Nonlinear panel data models arise naturally 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 likelihood approaches. We emphasize a link with Bayesian computation and Markov chain Monte Carlo, which provides a convenient approach to estimation and inference. The relaxation of 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 by reviewing recent progress on non-fixed-T approaches. In panel applications in which 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.
