b1-9d28-74891d530e93_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized&#160;loss&#160;position for more&#160;than&#160;12&#160;months</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAbstract_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Unrealized Loss Position, Accumulated Loss [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_d46b29e9-02b7-42f1-8357-dae58c7e9752_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustments to reconcile net income to net cash provided by operating activities:</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustments to Reconcile Net Income (Loss) to Cash Provided by (Used in) Operating Activities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_b0eb7043-072f-473f-a08c-4652dc5769c8_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MeasurementInputTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputTypeAxis" xlink:to="lab_us-gaap_MeasurementInputTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityReminderOfTheFiscalYear_37793c8e-215e-46c0-9aec-c7a369c440f5_terseLabel_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityReminderOfTheFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityReminderOfTheFiscalYear_label_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityReminderOfTheFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, Reminder Of The Fiscal Year</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityReminderOfTheFiscalYear_documentation_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityReminderOfTheFiscalYear" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, Reminder Of The Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LongTermDebtWithInterestRateResetMaturityReminderOfTheFiscalYear" xlink:href="agm-20240331.xsd#agm_LongTermDebtWithInterestRateResetMaturityReminderOfTheFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LongTermDebtWithInterestRateResetMaturityReminderOfTheFiscalYear" xlink:to="lab_agm_LongTermDebtWithInterestRateResetMaturityReminderOfTheFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestRateCashFlowHedgeGainLossToBeReclassifiedDuringNext12MonthsNet_26c9ba75-05f1-4851-9911-6db92d1219f4_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateCashFlowHedgeGainLossToBeReclassifiedDuringNext12MonthsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain expected to be reclassified from AOCI to earnings over next 12 months</link:label>
    <link:label id="lab_us-gaap_InterestRateCashFlowHedgeGainLossToBeReclassifiedDuringNext12MonthsNet_label_en-US" xlink:label="lab_us-gaap_InterestRateCashFlowHedgeGainLossToBeReclassifiedDuringNext12MonthsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Cash Flow Hedge Gain (Loss) to be Reclassified During Next 12 Months, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestRateCashFlowHedgeGainLossToBeReclassifiedDuringNext12MonthsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestRateCashFlowHedgeGainLossToBeReclassifiedDuringNext12MonthsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestRateCashFlowHedgeGainLossToBeReclassifiedDuringNext12MonthsNet" xlink:to="lab_us-gaap_InterestRateCashFlowHedgeGainLossToBeReclassifiedDuringNext12MonthsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLineItems_61607c95-0a06-46ee-af34-60f0ecea7b7b_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativeLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLineItems" xlink:to="lab_us-gaap_DerivativeLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationFromAociCurrentPeriodTax_1b114fea-cceb-4e50-b71b-8bb7a82551bb_negatedLabel_en-US" xlink:label="lab_us-gaap_ReclassificationFromAociCurrentPeriodTax" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Less reclassification adjustments, Provision (Benefit)</link:label>
    <link:label id="lab_us-gaap_ReclassificationFromAociCurrentPeriodTax_label_en-US" xlink:label="lab_us-gaap_ReclassificationFromAociCurrentPeriodTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification from AOCI, Current Period, Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationFromAociCurrentPeriodTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ReclassificationFromAociCurrentPeriodTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReclassificationFromAociCurrentPeriodTax" xlink:to="lab_us-gaap_ReclassificationFromAociCurrentPeriodTax" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgDiscLineItems_label_en-US" xlink:label="lab_ecd_AwardTmgDiscLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Disclosures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgDiscLineItems" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AwardTmgDiscLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgDiscLineItems" xlink:to="lab_ecd_AwardTmgDiscLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAccruedInterestBeforeAllowanceForCreditLoss_611723a1-ba9a-4c68-aedb-80be30048924_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Held-to-maturity, accrued interest excluded</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAccruedInterestBeforeAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Accrued Interest, before Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesHeldToMaturityAccruedInterestBeforeAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesHeldToMaturityAccruedInterestBeforeAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesHeldToMaturityAccruedInterestBeforeAllowanceForCreditLoss" xlink:to="lab_us-gaap_DebtSecuritiesHeldToMaturityAccruedInterestBeforeAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableRevolvingAbstract_345b6c75-9a67-43ba-b3b7-1b176028a59d_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivableRevolvingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revolving Loans - Amortized Cost Basis</link:label>
    <link:label id="lab_agm_FinancingReceivableRevolvingAbstract_label_en-US" xlink:label="lab_agm_FinancingReceivableRevolvingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Revolving [Abstract]</link:label>
    <link:label id="lab_agm_FinancingReceivableRevolvingAbstract_documentation_en-US" xlink:label="lab_agm_FinancingReceivableRevolvingAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Revolving</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableRevolvingAbstract" xlink:href="agm-20240331.xsd#agm_FinancingReceivableRevolvingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivableRevolvingAbstract" xlink:to="lab_agm_FinancingReceivableRevolvingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable_cc762568-332d-497c-a909-f8e99ba1b666_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Accounts, Notes, Loans and Financing Receivable [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accounts, Notes, Loans and Financing Receivable [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:to="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputConstantPrepaymentRateMember_e63cb413-c4f1-40ef-a462-cf3e9d0e394c_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputConstantPrepaymentRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CPR</link:label>
    <link:label id="lab_us-gaap_MeasurementInputConstantPrepaymentRateMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputConstantPrepaymentRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Constant Prepayment Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputConstantPrepaymentRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MeasurementInputConstantPrepaymentRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputConstantPrepaymentRateMember" xlink:to="lab_us-gaap_MeasurementInputConstantPrepaymentRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShorttermDebtAverageOutstandingAmount_32df0416-83e4-4485-94ae-dd5a11f39f4b_terseLabel_en-US" xlink:label="lab_us-gaap_ShorttermDebtAverageOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Average Outstanding, Amount</link:label>
