Abstract
This paper proposes simple new inference methods for over-identified Generalized Method of Moments (GMM) estimation which correct the standard error bias which arises when moments are possibly misspecified. We focus on the iterated GMM estimator, providing the first rigorous demonstration of existence, and the first distribution theory for iterated GMM under moment misspecification. Our distribution theory is asymptotic, allowing for either independent or clustered samples. Our simulation results show that our methods successfully remove the large biases in inference due to moment 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 finding further supports the conclusion of the former but is in sharp contrast to that of the latter.