Decomposing joint distributions via reweighting functions: an application to intergenerational economic mobility

We introduce a method that extends the traditional Oaxaca-Blinder decomposition to both the full distribution of an outcome of interest and to settings where group membership varies along a continuum. We achieve this by working directly with the joint distribution of outcome and group membership and comparing it to an independent joint distribution. Like all decompositions, we assume the difference is partially due to differences in characteristics between groups (a composition effect) and partially due to differences in returns to characteristics between groups (a structure effect). We use reweighting functions to estimate a counterfactual joint distribution representing the hypothetical if characteristics did not vary according to group while returns to characteristics did. The counterfactual allows us to decompose differences between the empirical and independent distributions into composition and structure effects. We demonstrate the method by decomposing multiple measures of immobility for white men in the U.S.