Second-order corrected likelihood for nonlinear panel models with fixed effects

We propose a second-order correction for nonlinear fixed-effect panel models. The correction is made via the log-likelihood function. It removes the two leading terms of the bias of the log-likelihood that arises from estimating the fixed effects. Maximizing the corrected likelihood gives a second-order bias-corrected estimator, with bias OT−3, where T is the number of time periods. The corrected likelihood also gives second-order corrected test statistics. The correction applies to general nonlinear fixed-effect models with independent observations. The bias correction properties are confirmed in simulations for binary-choice models.

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