    <link:label id="lab_us-gaap_ShorttermDebtAverageOutstandingAmount_label_en-US" xlink:label="lab_us-gaap_ShorttermDebtAverageOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Debt, Average Outstanding Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShorttermDebtAverageOutstandingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShorttermDebtAverageOutstandingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShorttermDebtAverageOutstandingAmount" xlink:to="lab_us-gaap_ShorttermDebtAverageOutstandingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeCollateralObligationToReturnCash_674934cd-25a8-4b31-941f-4d088cf25d8d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Cash collateral</link:label>
    <link:label id="lab_us-gaap_DerivativeCollateralObligationToReturnCash_label_en-US" xlink:label="lab_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, Collateral, Obligation to Return Cash Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeCollateralObligationToReturnCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:to="lab_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_8681f096-86d5-415f-a8dd-006193b02dbc_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid in Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AdditionalPaidInCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapital" xlink:to="lab_us-gaap_AdditionalPaidInCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityUnrealizedLossPositionNumberOfPositions_1479f72f-8c34-4419-a7f5-e64d1f858807_terseLabel_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityUnrealizedLossPositionNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Held-to-maturity, securities in unrealized loss positions</link:label>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityUnrealizedLossPositionNumberOfPositions_label_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityUnrealizedLossPositionNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-maturity, Unrealized Loss Position, Number of Positions</link:label>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityUnrealizedLossPositionNumberOfPositions_documentation_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityUnrealizedLossPositionNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-maturity, Unrealized Loss Position, Number of Positions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DebtSecuritiesHeldToMaturityUnrealizedLossPositionNumberOfPositions" xlink:href="agm-20240331.xsd#agm_DebtSecuritiesHeldToMaturityUnrealizedLossPositionNumberOfPositions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DebtSecuritiesHeldToMaturityUnrealizedLossPositionNumberOfPositions" xlink:to="lab_agm_DebtSecuritiesHeldToMaturityUnrealizedLossPositionNumberOfPositions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_86c2fca3-95d4-4d46-8e1b-406e0c7b1bcc_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after five years through ten years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, after Year 5 Through 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansReceivableFairValueDisclosure_645f6c48-e79b-4596-bbf6-f8646247dc43_terseLabel_en-US" xlink:label="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans</link:label>
    <link:label id="lab_us-gaap_LoansReceivableFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Receivable, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansReceivableFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LoansReceivableFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansReceivableFairValueDisclosure" xlink:to="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_GuaranteeAsset_06edf5c7-9571-4a78-91ee-25f170e79a9f_terseLabel_en-US" xlink:label="lab_agm_GuaranteeAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantee Asset</link:label>
    <link:label id="lab_agm_GuaranteeAsset_label_en-US" xlink:label="lab_agm_GuaranteeAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guarantee Asset</link:label>
    <link:label id="lab_agm_GuaranteeAsset_documentation_en-US" xlink:label="lab_agm_GuaranteeAsset" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Guarantee Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_GuaranteeAsset" xlink:href="agm-20240331.xsd#agm_GuaranteeAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_GuaranteeAsset" xlink:to="lab_agm_GuaranteeAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss_bce09b64-39d4-4111-8c9a-b5c9a4857675_verboseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Loans held for investment, at amortized cost</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss_f65f1ea3-ec5c-43e0-bc30-b1bd90c5ca55_netLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Loans held for investment in consolidated trusts, at amortized cost</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss_bc5cbf49-434c-4c50-9e10-c9abbdb58b59_totalLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss_3a063fd7-42b3-42e9-88c3-5a4b4a9c6f7b_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Loans</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, before Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DebtSecuritiesAvailableForSaleMember_f6fdd6fd-8c3b-4eaf-a84f-ad1680b92775_terseLabel_en-US" xlink:label="lab_agm_DebtSecuritiesAvailableForSaleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Available-for-Sale Securities</link:label>
    <link:label id="lab_agm_DebtSecuritiesAvailableForSaleMember_label_en-US" xlink:label="lab_agm_DebtSecuritiesAvailableForSaleMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-For-Sale [Member]</link:label>
    <link:label id="lab_agm_DebtSecuritiesAvailableForSaleMember_documentation_en-US" xlink:label="lab_agm_DebtSecuritiesAvailableForSaleMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-For-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DebtSecuritiesAvailableForSaleMember" xlink:href="agm-20240331.xsd#agm_DebtSecuritiesAvailableForSaleMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DebtSecuritiesAvailableForSaleMember" xlink:to="lab_agm_DebtSecuritiesAvailableForSaleMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtMaturityAfterYearFour_db18b9b7-184e-464c-a220-6bac07133367_terseLabel_en-US" xlink:label="lab_agm_LongTermDebtMaturityAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_agm_LongTermDebtMaturityAfterYearFour_label_en-US" xlink:label="lab_agm_LongTermDebtMaturityAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, after Year Four</link:label>
    <link:label id="lab_agm_LongTermDebtMaturityAfterYearFour_documentation_en-US" xlink:label="lab_agm_LongTermDebtMaturityAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, after Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LongTermDebtMaturityAfterYearFour" xlink:href="agm-20240331.xsd#agm_LongTermDebtMaturityAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LongTermDebtMaturityAfterYearFour" xlink:to="lab_agm_LongTermDebtMaturityAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain_64b3b4ad-0b3d-4b6c-9edd-667fc36e8fac_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentRedemptionPeriodDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingArrLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingArrLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Arrangements [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingArrLineItems" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_InsiderTradingArrLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingArrLineItems" xlink:to="lab_ecd_InsiderTradingArrLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward_bd962119-c801-4555-91a7-00c511334bc9_terseLabel_en-US" xlink:label="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent, Net of Tax [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward_label_en-US" xlink:label="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent, Net of Tax [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AOCIAttributableToParentNetOfTaxRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:to="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughFive_a2644991-1b67-4b16-b0e4-561b95240672_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after