Intergenerational Income Mobility: Counterfactual Distributions with a Continuous Treatment

A vast literature in labor economics documents the correlation between parents' income and their child’s income. This paper develops new methods to study the entire distribution of child's income as a function of parents' income while (possibly) adjusting for differences in background characteristics (e.g. race or parents' education) across children whose parents had different incomes. The main challenge is that parents' income is a continuous variable and existing methods for generating counterfactual distributions consider the case with discrete groups. We develop new semiparametric estimators for counterfactual distributions with a continuous treatment variable that are simple to implement and compute quickly. We show that our estimators converge uniformly to Gaussian processes and that the empirical bootstrap can be used to conduct uniformly valid inference across a range of values of parents' income. Our main analysis focuses on parameters such as (i) the fraction of children below the poverty line, (ii) "local" intergenerational elasticities (LIGE), and (iii) the variance of child's income that are functions of the counterfactual distribution. We find variation in these parameters across parents' income levels. And, after documenting large differences in background characteristics across parents' income levels, we find that adjusting for differences in background characteristics tends to reduce (though not eliminate) the overall effect of parents' income on child's income as well as reduce differences in the LIGE and variance of child's income across parents' income levels.