Semiparametric one-step estimation of a sample selection model with endogenous covariates

This paper considers semiparametric estimation of a sample selection model with endogenous covariates. In contrast to the existing literature, endogenous covariates are explicitly allowed in the main equation of interest as well as in the selection equation. A one-step GMM estimator based on polynomial approximations of unknown functions is proposed. It is shown that the estimator is consistent and has an asymptotic normal distribution. A small-scale simulation study indicates that the estimator performs well in finite samples and that estimators which do not account for the joint presence of sample selectivity and endogeneity of covariates are biased if both sample selectivity and endogeneity of covariates are indeed present. In an empirical application, it is demonstrated that the female returns to education are underestimated if one does not control for the joint presence of sample selectivity and endogeneity of education in main and selection equation.