We estimate rates of “absolute income mobility” – the fraction of children who earn more than their parents – by combining historical data from Census and CPS cross-sections with panel data for recent birth cohorts from de-identified tax records. Our approach overcomes the key data limitation that has hampered research on trends in intergenerational mobility: the lack of large panel datasets linking parents and children. We find that rates of absolute mobility have fallen from approximately 90% for children born in 1940 to 50% for children born in the 1980s. The result that absolute mobility has fallen sharply over the past half century is robust to the choice of price deflator, the definition of income, and accounting for taxes and transfers. In counterfactual simulations, we find that increasing GDP growth rates alone cannot restore absolute mobility to the rates experienced by children born in the 1940s. In contrast, changing the distribution of growth across income groups to the more equal distribution experienced by the 1940 birth cohort would reverse more than 70% of the decline in mobility. These results imply that reviving the “American Dream” of high rates of absolute mobility would require economic growth that is spread more broadly across the income distribution.