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

Fixed effects estimators in nonlinear panel models with fixed and short time series length T usually suffer from inconsistency because of the incidental parameters problem first noted by Neyman and Scott (1948). Moreover, even if T grows but at a rate not faster than the cross sectional sample size n, they are asymptotically biased, and therefore the associated confidence intervals have a large coverage error. This paper analyzes the properties of the parametric bootstrap bias corrected maximum likelihood (ML) estimators of nonlinear panel models with fixed effects. We assume that each time series follows a finite order Markov process. We show that the bootstrap bias corrected estimators are asymptotically normal and centered at the true parameter. In particular, we propose using the k-step parametric bootstrap procedure to alleviate the computational cost of implementing the standard bootstrap. We also apply the standard and k-step bootstrap bias correction to average marginal effect estimation and to the double bootstrap for confidence interval construction. Our Monte Carlo simulations show that the k-step bootstrap bias corrected estimator reduces the bias remarkably well in finite samples.