Root-n consistent semiparametric estimators of a dynamic panelsample-selection model

This paper considers the problem of identi\u85cation and estimation in panel-data sample-selection models with a binary selection rule when the latent equations contain possibly predetermined variables, lags of the dependent variables, and un-observed individual e¤ects. The selection equation contains lags of the dependent variables from both the latent and the selection equations as well as other possibly predetermined variables relative to the latent equations. We derive a set of condi-tional moment restrictions that are then exploited to construct a three-step sieve estimator for the parameters of the main equation including a nonparametric esti-mator of the sample-selection term. In the second step the unknown parameters of the selection equation are consistently estimated using a transformation approach in the spirit of Berksons minimum chi-square sieve method and a \u85rst-step kernel estimator for the selection probability. This second-step estimator is of interest in its own right. It can be used to semiparametrically estimate a panel-data binary response model with a nonparametric individual speci\u85c e¤ect without making any other distributional assumptions. We show that both estimators (second and third stage) are p n-consistent and asymptotically normal.