Integrated likelihood based inference for nonlinear panel data models with unobserved effects

We propose a new integrated likelihood based approach for estimating panel data models when the unobserved individual effects enter the model nonlinearly. Unlike existing integrated likelihoods in the literature, the one we propose is closer to a genuine likelihood. Although the statistical theory for the proposed estimator is developed in an asymptotic setting where the number of individuals and the number of time periods both approach infinity, results from a simulation study suggest that our methodology can work very well even in moderately sized panels of short duration in both static and dynamic models.