This paper develops an approach to intergenerational mobility in which the trajectories of parental incomes during childhood and adolescence are the conditioning objects for characterizing dependence across generations. We use functional regression methods to produce an intergenerational elasticity curve that measures how marginal changes in income at each age affect expected offspring permanent income. Using the PSID, estimates of this curve exhibit near monotonicity with respect to age, so that parental incomes in middle childhood and adolescence have larger marginal effects than incomes in early childhood. When interactions are allowed to occur between incomes at different ages, we find a complex pattern of substitutability between incomes at ages that are close in time versus complementarity between parental incomes for ages early childhood and adolescence. Qualitatively similar results hold for offspring education while we do not find evidence of age-specific effects for occupation. We conclude that important information about the links between parental incomes and children exists beyond the scalar characterization of parental permanent income.

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