On semiparametric estimation of the intercept of the sample selection model: a kernel approach

TL;DR

This paper introduces a kernel-based method for estimating the intercept in sample selection models, utilizing boundary transformation techniques to achieve consistency and asymptotic normality, with a data-driven bandwidth selection approach.

Contribution

It proposes a novel kernel estimation framework for the intercept at the boundary in sample selection models, extending identification at infinity to kernel and local linear estimators.

Findings

Estimators are nonparametric-rate consistent and asymptotically normal.

The method includes a data-driven bandwidth selection procedure.

Simulation results demonstrate good finite sample performance.

Abstract

This paper presents a new perspective on the identification at infinity for the intercept of the sample selection model as identification at the boundary via a transformation of the selection index. This perspective suggests generalizations 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.