one year through five years</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughFive_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Amortized Cost Excluding Accrued Interest, after Allowance for Credit Loss, Maturity, Allocated and Single Maturity Date, after Year One through Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughFive" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughFive" xlink:to="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughFive" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield_f1501dc4-913b-48cd-82c4-f866fbdf730c_verboseLabel_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Held-to-maturity investment securities weighted average yield</link:label>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield_265a43b7-f781-4942-9bc7-a2c130c91673_terseLabel_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total, Weighted- Average Yield</link:label>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield_label_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Held-To-Maturity Securities, Debt Maturities, Weighted-Average Yield</link:label>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield_documentation_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Held-To-Maturity Securities, Debt Maturities, Weighted-Average Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield" xlink:href="agm-20240331.xsd#agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield" xlink:to="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_8bdea8ea-911e-4a01-b11d-c2ba206dce37_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_terseLabel_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement</link:label>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_label_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_MtrlTermsOfTrdArrTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:to="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Method</link:label>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AwardTmgMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMethodTextBlock" xlink:to="lab_ecd_AwardTmgMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_459d0360-a72e-49ac-8064-2ec08736935c_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInOtherOperatingAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation, Amount</link:label>
    <link:label id="lab_ecd_AdjToCompAmt_label_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AdjToCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAmt" xlink:to="lab_ecd_AdjToCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_CompActuallyPaidVsNetIncomeTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote</link:label>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_label_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_PeerGroupIssuersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:to="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfLongTermDebt_d937527e-9630-43bc-bad7-a4875aef375b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payments to redeem medium-term notes</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfLongTermDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RepaymentsOfLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfLongTermDebt" xlink:to="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_4bc384c6-752c-4851-9190-08822701f3eb_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityCentralIndexKey"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCentralIndexKey" xlink:to="lab_dei_EntityCentralIndexKey" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts_30d5d7d1-9b2c-41f9-b714-c4143349f35a_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of debt premiums, discounts, and issuance costs</link:label>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts_label_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Debt Issuance Costs and Discounts</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AmortizationOfFinancingCostsAndDiscounts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:to="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract_c975646c-f668-4e95-b6c7-4a7faf4a223d_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities:</link:label>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Fair Value Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LiabilitiesFairValueDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:to="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1_1f2a5e55-121b-43fa-985b-90748c717b03_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Realized and unrealized losses included in Income</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Gain (Loss) Included in Earnings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMember_ef3f6f22-a47a-4d69-a475-2d74cc9888a2_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notes Payable</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMember_f0caf9b6-b113-4399-9798-f673f9c2e9b6_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Current portion of medium-term notes</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMember_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongTermDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMember" xlink:to="lab_us-gaap_LongTermDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_NonRule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:to="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearAbstract_e7b7c61b-bad9-4713-a056-1c2f7a24cc17_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearAbstract_label_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated Five or More Years before Latest Fiscal Year [Abstract]</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearAbstract_documentation_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated Five or More Years before Latest Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearAbstract" xlink:href="agm-20240331.xsd#agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearAbstract" xlink:to="lab_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DerivativeNetHedgeIneffectivenessGainLossComponentRecognizedOnHedgedItem_9ba8ac20-769b-480e-a89f-e86801006f31_negatedTerseLabel_en-US" xlink:label="lab_agm_DerivativeNetHedgeIneffectivenessGainLossComponentRecognizedOnHedgedItem" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Recognized on hedged items</link:label>
    <link:label id="lab_agm_DerivativeNetHedgeIneffectivenessGainLossComponentRecognizedOnHedgedItem_label_en-US" xlink:label="lab_agm_DerivativeNetHedgeIneffectivenessGainLossComponentRecognizedOnHedgedItem" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Net Hedge Ineffectiveness Gain Loss Component Recognized On Hedged Item</link:label>
    <link:label id="lab_agm_DerivativeNetHedgeIneffectivenessGainLossComponentRecognizedOnHedgedItem_documentation_en-US" xlink:label="lab_agm_DerivativeNetHedgeIneffectivenessGainLossComponentRecognizedOnHedgedItem" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Net Hedge Ineffectiveness Gain Loss Component Recognized On Hedged Item</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DerivativeNetHedgeIneffectivenessGainLossComponentRecognizedOnHedgedItem" xlink:href="agm-20240331.xsd#agm_DerivativeNetHedgeIneffectivenessGainLossComponentRecognizedOnHedgedItem"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DerivativeNetHedgeIneffectivenessGainLossComponentRecognizedOnHedgedItem" xlink:to="lab_agm_DerivativeNetHedgeIneffectivenessGainLossComponentRecognizedOnHedgedItem" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromCollectionOfLoansHeldForSale_3d87a91d-a30b-4860-9884-236a5c84a094_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromCollectionOfLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from repayment of loans purchased as held for sale</link:label>
