Decomposing Joint Distributions via Reweighting Functions: An Application to Intergenerational Economic Mobility

We propose a decomposition method that extends the traditional Oaxaca-Blinder decomposition to a continuous group membership setting that can be applied to any distributional measure of interest. This is achieved by reframing the problem as a decomposition of joint distributions: we decompose the difference between an empirical and a (hypothetical) independent joint distribution of membership index and an outcome of interest. Differences are divided into a composition effect and a structure effect. The method is based on the estimation of a counterfactual joint distribution via reweighting functions that can be caste into various distributional measures to investigate the drivers of the empirical relationship. We apply the method to U.S. intergenerational economic mobility and investigate multiple versions of the intergenerational elasticity of income (IGE): the traditional linear IGE, quantile regression counterparts, and a nonparametric IGE. Quantile results reveal a U-shaped effect which is primarily compositional in nature; nonparametric results indicate the composition effect is the main driver of the mean parental-offspring link at low levels of parental income while the structural effect is the main driver at high levels of parental income. Both of these effects are masked by the traditional IGE which implies an even 50-50 split between the composition and structure effect.