Asymptotic Refinements of a Misspecification-Robust Bootstrap for Generalized Empirical Likelihood Estimators

TL;DR

This paper introduces a robust bootstrap method for empirical likelihood estimators that provides improved inference accuracy and is resilient to model misspecification, supported by theoretical analysis and Monte Carlo simulations.

Contribution

It develops a new bootstrap procedure that achieves asymptotic refinements for empirical likelihood estimators, regardless of model correctness, a novel result in the literature.

Findings

Bootstrap achieves asymptotic refinements for t tests and confidence intervals.

Method is robust to model misspecification.

Application suggests higher returns to schooling than previously estimated.

Abstract

I propose a nonparametric iid bootstrap procedure for the empirical likelihood, the exponential tilting, and the exponentially tilted empirical likelihood estimators that achieves asymptotic refinements for t tests and confidence intervals, and Wald tests and confidence regions based on such estimators. Furthermore, the proposed bootstrap is robust to model misspecification, i.e., it achieves asymptotic refinements regardless of whether the assumed moment condition model is correctly specified or not. This result is new, because asymptotic refinements of the bootstrap based on these estimators have not been established in the literature even under correct model specification. Monte Carlo experiments are conducted in dynamic panel data setting to support the theoretical finding. As an application, bootstrap confidence intervals for the returns to schooling of Hellerstein and Imbens (1999) are calculated. The result suggests that the returns to schooling may be higher.