Approximate estimation in nonlinear panel data models

This paper is concerned with the estimation of a general class of nonlinear panel data models in which the conditional distribution of the dependent variable and the distribution of the heterogeneity factors are arbitrary. In general, exact analytical results for this problem do not exist. Here, Laplace and small-sigma appriximations for the marginal likelihood are presented. The computation of the MLE from both approximations is straightforward. It is shown that the accuracy of the Laplace approximation depends on both the sample size and the variance of the individual effects, whereas the accuracy of the small-sigma approximation is 0(1) with respect to the sample size. The results are applied to count, duration and probit panel data models. The accuracy of the approximations is evaluated through a Monte Carlo simulation experiment. The approximations are also applied in an analysis of youth unemployment in Australia.