The Behavior of the Fixed Effects Estimator in Nonlinear Models

The nonlinear fixed effects models in econometrics has often been avoided for two reasons one practical, one methodological. The practical obstacle relates to the difficulty of estimating nonlinear models with possibly thousands of coefficients. In fact, in a large number of models of interest to practitioners, estimation of the fixed effects model is feasible even in panels with very large numbers of groups. The more difficult, methodological question centers on the incidental parameters problem that raises questions about the statistical properties of the estimator. There is very little empirical evidence on the behavior of the fixed effects estimator. In this note, we use Monte Carlo methods to examine the small sample bias in the binary probit and logit models, the ordered probit model, the tobit model, the Poisson regression model for count data and the exponential regression model for a nonnegative random variable. We find three results of note: A widely accepted result that suggests that the probit estimator is actually relatively well behaved appears to be incorrect. Perhaps to some surprise, the tobit model, unlike the others, appears largely to be unaffected by the incidental parameters problem, save for a surprising result related to the disturbance variance estimator. Third, as apparently unexamined previously, the estimated asymptotic estimators for fixed effects estimators appear uniformly to be downward biased