Semiparametric Estimation of Oaxaca-Blinder Decompositions with Continuous Groups

Brantly Callaway, Weige Huang

Abstract

This paper considers Oaxaca-Blinder type decompositions with continuous groups. In particular, we decompose the differences between outcomes at a series of values of the group variable and at a particular value of the group variable into (i) a composition effect and (ii) a structure effect. The composition effect is due to differences in the distribution of observed characteristics (e.g. race or education) for individuals at two particular values of the continuous group variable. The structure effect is due to difference in the return to characteristics at two particular values of the continuous group variable. We also consider detailed decompositions of both the composition and structure effects. Our procedure is based on semiparametric smooth varying coefficient models that are essentially local (in terms of the continuous group variable) regressions. This approach is distinct from previous work on decompositions with continuous groups that invoke parametric models. We develop the limiting distribution of our estimator and show the validity of the wild bootstrap for conducting inference. We apply our method to decompose earnings differentials for individuals across different values of their parents’ income (i.e. parents’ income is the continuous group).