Nonlinear Panel Models with Interactive Effects∗

This paper considers estimation and inference on semiparametric nonlinear panel single index models with predetermined explanatory variables and interactive individual and time effects. These include static and dynamic probit, logit, and Poisson models. Fixed effects conditional maximum likelihood estimation is challenging because the log likelihood function is not concave in the individual and time effects. We propose an iterative two-step procedure to maximize the likelihood that is concave in each step. Under asymptotic sequences where both the cross section and time series dimensions of the panel pass to infinity at the same rate, we show that the fixed effects conditional maximum likelihood estimator is consistent, but it has bias in the asymptotic distribution due to the incidental parameter problem. We characterize the bias and develop analytical and jackknife bias corrections that remove the bias from the asymptotic distribution without increasing variance. In numerical examples, we find that the corrections substantially reduce the bias and rmse of the estimator in small samples, and produce confidence intervals with coverages that are close to their nominal levels.