Identification and N-consistent estimation of a nonlinear panel data model with correlated unobserved effects

This paper investigates identification and root-n-consistent estimation of a class of single-index panel data models in which the link function is unknown, the unobserved individual effects may be correlated with all the explanatory variables, and all the explanatory variables may be predetermined. We propose two sets of sufficient conditions, one in which link function is assumed to be strictly increasing, and the other in which it is not. We propose simple kernel-based estimators for the models, and derive consistency and asymptotic normality results for the proposed estimators. Finally, we present results of two Monte Carlo studies of the estimators.