A likelihood-Based Approximate Solution to the Incidental Parameter Problem in Dynamic Nonlinear Models with Multiple Effects

We discuss a modified objective function strategy to obtain estimators without bias to order 1/T in nonlinear dynamic panel models with multiple effects. Estimation proceeds from a bias-corrected objective function relative to some target infeasible criterion. We consider a determinant-based approach for likelihood settings, and a trace-based approach, which is not restricted to the likelihood setup. Both approaches depend exclusively on the Hessian and the outer product of the scores of the fixed effects. They produce simple and transparent corrections even in models with multiple effects. We analyze the asymptotic properties of both types of estimators when n and T grow at the same rate, and show that they are asymptotically normal and centered at the truth. Our strategy is to develop a theory for general bias-corrected estimating equations, so that we can obtain asymptotic results for a specific bias correction method using the first-order conditions.