On Semiparametric Estimation of the Intercept of the Sample Selection Model: A Kernel Approach

ABSTRACT This paper presents a novel perspective on the identification at infinity as identification at the boundary, for the intercept of the sample selection model, via a transformation of the selection index. This perspective suggests generalisations of estimation at infinity to kernel regression estimation at the boundary and further to local linear estimation at the boundary. The proposed kernel‐type estimators with an estimated transformation are proven to be nonparametric‐rate consistent and asymptotically normal under mild regularity conditions. A fully data‐driven method of selecting the optimal bandwidths for the estimators is developed. The Monte Carlo simulation shows the desirable finite sample properties of the proposed estimators and bandwidth selection procedures.