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Efficiency bounds for moment condition models with mixed identification strength

Author

Listed:
  • Prosper Dovonon

    (Concordia University)

  • Yves F. Atchadé

    (Boston University)

  • Firmin Doko Tchatoka

    (School of Economics & Public Policy, The University of Adelaide)

Abstract

Moment condition models with mixed identification strength are models that are point identified but with estimating moment functions that are allowed to drift to 0 uniformly over the parameter space. Even though identification fails in the limit, depending on how slow the moment functions vanish, consistent estimation is possible. Existing estimators such as the generalized method of moment (GMM) estimator exhibit a pattern of nonstandard or even heterogeneous rate of convergence that materializes by some parameter directions being estimated at a slower rate than others. This paper derives asymptotic semiparametric efficiency bounds for regular estimators of parameters of these models. We show that GMM estimators are regular and that the so-called two-step GMM estimator – using the inverse of estimating function’s variance as weighting matrix – is semiparametrically efficient as it reaches the minimum variance attainable by regular estimators. This estimator is also asymptotically minimax efficient with respect to a large family of loss functions. Monte Carlo simulations are provided that confirm these results.

Suggested Citation

  • Prosper Dovonon & Yves F. Atchadé & Firmin Doko Tchatoka, 2023. "Efficiency bounds for moment condition models with mixed identification strength," School of Economics and Public Policy Working Papers 2023-01 Classification-C0, University of Adelaide, School of Economics and Public Policy.
  • Handle: RePEc:adl:wpaper:2023-01
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    References listed on IDEAS

    as
    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Phillips, P C B, 1980. "The Exact Distribution of Instrumental Variable Estimators in an Equation Containing n + 1 Endogenous Variables," Econometrica, Econometric Society, vol. 48(4), pages 861-878, May.
    3. Donald W. K. Andrews & Xu Cheng, 2012. "Estimation and Inference With Weak, Semi‐Strong, and Strong Identification," Econometrica, Econometric Society, vol. 80(5), pages 2153-2211, September.
    4. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    5. Antoine, Bertille & Renault, Eric, 2012. "Efficient minimum distance estimation with multiple rates of convergence," Journal of Econometrics, Elsevier, vol. 170(2), pages 350-367.
    6. Tetsuya Kaji, 2021. "Theory of Weak Identification in Semiparametric Models," Econometrica, Econometric Society, vol. 89(2), pages 733-763, March.
    7. Antoine, Bertille & Renault, Eric, 2020. "Testing identification strength," Journal of Econometrics, Elsevier, vol. 218(2), pages 271-293.
    8. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    9. Sukjin Han & Adam McCloskey, 2019. "Estimation and inference with a (nearly) singular Jacobian," Quantitative Economics, Econometric Society, vol. 10(3), pages 1019-1068, July.
    10. James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
    11. Isaiah Andrews & Anna Mikusheva, 2022. "Optimal Decision Rules for Weak GMM," Econometrica, Econometric Society, vol. 90(2), pages 715-748, March.
    12. Bertille Antoine & Eric Renault, 2009. "Efficient GMM with nearly-weak instruments," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 135-171, January.
    13. Hahn, Jinyong & Kuersteiner, Guido, 2002. "Discontinuities of weak instrument limiting distributions," Economics Letters, Elsevier, vol. 75(3), pages 325-331, May.
    14. Prosper Dovonon & Yves F. Atchadé, 2020. "Efficiency bounds for semiparametric models with singular score functions," Econometric Reviews, Taylor & Francis Journals, vol. 39(6), pages 612-648, July.
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    More about this item

    Keywords

    Generalized method of moments; mixed identification strength; weak identification; estimation; efficiency bounds; semiparametric models.;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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