    <link:label id="lab_us-gaap_ProceedsFromCollectionOfLoansHeldForSale_label_en-US" xlink:label="lab_us-gaap_ProceedsFromCollectionOfLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Collection, Loan, Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromCollectionOfLoansHeldForSale" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromCollectionOfLoansHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromCollectionOfLoansHeldForSale" xlink:to="lab_us-gaap_ProceedsFromCollectionOfLoansHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsPreferredStockCash_c12f66c2-d80c-4748-abef-c48f92844177_negatedLabel_en-US" xlink:label="lab_us-gaap_DividendsPreferredStockCash" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Cash dividends, preferred stock</link:label>
    <link:label id="lab_us-gaap_DividendsPreferredStockCash_label_en-US" xlink:label="lab_us-gaap_DividendsPreferredStockCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Preferred Stock, Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsPreferredStockCash" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DividendsPreferredStockCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsPreferredStockCash" xlink:to="lab_us-gaap_DividendsPreferredStockCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedGainLossCashFlowHedgeIncludingNoncontrollingInterestMember_6a99c281-90f6-43ba-b216-750d85bb1504_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedGainLossCashFlowHedgeIncludingNoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash Flow Hedges</link:label>
    <link:label id="lab_us-gaap_AccumulatedGainLossCashFlowHedgeIncludingNoncontrollingInterestMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedGainLossCashFlowHedgeIncludingNoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Gain (Loss), Cash Flow Hedge, Including Noncontrolling Interest [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedGainLossCashFlowHedgeIncludingNoncontrollingInterestMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccumulatedGainLossCashFlowHedgeIncludingNoncontrollingInterestMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedGainLossCashFlowHedgeIncludingNoncontrollingInterestMember" xlink:to="lab_us-gaap_AccumulatedGainLossCashFlowHedgeIncludingNoncontrollingInterestMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndName_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_TrdArrIndName_label_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndName" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_TrdArrIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndName" xlink:to="lab_ecd_TrdArrIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_980ccf94-81ca-47ad-bfe3-dabb57333dec_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of Class C Common Stock</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_0cfb3c0b-d5cf-4979-91f0-bb35b1a54eb9_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AmendmentFlag_a740e176-087a-4575-becb-a3071bea8dd4_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:label id="lab_dei_AmendmentFlag_label_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_AmendmentFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AmendmentFlag" xlink:to="lab_dei_AmendmentFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_GuaranteeAssetMeasurementInput_baa716f2-f8da-4a46-8c79-e7f0838c8b6f_terseLabel_en-US" xlink:label="lab_agm_GuaranteeAssetMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantee asset, measurement input</link:label>
    <link:label id="lab_agm_GuaranteeAssetMeasurementInput_label_en-US" xlink:label="lab_agm_GuaranteeAssetMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guarantee Asset, Measurement Input</link:label>
    <link:label id="lab_agm_GuaranteeAssetMeasurementInput_documentation_en-US" xlink:label="lab_agm_GuaranteeAssetMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Guarantee Asset, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_GuaranteeAssetMeasurementInput" xlink:href="agm-20240331.xsd#agm_GuaranteeAssetMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_GuaranteeAssetMeasurementInput" xlink:to="lab_agm_GuaranteeAssetMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtNetOfHedgingAdjustments_1f0c5133-1170-4805-99c2-ddbe18a851b0_terseLabel_en-US" xlink:label="lab_agm_LongTermDebtNetOfHedgingAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notes payable</link:label>
    <link:label id="lab_agm_LongTermDebtNetOfHedgingAdjustments_2445671c-1505-4fba-8a53-bc223ceb6b74_totalLabel_en-US" xlink:label="lab_agm_LongTermDebtNetOfHedgingAdjustments" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_agm_LongTermDebtNetOfHedgingAdjustments_label_en-US" xlink:label="lab_agm_LongTermDebtNetOfHedgingAdjustments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-term Debt, Net of Hedging Adjustments</link:label>
    <link:label id="lab_agm_LongTermDebtNetOfHedgingAdjustments_documentation_en-US" xlink:label="lab_agm_LongTermDebtNetOfHedgingAdjustments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-term Debt, Net of Hedging Adjustments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LongTermDebtNetOfHedgingAdjustments" xlink:href="agm-20240331.xsd#agm_LongTermDebtNetOfHedgingAdjustments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LongTermDebtNetOfHedgingAdjustments" xlink:to="lab_agm_LongTermDebtNetOfHedgingAdjustments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset_3dd0316b-121e-49d6-8bc6-7e0ca51a418b_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Netting adjustments</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset_26f23a58-a06a-4982-aa51-4dff89f9c43a_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Amounts offset in the Consolidated Balance Sheet</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, Asset Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeLiabilityFairValueGrossAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:to="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueHedgingMember_9a617f38-3b7a-403d-b93f-dd8cf1d60ee5_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueHedgingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value hedges:</link:label>
    <link:label id="lab_us-gaap_FairValueHedgingMember_label_en-US" xlink:label="lab_us-gaap_FairValueHedgingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hedging [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueHedgingMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueHedgingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueHedgingMember" xlink:to="lab_us-gaap_FairValueHedgingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesTable_a04b0e06-2a9c-469c-8401-63ce9a76763c_terseLabel_en-US" xlink:label="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-sale and Trading Securities [Table]</link:label>
    <link:label id="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesTable_label_en-US" xlink:label="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-sale and Trading Securities [Table]</link:label>
    <link:label id="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesTable_documentation_en-US" xlink:label="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-sale and Trading Securities [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesTable" xlink:href="agm-20240331.xsd#agm_ScheduleOfAvailableForSaleAndTradingSecuritiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesTable" xlink:to="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestIncomeExpenseNet_8b675a60-db47-441e-963e-eb2e687536bc_totalLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net interest income</link:label>
    <link:label id="lab_us-gaap_InterestIncomeExpenseNet_7b53c3e8-0f4e-4bc5-9347-7763252af7be_terseLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net interest income</link:label>
