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On the Asymptotic Efficiency of GMM

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  • Jean-Pierre Florens
  • Marine Carrasco

Abstract

This paper derives conditions under which the generalized method of moments (GMM) estimator is as efficient as the maximum likelihood estimator (MLE). The data are supposed to be drawn from a parametric family and to be stationary Markov. We study the efficiency of GMM in a general framework where the set of moment conditions may be finite, countable infinite, or a continuum. Our main result is the following. GMM estimator is efficient if and only if the true score belongs to the closure of the linear space spanned by the moment conditions. This result extends former ones in two dimensions: (a) the moments may be correlated, (b) the number of moment restrictions may be infinite. It suggests a way to construct estimators that are as efficient as MLE. In the last part of this paper, we show how to calculate the greatest lower bound of instrumental variable estimators

Suggested Citation

  • Jean-Pierre Florens & Marine Carrasco, 2004. "On the Asymptotic Efficiency of GMM," Econometric Society 2004 North American Winter Meetings 436, Econometric Society.
    • Handle: RePEc:ecm:nawm04:436
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    1. Broze, Laurence & Francq, Christian & Zakoian, Jean-Michel, 2001. "Non-redundancy of high order moment conditions for efficient GMM estimation of weak AR processes," Economics Letters, Elsevier, vol. 71(3), pages 317-322, June.
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    10. Marine Carrasco & Jean-Pierre Florens, 2000. "Efficient GMM Estimation Using the Empirical Characteristic Function," Working Papers 2000-33, Center for Research in Economics and Statistics.
    11. Carrasco, Marine & Chernov, Mikhaël & Florens, Jean-Pierre & Ghysels, Eric, 2000. "Efficient Estimation of Jump Diffusions and General Dynamic Models with a Continuum of Moment Conditions," IDEI Working Papers 116, Institut d'Économie Industrielle (IDEI), Toulouse, revised 2002.
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    Citations

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    Cited by:

    1. Dante Amengual & Marine Carrasco & Enrique Sentana, 2017. "Testing Distributional Assumptions Using a Continuum of Moments," Working Papers wp2018_1709, CEMFI.
    2. Carrasco, Marine & Tchuente, Guy, 2015. "Regularized LIML for many instruments," Journal of Econometrics, Elsevier, vol. 186(2), pages 427-442.
    3. Carrasco, Marine & Chernov, Mikhaël & Florens, Jean-Pierre & Ghysels, Eric, 2000. "Efficient Estimation of Jump Diffusions and General Dynamic Models with a Continuum of Moment Conditions," IDEI Working Papers 116, Institut d'Économie Industrielle (IDEI), Toulouse, revised 2002.
    4. Yang, Xiye, 2020. "Time-invariant restrictions of volatility functionals: Efficient estimation and specification tests," Journal of Econometrics, Elsevier, vol. 215(2), pages 486-516.
    5. Shi, Zhentao, 2016. "Econometric estimation with high-dimensional moment equalities," Journal of Econometrics, Elsevier, vol. 195(1), pages 104-119.
    6. Amengual, Dante & Carrasco, Marine & Sentana, Enrique, 2020. "Testing distributional assumptions using a continuum of moments," Journal of Econometrics, Elsevier, vol. 218(2), pages 655-689.
    7. Gospodinov, Nikolay & Otsu, Taisuke, 2012. "Local GMM estimation of time series models with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 170(2), pages 476-490.
    8. Kim, Alex Jiyoung & Jang, Sungha & Shin, Hyun S., 2021. "How should retail advertisers manage multiple keywords in paid search advertising?," Journal of Business Research, Elsevier, vol. 130(C), pages 539-551.
    9. Carrasco, Marine & Chernov, Mikhail & Florens, Jean-Pierre & Ghysels, Eric, 2007. "Efficient estimation of general dynamic models with a continuum of moment conditions," Journal of Econometrics, Elsevier, vol. 140(2), pages 529-573, October.
    10. Andrew Bennett & Nathan Kallus, 2020. "Efficient Policy Learning from Surrogate-Loss Classification Reductions," Papers 2002.05153, arXiv.org.
    11. Zhou, Ling & Lin, Huazhen & Chen, Kani & Liang, Hua, 2019. "Efficient estimation and computation of parameters and nonparametric functions in generalized semi/non-parametric regression models," Journal of Econometrics, Elsevier, vol. 213(2), pages 593-607.
    12. Richard A. Davis & Thiago do Rêgo Sousa & Claudia Klüppelberg, 2021. "Indirect inference for time series using the empirical characteristic function and control variates," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(5-6), pages 653-684, September.
    13. Gagliardini, Patrick & Gouriéroux, Christian, 2019. "Identification by Laplace transforms in nonlinear time series and panel models with unobserved stochastic dynamic effects," Journal of Econometrics, Elsevier, vol. 208(2), pages 613-637.
    14. Christopher D. Walker, 2024. "Semiparametric Bayesian Inference for a Conditional Moment Equality Model," Papers 2410.16017, arXiv.org.
    15. Andrew Fleck & Edward Furman & Yang Shen, 2024. "Stochastic Loss Reserving: Dependence and Estimation," Papers 2410.14985, arXiv.org.

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    More about this item

    Keywords

    Asymptotic efficiency; GMM; infinity of moment conditions; reproducing kernel Hilbert space; efficiency bound.;
    All these keywords.

    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables

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