Accounting for the black-white wealth gap: A nonparametric approach

Many applications involve a decomposition of the mean intergroup difference in a given variable into the portion attributable to differences in the distribution of one or more explanatory variables and that due to differences in the conditional expectation function. This article notes two interrelated reasons why the Blinder-Oaxaca (B-O) method-the approach most commonly used in the literature-may yield misleading results. We suggest a natural solution that both provides a more reliable answer to the original problem and affords a richer examination of the sources of intergroup differences in the variable of interest. The conventional application of the B-O method requires a parametric assumption about the form of the conditional expectation function. Furthermore, it often uses estimates based on that functional form to extrapolate outside the range of the observed explanatory variables. We show that misspecification of the conditional expectation function is likely to result in nontrivial errors in inference regarding the portion attributable to differences in the distribution of explanatory variables, a problem compounded by the computation of conditional expectations outside the observed range of the conditioning variables. Here we propose a nonparametric alternative to the B-O method that reweights the empirical distribution of the outcome variable using weights that equalize the empirical distributions of the explanatory variable. We apply this method to the role of earnings in explaining the black-white wealth difference. The problems with the B-O method show up clearly in this application, because the function relating wealth to earnings is highly nonlinear (with a functional form unspecified by theory) and because the earnings distribution for blacks is shifted sharply to the left of that for whites. We argue that it is not possible to examine the hypothetical distribution of black wealth holdings conditional on the observed white earnings function. For the question that we can answer-the distribution of wealth for a synthetic sample of blacks and whites with comparable earnings-we find that two-thirds of the mean difference in wealth can appropriately be attributed to earnings. In addition. we fully characterize the distribution of white and black wealth conditional on earnings.