A Simple Data-Driven Estimator for the Semiparametric Sample Selection Model

This paper proposes a simple fully data-driven version of Powell's (2001) two-step semiparametric estimator for the sample selection model. The main feature of the proposal is that the bandwidth used to estimate the infinite-dimensional nuisance parameter is chosen by minimizing the mean squared error of the fitted semiparametric model. We formally justify data-driven inference. We introduce the concept of asymptotic normality, uniform in the bandwidth, and show that the proposed estimator achieves this property for a wide range of bandwidths. The method of proof is different from that in Powell (2001) and permits straightforward extensions to other semiparametric or even fully nonparametric specifications of the selection equation. The results of a small Monte Carlo suggest that our estimator has excellent finite sample performance, comparing well with other competing estimators based on alternative choices of smoothing parameters.