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Title: A doubly corrected robust variance estimator for linear GMM Authors:  Byunghoon Kang - Lancaster University (United Kingdom) [presenting]
Abstract: A new finite sample corrected variance estimator for the linear generalized method of moments (GMM) is proposed including the one-step, two-step, and iterated estimators. The formula additionally corrects for the over-identification bias on top of the commonly used finite sample Windmeijer correction, which corrects for the bias from estimating the efficient weight matrix, so is doubly corrected. The over identification bias arises from the fact that the over-identified sample moment condition is nonzero in finite sample while it converges in probability to zero under correct specification. The order of the over-identification bias equals the order of the sample moment condition. Thus, our double correction is higher-order under correct specification. However, our double correction becomes first-order under misspecification because the sample moment condition does not converge in probability to zero. This implies that the conventional variance estimator and the Windmeijer correction are inconsistent, while our doubly corrected variance estimator is consistent even when the moment condition model is misspecified. That is, the proposed formula provides a convenient way to obtain improved inference under correct specification and robustness against misspecification at the same time.