Likelihood-based inference for nonlinear models with both individual and time effects

We propose a bias correction method for nonlinear models with both individual and time effects. Under the presence of the incidental parameter problem, the maximum likelihood estimator derived from such models may be severely biased. Our method produces an approximation to an infeasible log-likelihood function that is not exposed to the incidental parameter problem. The maximizer derived from the approximating function serves as a bias-corrected estimator that is asymptotically unbiased when the sequence N=T converges to a constant. The proposed method is general in several perspectives. The method can be extended to models with multiple fixed effects and can be easily modified to accommodate dynamic models.