A doubly corrected robust variance estimator for linear GMM

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 also corrects the over-identification bias in variance estimation on top of the commonly used finite sample correction of Windmeijer (2005), which corrects 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 double correction formula proposed in this paper provides a convenient way to obtain improved inference under correct specification and robustness against misspecification at the same time. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper proposes a new finite sample corrected variance estimator for linear generalized method of moments (GMM), which can correct the bias from estimating the efficient weight matrix and the over-identification bias in variance estimation. It also automatically provides robustness to misspecification of the moment condition, improving inference under correct specification and robustness against misspecification.