Distribution Regression with Censored Selection

TL;DR

This paper introduces a semi-parametric distribution regression model with censored selection, enabling analysis of entire outcome distributions and heterogeneous effects, with applications to labor supply and wage gap analysis.

Contribution

It extends the Heckman model to the full distribution with censored selection, accommodating non-Gaussian errors and heterogeneous covariate effects.

Findings

Selection effects influence gender wage gaps across quantiles.

Different selection patterns observed for full-time and overtime work.

Model reveals richer selection behaviors than binary models.

Abstract

We develop a distribution regression model with a censored selection rule, offering a semi-parametric generalization of the Heckman selection model. Our approach applies to the entire distribution, extending beyond the mean or median, accommodates non-Gaussian error structures, and allows for heterogeneous effects of covariates on both the selection and outcome distributions. By employing a censored selection rule, our model can uncover richer selection patterns according to both outcome and selection variables, compared to the binary selection case. We analyze identification, estimation, and inference of model functionals such as sorting parameters and distributions purged of sample selection. An application to labor supply using data from the UK reveals different selection patterns into full-time and overtime work across gender, marital status, and time. Additionally, decompositions of wage distributions by gender show that selection effects contribute to a decrease in the observed gender wage gap at low quantiles and an increase in the gap at high quantiles for full-time workers. The observed gender wage gap among overtime workers is smaller, which may be driven by different selection behaviors into overtime work across genders.