TESTING AND CORRECTING FOR ENDOGENEITY IN NONLINEAR UNOBSERVED EFFECTS MODELS
We study testing and estimation in panel data models with two potential sources of
endogeneity: that due to correlation of covariates with time-constant, unobserved heterogeneity
and that due to correlation of covariates with time-varying idiosyncratic errors. In the linear
case, we show that two control function approaches allow us to test exogeneity with respect to
the idiosyncratic errors while being silent on exogeneity with respect to heterogeneity. The
linear case suggests a general approach for nonlinear models. We consider two leading cases of nonlinear models: an exponential conditional mean function for nonnegative responses and a
probit conditional mean function for binary or fractional responses. In the former case, we
exploit the full robustness of the fixed effects Poisson quasi-MLE, and for the probit case we
propose correlated random effects