Convergence Rates of GMM Estimators with Nonsmooth Moments under Misspecification

Byunghoon Kang ; Seojeong Lee ; Juha Song

Byunghoon Kang, Department of Economics, Lancaster University, UK b.kang1@lancaster.ac.uk
Seojeong Lee (Corresponding author), Department of Economics, Seoul National University, South Korea s.jay.lee@snu.ac.kr
Juha Song, Department of Economics, Seoul National University, South Korea yuyuhee2@snu.ac.kr

JEL Classification: C13, C15, C21

Abstract

The asymptotic behavior of generalized method of moments (GMM) estimators depends critically on whether the underlying moment condition model is correctly specified. Hong and Li (2024) showed that GMM estimators with nonsmooth (nondirectionally differentiable) moment functions are at best n^1/3 consistent under misspecification. Through simulations, we verify the decelerated convergence rate of GMM estimators in such cases. For the two-step GMM estimator with an estimated weight matrix, our results align with the 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, Nondifferentiable moment, Instrumental variables quantile regression

Acknowledgments

Lee acknowledges that this work was supported by the New Faculty Startup Fund from Seoul National University.

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