Regression-based decomposition of differences in distribution

Counterfactual decomposition methods are often used to study differences in labor-market outcomes between groups (sex, race, etc.). The observed wage differential is divided into a part that is explained by group differences in characteristics and a residual part that is often used as a measure of discrimination. I will review regression-based estimators of the entire marginal counterfactual distributions of the outcome. The estimation of the conditional distribution can be based on the main regression methods, including classical, quantile, duration, and distribution regressions. The literature provides not only pointwise but also functional confidence bands, which cover the entire functions with prespecified probability and can be used to test functional hypotheses such as no effect, positive effect, or stochastic dominance. I will also discuss recent developments concerning (i) inference for discrete or mixed outcomes, (ii) detailed decomposition of the explained component, and (iii) algorithms to estimate quickly the whole quantile or distribution regression process.