No abstract

I propose an alternative bootstrap procedure for the generalized method of moments (GMM) estimators that achieves asymptotic refinements for t tests and confidence intervals. I extend the results in the existing literature by establishing the same magnitude of asymptotic refinements without recentering the bootstrap moment function and without assuming correct specification of the moment condition model. As a result, the proposed bootstrap is robust to model misspecification, while the conventional bootstrap is not. The key procedure is to use a misspecification-robust variance estimator for GMM in constructing the t statistic and confidence intervals. Two examples of overidentified and possibly misspecified moment condition models are provided: (i) Combining data sets, and (ii) using invalid instrumental variables. Monte Carlo simulation results are provided as well.

This paper develops inference methods for the iterated overidentified Generalized Method of Moments (GMM) estimator. We provide conditions for the existence of the iterated estimator and an asymptotic distribution theory, which allows for mild misspecification. Moment misspecification causes bias in conventional GMM variance estimators, which can lead to severely oversized hypothesis tests. We show how to consistently estimate the correct asymptotic variance matrix. Our simulation results show that our methods are properly sized under both correct specification and mild to moderate misspecification. We illustrate the method with an application to the model of Acemoglu, Johnson, Robinson, and Yared (2008).

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 heteroskedasticityrobust 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 arbitrariness 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.

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. Formal stochastic expansions are derived to show the proposed double correction estimates the variance of some higher-order terms in the expansion. In addition, the proposed double correction 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.