Distribution Regression with Sample Selection and UK Wage Decomposition

Abstract

We develop a distribution regression model under endogenous sample selection. This model is a semiparametric generalization of the Heckman selection model, which accommodates much richer patterns of heterogeneity in the effect of covariates and selection process and allows for departures from Gaussian errors while maintaining the same level of tractability. The model applies to continuous, discrete, and mixed outcomes. We provide identification, estimation, and inference methods and apply them to obtain wage decompositions in the United Kingdom. Here we decompose the difference between the male and female wage distributions into composition, wage structure, selection structure, and selection sorting effects.