Bootstrap Inference in Nonlinear Panel Data Models with Interactive Fixed Effects

TL;DR

This paper demonstrates that the parametric bootstrap provides valid inference for nonlinear panel data models with interactive fixed effects, offering asymptotic correctness and improved finite-sample performance.

Contribution

It establishes the validity of the parametric bootstrap for inference in nonlinear panel models with interactive fixed effects, complementing existing bias correction methods.

Findings

Parametric bootstrap replicates the asymptotic distribution of the MLE.

Bootstrap confidence sets have asymptotically correct coverage.

Transformation-based bootstrap improves finite-sample performance.

Abstract

The maximum likelihood estimator in nonlinear panel data models with interactive fixed effects is biased. Several bias correction methods, such as analytical and jackknife approaches, have been proposed to enable valid inference. This paper shows that the parametric bootstrap also enables valid inference in such models. In particular, we show that the parametric bootstrap replicates the asymptotic distribution of the maximum likelihood estimator. Therefore, it yields asymptotically unbiased estimates and confidence sets with asymptotically correct coverage. We also propose a transformation-based bootstrap confidence interval that delivers improved finite-sample performance. Simulation results support the theoretical findings. Finally, we apply the proposed method to examine technological and product market spillover effects on firms' innovation behavior.