Bootstrap inference for fixed-effect models

TL;DR

This paper demonstrates that the parametric bootstrap can accurately replicate the distribution of the maximum-likelihood estimator in fixed-effect models, enabling valid inference without bias correction.

Contribution

It shows that bootstrap methods can be used directly for inference in fixed-effect models, bypassing the need for bias correction techniques.

Findings

Bootstrap replicates the distribution of the MLE in large samples.

Standard bootstrap confidence sets are justified without bias adjustment.

No bias correction is necessary for valid inference.

Abstract

The maximum-likelihood estimator of nonlinear panel data models with fixed effects is consistent but asymptotically-biased under rectangular-array asymptotics. The literature has thus far concentrated its effort on devising methods to correct the maximum-likelihood estimator for its bias as a means to salvage standard inferential procedures. Instead, we show that the parametric bootstrap replicates the distribution of the (uncorrected) maximum-likelihood estimator in large samples. This justifies the use of confidence sets constructed via standard bootstrap percentile methods. No adjustment for the presence of bias needs to be made.