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Second-Order Corrected Likelihood for Nonlinear Models with Fixed Effects

We introduce a second-order correction technique for nonlinear fixed-effect models exposed to the incidental parameter problem. This technique produces a bias-corrected log-likelihood function that possesses a bias only to the order (in expectation) of O (T-3) where T is the number of time periods. As a consequence, the maximizer of the corrected log-likelihood, the corrected estimator, is also only biased to the order of O (T-3). The technique applies to static nonlinear fixed-effect models in which N, the number of individuals, is allowed to grow rapidly and T is assumed to grow at a rate satisfying N/T5 converging to 0. The proposed technique is general in the sense that it does not depend on a specific functional form of the log-likelihood function.