Convergence Rates of GMM Estimators with Nonsmooth Moments under Misspecification

David Kang, Seojeong Lee and Juha Song

No 423283930, Working Papers from Lancaster University Management School, Economics Department

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.

Keywords: generalized method of moments; non-differentiable moment; nstrumental variables quantile regression (search for similar items in EconPapers)
JEL-codes: C13 C15 C21 (search for similar items in EconPapers)
Date: 2025
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Working Paper: Convergence Rates of GMM Estimators with Nonsmooth Moments under Misspecification (2025)
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