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      <link:loc xlink:type="locator" xlink:href="agm-20221231.xsd#agm_ServiceCostForCoveredFiscalYearMember" xlink:label="agm_ServiceCostForCoveredFiscalYearMember" />
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      <link:loc xlink:type="locator" xlink:href="agm-20221231.xsd#agm_AggregateValueForStockAwardsAndOptionAwardsIncludedInSctAmountsForCoveredFiscalYearMember" xlink:label="agm_AggregateValueForStockAwardsAndOptionAwardsIncludedInSctAmountsForCoveredFiscalYearMember" />
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      <link:label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="agm_VestingDateFairValueOfAwardsGrantedAndVestedDuringCoveredFiscalYearMember_lbl" xml:lang="en-US">Vesting date fair value of awards granted and vested during the covered fiscal year</link:label>
      <link:loc xlink:type="locator" xlink:href="agm-20221231.xsd#agm_ChangeAsOfVestingDateFromEndOfPriorFiscalYearInFairValueOfAwardsGrantedInAnyPriorFiscalYearForWhichVestingConditionsWereSatisfiedDuringCoveredFiscalYearMember" xlink:label="agm_ChangeAsOfVestingDateFromEndOfPriorFiscalYearInFairValueOfAwardsGrantedInAnyPriorFiscalYearForWhichVestingConditionsWereSatisfiedDuringCoveredFiscalYearMember" />
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      <link:label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="agm_ChangeAsOfVestingDateFromEndOfPriorFiscalYearInFairValueOfAwardsGrantedInAnyPriorFiscalYearForWhichVestingConditionsWereSatisfiedDuringCoveredFiscalYearMember_lbl" xml:lang="en-US">Change as of the vesting date (from the end of the prior fiscal year) in fair value of awards granted in any prior fiscal year for which vesting conditions were satisfied during the covered fiscal year</link:label>
      <link:loc xlink:type="locator" xlink:href="agm-20221231.xsd#agm_FairValueAtEndOfPriorFiscalYearOfAwardsGrantedInAnyPriorFiscalYearThatFailedToMeetApplicableVestingConditionsDuringCoveredFiscalYearMember" xlink:label="agm_FairValueAtEndOfPriorFiscalYearOfAwardsGrantedInAnyPriorFiscalYearThatFailedToMeetApplicableVestingConditionsDuringCoveredFiscalYearMember" />
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      <link:label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="agm_FairValueAtEndOfPriorFiscalYearOfAwardsGrantedInAnyPriorFiscalYearThatFailedToMeetApplicableVestingConditionsDuringCoveredFiscalYearMember_lbl" xml:lang="en-US">Fair value at end of prior fiscal year of awards granted in any prior fiscal year that failed to meet the applicable vesting conditions during the covered fiscal year</link:label>
      <link:loc xlink:type="locator" xlink:href="agm-20221231.xsd#agm_DividendsOrOtherEarningsPaidOnStockOrOptionAwardsInCoveredFiscalYearPriorToVestingIfNotOtherwiseIncludedInTotalCompensationForCoveredFiscalYearMember" xlink:label="agm_DividendsOrOtherEarningsPaidOnStockOrOptionAwardsInCoveredFiscalYearPriorToVestingIfNotOtherwiseIncludedInTotalCompensationForCoveredFiscalYearMember" />
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      <link:label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_DocumentType_lbl" xml:lang="en-US">Document Type</link:label>
      <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2022q4/dei-2022q4.xsd#dei_EntityRegistrantName" xlink:label="dei_EntityRegistrantName" />
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      <link:label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityRegistrantName_lbl" xml:lang="en-US">Entity Registrant Name</link:label>
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      <link:label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="agm_CumulativeAdditionsToSCTTotalMember_doc" xml:lang="en-US">Cumulative Additions to SCT Total</link:label>
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      <link:label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="agm_ServiceCostForCoveredFiscalYearMember_doc" xml:lang="en-US">Service cost for the covered fiscal year</link:label>
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      <link:label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="agm_PriorServiceCostForCoveredFiscalYearMember_doc" xml:lang="en-US">Prior service cost for the covered fiscal year</link:label>
      <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="agm_AggregateValueForStockAwardsAndOptionAwardsIncludedInSctAmountsForCoveredFiscalYearMember" xlink:to="agm_AggregateValueForStockAwardsAndOptionAwardsIncludedInSctAmountsForCoveredFiscalYearMember_doc" xlink:type="arc" />
      <link:label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="agm_AggregateValueForStockAwardsAndOptionAwardsIncludedInSctAmountsForCoveredFiscalYearMember_doc" xml:lang="en-US">Aggregate value for stock awards and option awards included in SCT Amounts for the covered fiscal year</link:label>
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