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Convergence Rates of GMM Estimators with Nonsmooth Moments under Misspecification

Author

Listed:
  • David Kang
  • Seojeong Lee
  • Juha Song

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.

Suggested Citation

  • David Kang & Seojeong Lee & Juha Song, 2025. "Convergence Rates of GMM Estimators with Nonsmooth Moments under Misspecification," Working Papers 423283930, Lancaster University Management School, Economics Department.
    • Handle: RePEc:lan:wpaper:423283930
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    Keywords

    generalized method of moments; non-differentiable moment; nstrumental variables quantile regression;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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