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Income Taxes, Income Tax Expense and Tax Rate Reconciliation (Details) - USD ($) $ in Millions | 12 Months Ended
--- | ---
Dec. 31, 2018 | Dec. 31, 2017 | Dec. 31, 2016
Increase (reduction) in income taxes from: |  |  |
Computed expected tax expense | $ 148.3 | $ 187.5 | $ 162.3
State and local income taxes, net of federal income tax benefit | 2.8 | (0.1) | 5.9
Amortization of goodwill and other intangibles | (3.4) | (6.7) | (5.7)
Nondeductible expenses | 14.6 | 7.0 | 6.7
International earnings taxed at various rates | (21.1) | (69.0) | (59.8)
Valuation allowances | 12.4 | 5.8 | 8.3
Effective Income Tax Rate Reconciliation, Repatriation of Foreign Earnings, Amount | 47.0 | 125.9 | 0.0
Other, net | 13.7 | 5.9 | 0.1
Total provision for income taxes | 214.3 | $ 256.3 | $ 117.8
Tax Expense for 2018 Income Tax Provision Transition Tax | $ 47.0 |  |
Increase (reduction) in income taxes from: |  |  |
U.S. federal income tax rate | 21.00% | 35.00% | 35.00%
State and local income taxes, net of federal income tax benefit | 0.40% | 0.00% | 1.30%
Amortization of goodwill and other intangibles | (0.50%) | (1.30%) | (1.20%)
Nondeductible expenses | 2.10% | 1.30% | 1.40%
International earnings taxed at various rates | (3.00%) | (12.90%) | (12.90%)
Valuation allowances | 1.80% | 1.10% | 1.80%
Effective Income Tax Rate Reconciliation, Repatriation of Foreign Earnings, Percent | 6.70% | 23.50% | 0.00%
Other, net | 1.90% | 1.10% | 0.10%
Total | 30.40% | 47.80% | 25.50%
Expense associated with the Tax Cuts and Jobs Act |  | $ 172.9 |
Tax Liability on Deemed Repatriation of Foreign Earnings |  | $ 184.4 |

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