Blinder-Oaxaca decomposition with recursive tree-based methods: A technical note

The Blinder-Oaxaca decomposition was developed in order to detect and characterize discriminatory treatment, and one of its most frequent use has been the study of wage discrimination. It recognizes that the mere difference between the average wages of two groups may not mean discrimination (in a very wide sense of the word), but the difference can be due to different characteristics the groups possess. It decomposes average differences in the variable of interest into two parts: one explained by observable features of the two group, and an unexplained part, which may signal discrimination. The methodology was originally developed for OLS estimates, but it has been generalized in several nonlinear directions. In this paper we describe a further extension of the basic idea: we apply Random Forest (RF) regression to estimate the explained and unexplained parts, and then we employ the CART (Classification and Regression Tree) methodology to identify the groups for which discrimination is most or least severe.