    <link:label id="lab_us-gaap_InterestIncomeExpenseNet_label_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income (Expense), Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeExpenseNet" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InterestIncomeExpenseNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestIncomeExpenseNet" xlink:to="lab_us-gaap_InterestIncomeExpenseNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_ed9e9a96-d92a-495a-a5ae-2f213d2cc651_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets:</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsFairValueDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosureAbstract" xlink:to="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodFourMember_29146d88-ed14-4179-a709-8b06c9b799ce_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodFourMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Four years</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodFourMember_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodFourMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period Four [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodFourMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentRedemptionPeriodFourMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPeriodFourMember" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPeriodFourMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_5bf94b2b-5aaa-4528-8be0-311b6328c8b3_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due within one year</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtNoncurrent_fd8e9a2e-8ae2-4297-999a-da65ecd831da_totalLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtNoncurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total due after one year</link:label>
    <link:label id="lab_us-gaap_LongTermDebtNoncurrent_label_en-US" xlink:label="lab_us-gaap_LongTermDebtNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Excluding Current Maturities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongTermDebtNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtNoncurrent" xlink:to="lab_us-gaap_LongTermDebtNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_AgricultureFinanceCorporateAgFinanceSegmentMember_c55cb162-8c41-41dd-a7a5-887c65460a3c_terseLabel_en-US" xlink:label="lab_agm_AgricultureFinanceCorporateAgFinanceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Corporate AgFinance</link:label>
    <link:label id="lab_agm_AgricultureFinanceCorporateAgFinanceSegmentMember_label_en-US" xlink:label="lab_agm_AgricultureFinanceCorporateAgFinanceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Agriculture Finance, Corporate AgFinance Segment [Member]</link:label>
    <link:label id="lab_agm_AgricultureFinanceCorporateAgFinanceSegmentMember_documentation_en-US" xlink:label="lab_agm_AgricultureFinanceCorporateAgFinanceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Agriculture Finance, Corporate AgFinance Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_AgricultureFinanceCorporateAgFinanceSegmentMember" xlink:href="agm-20240331.xsd#agm_AgricultureFinanceCorporateAgFinanceSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_AgricultureFinanceCorporateAgFinanceSegmentMember" xlink:to="lab_agm_AgricultureFinanceCorporateAgFinanceSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_b3642be2-52a4-4626-866e-9ed1bf15f89d_totalLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Weighted-Average Shares, diluted EPS (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:to="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetsAbstract_677ae7c5-739d-4bac-b432-532fddd595cb_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetsAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeAssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetsAbstract" xlink:to="lab_us-gaap_DerivativeAssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermStandbyPurchaseCommitmentsMember_03c6abcd-ba36-40a5-993c-e3baf2e84478_terseLabel_en-US" xlink:label="lab_agm_LongTermStandbyPurchaseCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Standby Purchase Commitments</link:label>
    <link:label id="lab_agm_LongTermStandbyPurchaseCommitmentsMember_cc509ce5-fab1-4b39-813d-1e80c4b40fca_verboseLabel_en-US" xlink:label="lab_agm_LongTermStandbyPurchaseCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Rural Infrastructure Finance</link:label>
    <link:label id="lab_agm_LongTermStandbyPurchaseCommitmentsMember_label_en-US" xlink:label="lab_agm_LongTermStandbyPurchaseCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Standby Purchase Commitments [Member]</link:label>
    <link:label id="lab_agm_LongTermStandbyPurchaseCommitmentsMember_documentation_en-US" xlink:label="lab_agm_LongTermStandbyPurchaseCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Standby Purchase Commitments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LongTermStandbyPurchaseCommitmentsMember" xlink:href="agm-20240331.xsd#agm_LongTermStandbyPurchaseCommitmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LongTermStandbyPurchaseCommitmentsMember" xlink:to="lab_agm_LongTermStandbyPurchaseCommitmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DebtSecurityInvestmentCategoryDomain_afa7a919-129e-482c-baca-8ce4246bcaa4_terseLabel_en-US" xlink:label="lab_agm_DebtSecurityInvestmentCategoryDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Security Investment Category [Domain]</link:label>
    <link:label id="lab_agm_DebtSecurityInvestmentCategoryDomain_label_en-US" xlink:label="lab_agm_DebtSecurityInvestmentCategoryDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Security Investment Category [Domain]</link:label>
    <link:label id="lab_agm_DebtSecurityInvestmentCategoryDomain_documentation_en-US" xlink:label="lab_agm_DebtSecurityInvestmentCategoryDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Security Investment Category [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DebtSecurityInvestmentCategoryDomain" xlink:href="agm-20240331.xsd#agm_DebtSecurityInvestmentCategoryDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DebtSecurityInvestmentCategoryDomain" xlink:to="lab_agm_DebtSecurityInvestmentCategoryDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingDerivativeAssetsAbstract_1a091d22-a094-46e8-bec2-bdf705283e36_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingDerivativeAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets:</link:label>
    <link:label id="lab_us-gaap_OffsettingDerivativeAssetsAbstract_label_en-US" xlink:label="lab_us-gaap_OffsettingDerivativeAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Derivative Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingDerivativeAssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OffsettingDerivativeAssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingDerivativeAssetsAbstract" xlink:to="lab_us-gaap_OffsettingDerivativeAssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_CoSelectedMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureAmt" xlink:to="lab_ecd_CoSelectedMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfHeldToMaturitySecuritiesTable_38772cb9-29e1-4129-95f8-d518832cffd0_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfHeldToMaturitySecuritiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-maturity [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfHeldToMaturitySecuritiesTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfHeldToMaturitySecuritiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfHeldToMaturitySecuritiesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfHeldToMaturitySecuritiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfHeldToMaturitySecuritiesTable" xlink:to="lab_us-gaap_ScheduleOfHeldToMaturitySecuritiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_373e13e5-a59d-437c-ab02-4f8fe2ff5a64_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Assets</link:label>
