Nonlinear Panel Data Analysis

Nonlinear panel data models naturally arise in economic applications, yet their analysis is challenging. Here we provide a progress report on some recent advances in the area. We start by reviewing the properties of random-effects maximum likelihood. We emphasize a link with Bayesian computation and Markov Chain Monte Carlo, which provides a convenient approach to estimation and inference. Relaxing parametric assumptions on the distribution of individual effects raises serious identification problems. In discrete choice models, common parameters and average marginal effects are generally set-identified. The availability of continuous outcomes, however, provides opportunities for point-identification. We end the paper by reviewing recent progress on non fixed-T approaches. In panel applications where the time dimension is not negligible relative to the size of the cross-section, it makes sense to view the estimation problem as a time-series finite sample bias. Several perspectives to bias reduction are now available. We review their properties, with a special emphasis on random-effects methods. JEL codes: C23.