Inference for Iterated GMM under Misspecification
with Bruce E. Hansen (University of Wisconsin-Madison), Econometrica (2021) 89(3), 1419-1447
This paper develops inference methods for the iterated over-identified 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 over-sized 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).
Matlab code [updated on Feb 20, 2019]
Replicates Acemoglu, Johnson, Robinson, and Yared (2008, AER) and Cervellati, Jung, Sunde, and Vischer (2014, AER)
Calculates the one-step, two-step, and iterated GMM estimators
Calculates the new misspecification-robust, the Windmeijer (2005, Journal of Econometrics), the conventional GMM standard errors
Figure 1 from the paper. It shows the GMM estimator for each step with the efficient weight matrix evaluated at different initial values. Two researchers using the efficient two-step GMM can reach the opposite conclusions due to different initial values. The iterated estimator converges to the same limit regardless of the initial value.
