Point-Identifying Semiparametric Sample Selection Models with No Excluded Variable

TL;DR

This paper introduces a semiparametric sample selection model that achieves point identification without exclusion restrictions, using minimal assumptions and a straightforward estimator, improving upon existing bounds.

Contribution

It develops a novel semiparametric identification method that does not require exclusion restrictions, expanding the toolkit for sample selection analysis.

Findings

Estimator is root-n consistent and asymptotically normal.

Simulation shows excellent finite-sample performance.

Application reveals wage disparities outside previous bounds.

Abstract

Sample selection is pervasive in applied economic studies. This paper develops semiparametric selection models that achieve point identification without relying on exclusion restrictions, an assumption long believed necessary for identification in semiparametric selection models. Our identification conditions require at least one continuously distributed covariate and certain nonlinearity in the selection process. We propose a two-step plug-in estimator that is root-n-consistent, asymptotically normal, and computationally straightforward (readily available in statistical software), allowing for heteroskedasticity. Our approach provides a middle ground between Lee (2009)'s nonparametric bounds and Honor\'e and Hu (2020)'s linear selection bounds, while ensuring point identification. Simulation evidence confirms its excellent finite-sample performance. We apply our method to estimate the racial and gender wage disparity using data from the US Current Population Survey. Our estimates tend to lie outside the Honor\'e and Hu bounds.