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Inference for Iterated GMM Under Misspecification and Clustering

Bruce Hansen () and Seojeong Lee ()
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Bruce Hansen: Department of Economics, University of Wisconsin-Madison

No 2018-07, Discussion Papers from School of Economics, The University of New South Wales

Abstract: This paper develops a new distribution theory and inference methods for over-identified Generalized Method of Moments (GMM) estimation focusing on the iterated GMM estimator, allowing for moment misspecification, and for clustered dependence with heterogeneous and growing cluster sizes. This paper is the first to provide a rigorous theory for the iterated GMM estimator. We provide conditions for its existence by demonstrating that the iteration sequence is a contraction mapping. Our asymptotic theory allows the moments to be possibly misspecified, which is a general feature of approximate over-identified models. This form of moment misspecification causes bias in conventional standard error estimation. Our results show how to correct for this standard error bias. Our paper is also the first to provide a rigorous distribution theory for the GMM estimator under cluster dependence. Our distribution theory is asymptotic, and allows for heterogeneous and growing cluster sizes. Our results cover standard smooth moment condition models, including dynamic panels, which is a common application for GMM with cluster dependence. Our simulation results show that conventional heteroskedasticity-robust standard errors are highly biased under moment misspecification, severely understating estimation uncertainty, and resulting in severely over-sized hypothesis tests. In contrast, our misspecification-robust standard errors are approximately unbiased and properly sized under both correct specification and misspecification. We illustrate the method by extending the empirical work reported in Acemoglu, Johnson, Robinson, and Yared (2008, American Economic Review) and Cervellati, Jung, Sunde, and Vischer (2014, American Economic Review). Our results reveal an enormous effect of iterating the GMM estimator, demonstrating the arbitrari- ness of using one-step and two-step estimators. Our results also show a large effect of using misspecification robust standard errors instead of the Arellano-Bond standard errors. Our results support Acemoglu, Johnson, Robinson, and Yared’s conclusion of an insignificant effect of income on democracy, but reveal that the heterogeneous effects documented by Cervellati, Jung, Sunde, and Vischer are less statistically significant than previously claimed.

Keywords: generalized method of moments; misspecification; clustering; robust inference; contraction mapping (search for similar items in EconPapers)
JEL-codes: C12 C13 C31 C33 C36 (search for similar items in EconPapers)
Pages: 40 pages
Date: 2018-04
New Economics Papers: this item is included in nep-ecm
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