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On the Asymptotic Efficiency of GMM

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  • Carrasco, Marine
  • Florens, Jean-Pierre

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 Institut d'Économie Industrielle (IDEI), Toulouse in its series IDEI Working Papers with number 173.

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Date of creation: 2003
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Publication status: Published in Econometric Theory, vol.�30, n°2, avril 2014, p.�372-406.
Handle: RePEc:ide:wpaper:1044

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References

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  1. 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.
  2. 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.
  3. 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.
  4. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
  5. Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, vol. 16(06), pages 797-834, December.
  6. Tauchen, George E. & Gallant, A. Ronald, 1995. "Which Moments to Match," Working Papers 95-20, Duke University, Department of Economics.
  7. Marine Carrasco & Jean-Pierre Florens, 2000. "Efficient GMM Estimation Using the Empirical Characteristic Function," Working Papers 2000-33, Centre de Recherche en Economie et Statistique.
  8. Gourieroux, C. & Monfort, A. & Renault, E., 1992. "Indirect Inference," Papers 92.279, Toulouse - GREMAQ.
  9. 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 1043-50, November.
  10. Anatolyev, Stanislav, 2007. "Redundancy Of Lagged Regressors Revisited," Econometric Theory, Cambridge University Press, vol. 23(02), pages 364-368, April.
  11. Hall, Alastair R., 2004. "Generalized Method of Moments," OUP Catalogue, Oxford University Press, number 9780198775201, September.
  12. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
  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 482-92, October.
  14. 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.
  15. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March.
  16. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  17. 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.
  18. 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.
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Citations

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Cited by:
  1. 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 2003s-02, CIRANO.
  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, vol. 140(2), pages 529-573, October.
  3. 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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