    <link:label id="lab_us-gaap_Assets_93b59072-521f-44da-8992-331684d0d243_terseLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AwardsCloseToMnpiDiscIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:to="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilityFairValueGrossLiabilityIncludingNotSubjectToMasterNettingArrangement_09777c99-5286-46ba-9338-3e1c35a5b901_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityFairValueGrossLiabilityIncludingNotSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Net Amount Presented in the Consolidated Balance Sheet</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityFairValueGrossLiabilityIncludingNotSubjectToMasterNettingArrangement_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityFairValueGrossLiabilityIncludingNotSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Fair Value, Gross Liability Including Not Subject to Master Netting Arrangement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityFairValueGrossLiabilityIncludingNotSubjectToMasterNettingArrangement" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeLiabilityFairValueGrossLiabilityIncludingNotSubjectToMasterNettingArrangement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityFairValueGrossLiabilityIncludingNotSubjectToMasterNettingArrangement" xlink:to="lab_us-gaap_DerivativeLiabilityFairValueGrossLiabilityIncludingNotSubjectToMasterNettingArrangement" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_HeldtoMaturitySecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield_40b52abc-c849-49d7-82a0-8629c893ad69_terseLabel_en-US" xlink:label="lab_agm_HeldtoMaturitySecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after ten years</link:label>
    <link:label id="lab_agm_HeldtoMaturitySecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield_label_en-US" xlink:label="lab_agm_HeldtoMaturitySecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Held-to-Maturity Securities, Debt Maturities, After Ten Years, Weighted-Average Yield</link:label>
    <link:label id="lab_agm_HeldtoMaturitySecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield_documentation_en-US" xlink:label="lab_agm_HeldtoMaturitySecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Held-to-Maturity Securities, Debt Maturities, After Ten Years, Weighted-Average Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_HeldtoMaturitySecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:href="agm-20240331.xsd#agm_HeldtoMaturitySecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_HeldtoMaturitySecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:to="lab_agm_HeldtoMaturitySecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_3ce2b838-87b9-41da-b101-305d127284b9_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock-based compensation cost</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:to="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive_21e3bcfd-5e48-428f-ad17-911f2e29e4a8_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Five years</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LaborAndRelatedExpense_980541a7-641a-4f05-bb8f-67006a659189_terseLabel_en-US" xlink:label="lab_us-gaap_LaborAndRelatedExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation and employee benefits</link:label>
    <link:label id="lab_us-gaap_LaborAndRelatedExpense_label_en-US" xlink:label="lab_us-gaap_LaborAndRelatedExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Labor and Related Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LaborAndRelatedExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LaborAndRelatedExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LaborAndRelatedExpense" xlink:to="lab_us-gaap_LaborAndRelatedExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MaterialReconcilingItemsMember_9bab1639-22fa-4695-86f1-dda930df839a_terseLabel_en-US" xlink:label="lab_us-gaap_MaterialReconcilingItemsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reconciling Adjustments</link:label>
    <link:label id="lab_us-gaap_MaterialReconcilingItemsMember_label_en-US" xlink:label="lab_us-gaap_MaterialReconcilingItemsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reconciling Items [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MaterialReconcilingItemsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MaterialReconcilingItemsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MaterialReconcilingItemsMember" xlink:to="lab_us-gaap_MaterialReconcilingItemsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateDuringPeriod_e9ffd3f8-81f1-4f17-858e-ed0237e18453_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Average Outstanding, Weighted - average rate (as a percent)</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateDuringPeriod_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate During Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateDuringPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentInterestRateDuringPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateDuringPeriod" xlink:to="lab_us-gaap_DebtInstrumentInterestRateDuringPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonNeosMember_terseLabel_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-NEOs</link:label>
    <link:label id="lab_ecd_NonNeosMember_label_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-NEOs [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonNeosMember" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_NonNeosMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonNeosMember" xlink:to="lab_ecd_NonNeosMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearAbstract_99c96e77-82d5-48ac-8d4b-b83dca916345_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year Four</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearAbstract_label_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated Three Years before Latest Fiscal Year [Abstract]</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearAbstract_documentation_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated Three Years before Latest Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearAbstract" xlink:href="agm-20240331.xsd#agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearAbstract" xlink:to="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_SegmentCoreEarnings_90ed7c03-5c93-4ced-b814-b4a9ff42c3ac_totalLabel_en-US" xlink:label="lab_agm_SegmentCoreEarnings" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Segment core earnings/(losses)</link:label>
    <link:label id="lab_agm_SegmentCoreEarnings_label_en-US" xlink:label="lab_agm_SegmentCoreEarnings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Core Earnings</link:label>
    <link:label id="lab_agm_SegmentCoreEarnings_documentation_en-US" xlink:label="lab_agm_SegmentCoreEarnings" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Segment core earnings - net income (loss) available to common shareholders, basic, adjusted for reconciling items related to segment reporting</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_SegmentCoreEarnings" xlink:href="agm-20240331.xsd#agm_SegmentCoreEarnings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_SegmentCoreEarnings" xlink:to="lab_agm_SegmentCoreEarnings" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_HeldtoMaturitySecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield_5c07be81-a145-4d2b-8313-19fcae3316a8_terseLabel_en-US" xlink:label="lab_agm_HeldtoMaturitySecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after one year through five years</link:label>
    <link:label id="lab_agm_HeldtoMaturitySecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield_label_en-US" xlink:label="lab_agm_HeldtoMaturitySecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Held-to-Maturity Securities, Debt Maturities, Year Two Through Five, Weighted-Average Yield</link:label>
