Root-N Consistent Semiparametric Eestimators of a Dynamic Panel Sample Selection Model

Abstract. This paper considers the problem of identification and estimation in panel data sample selection models with a binary selection rule when the latent equations contain possible predetermined variables, lags of the dependent variables, and unobserved individual effects. The selection equation contains lags of the dependent variables from both the latent and the selection equations as well as other possible predetermined variables relative to the latent equations. We derive a set of conditional moment restrictions that are then exploited to construct a three-step GMM sieve estimator for the parameters of the main equation including a nonparametric estimator 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 Berkson’s minimum chi-square sieve method and a first-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 correlated random effects without making any distributional assumptions. We show that both estimators (second and third stage) are vn-consistent and asymptotically normal.