A Doubly Corrected Robust Variance Estimator for Linear GMM

TL;DR

This paper introduces a doubly corrected finite sample variance estimator for linear GMM that improves inference accuracy and robustness, especially under model misspecification, by correcting for both over-identification bias and estimation bias.

Contribution

It presents a novel variance estimator for linear GMM that combines finite sample correction with over-identification bias correction, enhancing robustness to misspecification.

Findings

The proposed estimator is doubly corrected for bias.

It provides consistent inference under misspecification.

Simulation results show improved accuracy over existing methods.

Abstract

We propose a new finite sample corrected variance estimator for the linear generalized method of moments (GMM) including the one-step, two-step, and iterated estimators. Our formula additionally corrects for the over-identification bias in variance estimation on top of the commonly used finite sample correction of Windmeijer (2005) which corrects for the bias from estimating the efficient weight matrix, so is doubly corrected. An important feature of the proposed double correction is that it automatically provides robustness to misspecification of the moment condition. In contrast, the conventional variance estimator and the Windmeijer correction are inconsistent under misspecification. That is, the proposed double correction formula provides a convenient way to obtain improved inference under correct specification and robustness against misspecification at the same time.