    <link:label id="lab_agm_HeldtoMaturitySecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield_documentation_en-US" xlink:label="lab_agm_HeldtoMaturitySecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Held-to-Maturity Securities, Debt Maturities, Year Two Through Five, Weighted-Average Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_HeldtoMaturitySecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield" xlink:href="agm-20240331.xsd#agm_HeldtoMaturitySecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_HeldtoMaturitySecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield" xlink:to="lab_agm_HeldtoMaturitySecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearOne_70c4f8d8-2915-486f-a396-ea8fdaff0ffb_terseLabel_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearOne" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearOne_label_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearOne" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, Year One</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearOne_documentation_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearOne" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LongTermDebtWithInterestRateResetMaturityYearOne" xlink:href="agm-20240331.xsd#agm_LongTermDebtWithInterestRateResetMaturityYearOne"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LongTermDebtWithInterestRateResetMaturityYearOne" xlink:to="lab_agm_LongTermDebtWithInterestRateResetMaturityYearOne" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_194b8997-5329-4f86-86f3-81a19a3e6a3d_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotionalAmountOfDerivativesAbstract_04ac5ddf-74d6-454d-b025-3f76fda235e5_terseLabel_en-US" xlink:label="lab_us-gaap_NotionalAmountOfDerivativesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notional Disclosures [Abstract]</link:label>
    <link:label id="lab_us-gaap_NotionalAmountOfDerivativesAbstract_label_en-US" xlink:label="lab_us-gaap_NotionalAmountOfDerivativesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notional Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotionalAmountOfDerivativesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NotionalAmountOfDerivativesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotionalAmountOfDerivativesAbstract" xlink:to="lab_us-gaap_NotionalAmountOfDerivativesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesWeightedAverageYield_900a75b7-bff8-4e19-a9f4-fcf230134c61_terseLabel_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average yield</link:label>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesWeightedAverageYield_label_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Available-for-sale Securities, Debt Maturities, Weighted-Average Yield</link:label>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesWeightedAverageYield_documentation_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Available-for-sale Securities, Debt Maturities, Weighted-Average Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_AvailableForSaleSecuritiesDebtMaturitiesWeightedAverageYield" xlink:href="agm-20240331.xsd#agm_AvailableForSaleSecuritiesDebtMaturitiesWeightedAverageYield"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_AvailableForSaleSecuritiesDebtMaturitiesWeightedAverageYield" xlink:to="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesWeightedAverageYield" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_4a1e2148-9e2f-498f-babf-d196a0b193b7_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from financing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Financing Activities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_InterestRateSwapPayFixedNonCallableMember_e707ad03-5b3d-4f97-9fc6-b5bb39652935_terseLabel_en-US" xlink:label="lab_agm_InterestRateSwapPayFixedNonCallableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay fixed non-callable</link:label>
    <link:label id="lab_agm_InterestRateSwapPayFixedNonCallableMember_label_en-US" xlink:label="lab_agm_InterestRateSwapPayFixedNonCallableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swap, Pay Fixed Non-Callable [Member]</link:label>
    <link:label id="lab_agm_InterestRateSwapPayFixedNonCallableMember_documentation_en-US" xlink:label="lab_agm_InterestRateSwapPayFixedNonCallableMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Rate Swap, Pay Fixed Non-Callable [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_InterestRateSwapPayFixedNonCallableMember" xlink:href="agm-20240331.xsd#agm_InterestRateSwapPayFixedNonCallableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_InterestRateSwapPayFixedNonCallableMember" xlink:to="lab_agm_InterestRateSwapPayFixedNonCallableMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableRevolvingExcludingAccruedInterestAllowanceForCreditLossWriteOff_af6f19b2-17be-441c-aadd-d89283906eb6_negatedTerseLabel_en-US" xlink:label="lab_agm_FinancingReceivableRevolvingExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Current period charge-offs</link:label>
    <link:label id="lab_agm_FinancingReceivableRevolvingExcludingAccruedInterestAllowanceForCreditLossWriteOff_75638e84-32c2-4907-8324-a8410b57c348_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivableRevolvingExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current period charge-offs</link:label>
    <link:label id="lab_agm_FinancingReceivableRevolvingExcludingAccruedInterestAllowanceForCreditLossWriteOff_label_en-US" xlink:label="lab_agm_FinancingReceivableRevolvingExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Revolving, Excluding Accrued Interest, Allowance for Credit Loss, Write-Off</link:label>
    <link:label id="lab_agm_FinancingReceivableRevolvingExcludingAccruedInterestAllowanceForCreditLossWriteOff_documentation_en-US" xlink:label="lab_agm_FinancingReceivableRevolvingExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Revolving, Excluding Accrued Interest, Allowance for Credit Loss, Write-Off</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableRevolvingExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:href="agm-20240331.xsd#agm_FinancingReceivableRevolvingExcludingAccruedInterestAllowanceForCreditLossWriteOff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivableRevolvingExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:to="lab_agm_FinancingReceivableRevolvingExcludingAccruedInterestAllowanceForCreditLossWriteOff" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract_5ee63990-bc2f-429e-9958-9f4450595fdc_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Amortized Cost, after Allowance for Credit Loss, Maturity, Allocated and Single Maturity Date [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoMember_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO</link:label>
    <link:label id="lab_ecd_NonPeoNeoMember_label_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoMember" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_NonPeoNeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoMember" xlink:to="lab_ecd_NonPeoNeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MarketableSecurities_94a77dd6-2bf0-41df-b56f-cf0ffeb01f4f_totalLabel_en-US" xlink:label="lab_us-gaap_MarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Securities</link:label>
    <link:label id="lab_us-gaap_MarketableSecurities_label_en-US" xlink:label="lab_us-gaap_MarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketable Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MarketableSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MarketableSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MarketableSecurities" xlink:to="lab_us-gaap_MarketableSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UsTreasuryUstInterestRateMember_761e7e3c-b111-45f5-a2f1-de2912d40ef6_terseLabel_en-US" xlink:label="lab_us-gaap_UsTreasuryUstInterestRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Floating rate U.S. Treasuries</link:label>
