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On The Asymptotic Efficiency Of Gmm

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  • Carrasco, Marine
  • Florens, Jean-Pierre

Abstract

The efficiency of the generalized method of moment (GMM) estimator is addressed by using a characterization of its variance as an inner product in a reproducing kernel Hilbert space. We show that the GMM estimator is asymptotically as efficient as the maximum likelihood estimator if and only if the true score belongs to the closure of the linear space spanned by the moment conditions. This result generalizes former ones to autocorrelated moments and possibly infinite number of moment restrictions. Second, we derive the semiparametric efficiency bound when the observations are known to be Markov and satisfy a conditional moment restriction. We show that it coincides with the asymptotic variance of the optimal GMM estimator, thus extending results by Chamberlain (1987, Journal of Econometrics 34, 305–33) to a dynamic setting. Moreover, this bound is attainable using a continuum of moment conditions.

Suggested Citation

  • Carrasco, Marine & Florens, Jean-Pierre, 2014. "On The Asymptotic Efficiency Of Gmm," Econometric Theory, Cambridge University Press, vol. 30(2), pages 372-406, April.
  • Handle: RePEc:cup:etheor:v:30:y:2014:i:02:p:372-406_00
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    References listed on IDEAS

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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.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Hansen, Lars Peter, 1985. "A method for calculating bounds on the asymptotic covariance matrices of generalized method of moments estimators," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 203-238.
    4. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 85-118, Suppl. De.
    5. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
    6. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    7. West, Kenneth D, 2001. "On Optimal Instrumental Variables Estimation of Stationary Time Series Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(4), pages 1043-1050, November.
    8. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(4), pages 657-681, October.
    9. 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.
    10. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.),Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245, Elsevier.
    11. Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, vol. 16(6), pages 797-834, December.
    12. Kim, Yangseon & Qian, Hailong & Schmidt, Peter, 1999. "Efficient GMM and MD estimation of autoregressive models," Economics Letters, Elsevier, vol. 62(3), pages 265-270, March.
    13. Carrasco, Marine & Florens, Jean-Pierre, 2002. "Simulation-Based Method of Moments and Efficiency," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 482-492, October.
    14. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    15. Hall, Alastair R., 2004. "Generalized Method of Moments," OUP Catalogue, Oxford University Press, number 9780198775201.
    16. Anatolyev, Stanislav, 2007. "Redundancy Of Lagged Regressors Revisited," Econometric Theory, Cambridge University Press, vol. 23(2), pages 364-368, April.
    17. 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.
    18. Singleton, Kenneth J., 2001. "Estimation of affine asset pricing models using the empirical characteristic function," Journal of Econometrics, Elsevier, vol. 102(1), pages 111-141, May.
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    Cited by:

    1. 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.
    2. Dante Amengual & Marine Carrasco & Enrique Sentana, 2017. "Testing Distributional Assumptions Using a Continuum of Moments," Working Papers wp2018_1709, CEMFI.
    3. Carrasco, Marine & Tchuente, Guy, 2015. "Regularized LIML for many instruments," Journal of Econometrics, Elsevier, vol. 186(2), pages 427-442.
    4. 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.
    5. Andrew Bennett & Nathan Kallus, 2020. "Efficient Policy Learning from Surrogate-Loss Classification Reductions," Papers 2002.05153, arXiv.org.
    6. Yang, Xiye, 2020. "Time-invariant restrictions of volatility functionals: Efficient estimation and specification tests," Journal of Econometrics, Elsevier, vol. 215(2), pages 486-516.
    7. 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.
    8. Dante Amengual & Marine Carrasco & Enrique Sentana, 2017. "Testing Distributional Assumptions Using a Continuum of Moments," Working Papers wp2017_1709, CEMFI.
    9. 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.
    10. Shi, Zhentao, 2016. "Econometric estimation with high-dimensional moment equalities," Journal of Econometrics, Elsevier, vol. 195(1), pages 104-119.
    11. 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.

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    JEL classification:

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

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