Fixed and Random Effects in Nonlinear Models

This paper surveys recently developed approaches to analyzing panel data with nonlinear models. We summarize a number of results on estimation of fixed and random effects models in nonlinear modeling frameworks such as discrete choice, count data, duration, censored data, sample selection, stochastic frontier and, generally, models that are nonlinear both in parameters and variables. We show that notwithstanding their methodological shortcomings, fixed effects are much more practical than heretofore reflected in the literature. For random effects models, we develop an extension of a random parameters model that has been used extensively, but only in the discrete choice literature. This model subsumes the random effects model, but is far more flexible and general, and overcomes some of the familiar shortcomings of the simple additive random effects model as usually formulated. Once again, the range of applications is extended beyond the familiar discrete choice setting. Finally, we draw together several strands of applications of a model that has taken a semiparametric approach to individual heterogeneity in panel data, the latent class model. A fairly straightforward extension is suggested that should make this more widely useable by practitioners. Many of the underlying results already appear in the literature, but, once again, the range of applications is smaller than it could be.