Asymptotic Refinements of a Misspecification-Robust Bootstrap for Generalized Method of Moments Estimators

TL;DR

This paper introduces a nonparametric iid bootstrap method that provides asymptotic refinements for GMM-based t tests and confidence intervals, even under model misspecification, without needing recentering of the moment function.

Contribution

It develops a misspecification-robust bootstrap that achieves asymptotic refinements without recentering, linking to GMM theory under misspecification.

Findings

Achieves asymptotic refinements similar to conventional bootstrap methods

Works under model misspecification without recentering

Validated through examples involving data combination and invalid instruments

Abstract

I propose a nonparametric iid bootstrap that achieves asymptotic refinements for t tests and confidence intervals based on GMM estimators even when the model is misspecified. In addition, my bootstrap does not require recentering the moment function, which has been considered as critical for GMM. Regardless of model misspecification, the proposed bootstrap achieves the same sharp magnitude of refinements as the conventional bootstrap methods which establish asymptotic refinements by recentering in the absence of misspecification. The key idea is to link the misspecified bootstrap moment condition to the large sample theory of GMM under misspecification of Hall and Inoue (2003). Two examples are provided: Combining data sets and invalid instrumental variables.