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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

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 North American Winter Meetings with number 436.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nawm04:436

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Keywords: Asymptotic efficiency; GMM; infinity of moment conditions; reproducing kernel Hilbert space; efficiency bound.;

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References

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  1. BROZE, Laurence & FRANCQ , Christian & ZAKOIAN, Jean-Michel, . "Non-redundancy of high order moment conditions for efficient GMM estimation of weak AR processes," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -1576, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, Elsevier, vol. 34(3), pages 305-334, March.
  3. Carrasco, Marine & Florens, Jean-Pierre, 2002. "Simulation-Based Method of Moments and Efficiency," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(4), pages 482-92, October.
  4. Tauchen, George E. & Gallant, A. Ronald, 1995. "Which Moments to Match," Working Papers, Duke University, Department of Economics 95-20, Duke University, Department of Economics.
  5. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, Elsevier, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245 Elsevier.
  6. Kim, Yangseon & Qian, Hailong & Schmidt, Peter, 1999. "Efficient GMM and MD estimation of autoregressive models," Economics Letters, Elsevier, Elsevier, vol. 62(3), pages 265-270, March.
  7. Marine Carrasco & Jean-Pierre Florens, 2000. "Efficient GMM Estimation Using the Empirical Characteristic Function," Working Papers, Centre de Recherche en Economie et Statistique 2000-33, Centre de Recherche en Economie et Statistique.
  8. Hansen, Lars Peter, 1985. "A method for calculating bounds on the asymptotic covariance matrices of generalized method of moments estimators," Journal of Econometrics, Elsevier, Elsevier, vol. 30(1-2), pages 203-238.
  9. Singleton, Kenneth J., 2001. "Estimation of affine asset pricing models using the empirical characteristic function," Journal of Econometrics, Elsevier, Elsevier, vol. 102(1), pages 111-141, May.
  10. Anatolyev, Stanislav, 2007. "Redundancy Of Lagged Regressors Revisited," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 23(02), pages 364-368, April.
  11. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 8(S), pages S85-118, Suppl. De.
  12. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 1029-54, July.
  13. 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, Institut d'Économie Industrielle (IDEI), Toulouse 116, Institut d'Économie Industrielle (IDEI), Toulouse, revised 2002.
  14. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
  15. Hall, Alastair R., 2004. "Generalized Method of Moments," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780198775201, October.
  16. Kenneth D. West, 2000. "On Optimal Instrumental Variables Estimation of Stationary Time Series Models," NBER Technical Working Papers 0249, National Bureau of Economic Research, Inc.
  17. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, Econometric Society, vol. 55(2), pages 363-90, March.
  18. Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 16(06), pages 797-834, December.
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Cited by:
  1. Gospodinov, Nikolay & Otsu, Taisuke, 2012. "Local GMM estimation of time series models with conditional moment restrictions," Journal of Econometrics, Elsevier, Elsevier, vol. 170(2), pages 476-490.
  2. 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, Elsevier, vol. 140(2), pages 529-573, October.
  3. Eric Ghysels & Jean-Pierre Florens & Mikhail Chernov & Marine Carrasco, 2003. "Efficient Estimation of Jump Diffusions and General Dynamic Models with a Continuum of Moment Conditions," CIRANO Working Papers, CIRANO 2003s-02, CIRANO.

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