Varying coefficient panel data model in the presence of endogenous selectivity and fixed effects

This paper considers a flexible panel data sample selection model in which (i) the outcome equation is permitted to take a semiparametric, varying coefficient form to capture potential parameter heterogeneity in the relationship of interest, (ii) both the outcome and (parametric) selection equations contain unobserved fixed effects and (iii) selection is generalized to a polychotomous case. We propose a two-stage estimator. Given consistent parameter estimates from the selection equation obtained in the first stage, we estimate the semiparametric outcome equation using data for the observed individuals whose likelihood of being selected into the sample stays approximately the same over time. The selection bias term is then "asymptotically" removed from the equation along with fixed effects using kernel-based weights. The proposed estimator is consistent and asymptotically normal. We showcase our estimator by applying it to study production technologies of US retail credit unions from 2002 to 2006.