k-Step Bootstrap Bias Correction for Fixed Effects Estimators in Nonlinear Panel Models

Fixed effects estimators in nonlinear panel models with fixed T usually suffer from inconsistency because of the incidental parameters problem first noted by Neyman and Scott (1948). Moreover, even though T grows at the same rate as n, they are asymptotically biased and therefore the associated confidence interval has a large coverage error. This paper proposes a k-step parametric bootstrap bias corrected estimator. We prove that our estimator is asymptotically normal and is centered at the true parameter if T grows faster than ∛n. In addition to bias correction, we construct a confidence interval with a double bootstrap procedure, and Monte Carlo experiments confirm that the error in coverage probability of our CI’s is smaller than those of the alternatives. We also propose bias correction for average marginal effects