A Bootstrap Specification Test for Semiparametric Models with Generated Regressors

TL;DR

This paper introduces a new specification test for semiparametric models with generated regressors, utilizing residuals and a wild bootstrap for valid inference, applicable to models with endogenous regressors and sample selection issues.

Contribution

It develops a novel test for semiparametric models with nonparametrically generated regressors, incorporating bias correction and a wild bootstrap for practical implementation.

Findings

Test performs well in small samples

Application demonstrates usefulness in labor economics

Bootstrap method provides valid critical values

Abstract

This paper provides a specification test for semiparametric models with nonparametrically generated regressors. Such variables are not observed by the researcher but are nonparametrically identified and estimable. Applications of the test include models with endogenous regressors identified by control functions, semiparametric sample selection models, or binary games with incomplete information. The statistic is built from the residuals of the semiparametric model. A novel wild bootstrap procedure is shown to provide valid critical values. We consider nonparametric estimators with an automatic bias correction that makes the test implementable without undersmoothing. In simulations the test exhibits good small sample performances, and an application to women's labor force participation decisions shows its implementation in a real data context.