Convergence Rates of GMM Estimators with Nonsmooth Moments under Misspecification

2025/01/16 by Byunghoon Kang, Kang, Byunghoon, Seojeong Lee +2
Mathematics · #Econometrics (econ.EM) #FOS: Economics and business #Statistical Distribution Estimation and Applications #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2501.09540

openalex publication_date 2025/01/16 · openalex created_date 2025/01/18 · openalex updated_date 2026/08/04

Abstract

The asymptotic behavior of GMM estimators depends critically on whether the underlying moment condition model is correctly specified. Hong and Li (2023, Econometric Theory) showed that GMM estimators with nonsmooth (non-directionally differentiable) moment functions are at best n^1/3-consistent under misspecification. Through simulations, we verify the slower convergence rate of GMM estimators in such cases. For the two-step GMM estimator with an estimated weight matrix, our results align with theory. However, for the one-step GMM estimator with the identity weight matrix, the convergence rate remains √(n), even under severe misspecification.

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