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An Averaging GMM Estimator Robust to Misspecification

Author

Listed:
  • Ruoyao Shi

    (Department of Economics, University of California Riverside)

  • Zhipeng Liao

    (UCLA Economics)

Abstract

This paper studies the averaging GMM estimator that combines a conservative GMM estimator based on valid moment conditions and an aggressive GMM estimator based on both valid and possibly misspecified moment conditions, where the weight is the sample analog of an infeasible optimal weight. We establish asymptotic theory on uniform approximation of the upper and lower bounds of the finite-sample truncated risk difference between any two estimators, which is used to compare the averaging GMM estimator and the conservative GMM estimator. Under some sufficient conditions, we show that the asymptotic lower bound of the truncated risk difference between the averaging estimator and the conservative estimator is strictly less than zero, while the asymptotic upper bound is zero uniformly over any degree of misspecification. Extending seminal results on the James-Stein estimator, this uniform dominance is established in non-Gaussian semiparametric nonlinear models. The simulation results support our theoretical findings.

Suggested Citation

  • Ruoyao Shi & Zhipeng Liao, 2018. "An Averaging GMM Estimator Robust to Misspecification," Working Papers 201803, University of California at Riverside, Department of Economics.
    • Handle: RePEc:ucr:wpaper:201803
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    References listed on IDEAS

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