    <link:label id="lab_us-gaap_UsTreasuryUstInterestRateMember_label_en-US" xlink:label="lab_us-gaap_UsTreasuryUstInterestRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Treasury (UST) Interest Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UsTreasuryUstInterestRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_UsTreasuryUstInterestRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UsTreasuryUstInterestRateMember" xlink:to="lab_us-gaap_UsTreasuryUstInterestRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAxis_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation:</link:label>
    <link:label id="lab_ecd_AdjToCompAxis_label_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAxis" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_AdjToCompAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAxis" xlink:to="lab_ecd_AdjToCompAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_UnclearedSwapsMember_2e11671e-723b-4b72-842a-014c25cc8964_terseLabel_en-US" xlink:label="lab_agm_UnclearedSwapsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Uncleared Swaps</link:label>
    <link:label id="lab_agm_UnclearedSwapsMember_label_en-US" xlink:label="lab_agm_UnclearedSwapsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Uncleared Swaps [Member]</link:label>
    <link:label id="lab_agm_UnclearedSwapsMember_documentation_en-US" xlink:label="lab_agm_UnclearedSwapsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Uncleared Swaps</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_UnclearedSwapsMember" xlink:href="agm-20240331.xsd#agm_UnclearedSwapsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_UnclearedSwapsMember" xlink:to="lab_agm_UnclearedSwapsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetFairValueGrossLiability_f18c9194-e58b-4e6b-9c40-13f373d4519d_negatedLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Netting adjustments</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetFairValueGrossLiability_bf802d03-21e8-4914-895b-6d5353c0d45e_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Gross Amounts offset in the Consolidated Balance Sheet</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetFairValueGrossLiability_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, Liability Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeAssetFairValueGrossLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:to="lab_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_15feec1d-b01b-452a-b2bb-54c64a2be874_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_c902163b-01e9-41df-84f6-eba0daa5d995_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income attributable to common stockholders (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DueYearOneMember_d3ed414c-e0fe-4f52-abbf-fc64d8cb8137_terseLabel_en-US" xlink:label="lab_agm_DueYearOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year one</link:label>
    <link:label id="lab_agm_DueYearOneMember_label_en-US" xlink:label="lab_agm_DueYearOneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Due year one [Member]</link:label>
    <link:label id="lab_agm_DueYearOneMember_documentation_en-US" xlink:label="lab_agm_DueYearOneMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Due year one</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DueYearOneMember" xlink:href="agm-20240331.xsd#agm_DueYearOneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DueYearOneMember" xlink:to="lab_agm_DueYearOneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription_9553b591-1bc4-43d1-825b-fbf56beb89d8_terseLabel_en-US" xlink:label="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassifications</link:label>
    <link:label id="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription_label_en-US" xlink:label="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification, Comparability Adjustment [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PriorPeriodReclassificationAdjustmentDescription"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:to="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember_6a62280a-4044-4440-8910-468b8d9b0243_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Two years</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period Two [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentRedemptionPeriodTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTable_terseLabel_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure</link:label>
    <link:label id="lab_ecd_PvpTable_label_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTable" xlink:href="https://xbrl.sec.gov/ecd/2023/ecd-2023.xsd#ecd_PvpTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTable" xlink:to="lab_ecd_PvpTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSecuritizationsOfLoansHeldForInvestment_7fc783cf-4bb3-4bf0-b6de-7bd7bcd7c8d0_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSecuritizationsOfLoansHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from new securitizations</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSecuritizationsOfLoansHeldForInvestment_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSecuritizationsOfLoansHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Securitization, Loan, Held-for-Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSecuritizationsOfLoansHeldForInvestment" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromSecuritizationsOfLoansHeldForInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSecuritizationsOfLoansHeldForInvestment" xlink:to="lab_us-gaap_ProceedsFromSecuritizationsOfLoansHeldForInvestment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementLineItems_2e39e7e2-7e5c-4d8e-b3f7-bff945f8d6d2_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_UnclearedDerivativesMember_5a0c41fd-bcfc-438b-b06a-d5b7653ec783_terseLabel_en-US" xlink:label="lab_agm_UnclearedDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Uncleared derivatives</link:label>
    <link:label id="lab_agm_UnclearedDerivativesMember_label_en-US" xlink:label="lab_agm_UnclearedDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Uncleared Derivatives [Member]</link:label>
    <link:label id="lab_agm_UnclearedDerivativesMember_documentation_en-US" xlink:label="lab_agm_UnclearedDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Uncleared Derivatives</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_UnclearedDerivativesMember" xlink:href="agm-20240331.xsd#agm_UnclearedDerivativesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_UnclearedDerivativesMember" xlink:to="lab_agm_UnclearedDerivativesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_658b4012-8e99-4260-b949-9e480210212e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Instruments in Statement of Financial Position</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Instruments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfDerivativeInstrumentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingInformationProfitLossAbstract_a950a146-29c8-4c48-900d-6f7a26f89a41_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationProfitLossAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting Information, Profit (Loss) [Abstract]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingInformationProfitLossAbstract_label_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationProfitLossAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting Information, Profit (Loss) [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationProfitLossAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SegmentReportingInformationProfitLossAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingInformationProfitLossAbstract" xlink:to="lab_us-gaap_SegmentReportingInformationProfitLossAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_ee1269e7-535d-4fc8-9bc4-400121822ed8_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Debt</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Debt [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDebtTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfDebtTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDebtTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:type="arc" order="1"/>
  </link:labelLink>
</link:linkbase>
