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Large sample properties of the three-step euclidean likelihood estimators under model misspecification

  • Dovonon, Prosper

This paper studies the three-step Euclidean likelihood (3S) estimator and its corrected version as proposed by Antoine, Bonnal and Renault (2007) in globally misspecified models. We establish that the 3S estimator stays √n-convergent and asymptotically Gaussian. The discontinuity in the shrinkage factor makes the analysis of the corrected-3S estimator harder to carry out in misspecified models. We propose a slight modification to this factor to control its rate of divergence in case of misspecification. We show that the resulting modified-3S estimator is also higher order equivalent to the maximum empirical likelihood (EL) estimator in well specified models and √n-convergent and asymptotically Gaussian in misspecified models. Its asymptotic distribution robust to misspecification is also provided. Because of these properties, both the 3S and the modified-3S estimators could be considered as computationally attractive alternatives to the exponentially tilted empirical likelihood estimator proposed by Schennach (2007) which also is higher order equivalent to EL in well specified models and √n-convergent in misspecified models.

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File URL: http://mpra.ub.uni-muenchen.de/40025/1/MPRA_paper_40025.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 40025.

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Date of creation: 18 Nov 2008
Date of revision: 16 May 2010
Handle: RePEc:pra:mprapa:40025
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  1. Susanne M. Schennach, 2007. "Point estimation with exponentially tilted empirical likelihood," Papers 0708.1874, arXiv.org.
  2. Hélène Bonnal & Éric Renault, 2004. "On the Efficient Use of the Informational Content of Estimating Equations: Implied Probabilities and Euclidean Empirical Likelihood," CIRANO Working Papers 2004s-18, CIRANO.
  3. Torben G. Andersen & Hyung-Jin Chung & Bent E. Sorensen, . "EMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study," Computing in Economics and Finance 1997 6, Society for Computational Economics.
  4. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2003. "Empirical likelihood estimation and consistent tests with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 117(1), pages 55-93, November.
  5. Brown, Bryan W & Newey, Whitney K, 2002. "Generalized Method of Moments, Efficient Bootstrapping, and Improved Inference," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 507-17, October.
  6. Back, Kerry & Brown, David P, 1993. "Implied Probabilities in GMM Estimators," Econometrica, Econometric Society, vol. 61(4), pages 971-75, July.
  7. Alastair R. Hall, 2000. "Covariance Matrix Estimation and the Power of the Overidentifying Restrictions Test," Econometrica, Econometric Society, vol. 68(6), pages 1517-1528, November.
  8. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  9. Robinson, Peter M, 1988. "The Stochastic Difference between Econometric Statistics," Econometrica, Econometric Society, vol. 56(3), pages 531-48, May.
  10. Yuichi Kitamura & Gautam Tripathi & Hyungtaik Ahn, 2001. "Empirical Likelihood-Based Inference in Conditional Moment Restriction Models," CIRJE F-Series CIRJE-F-124, CIRJE, Faculty of Economics, University of Tokyo.
  11. Altonji, Joseph G & Segal, Lewis M, 1996. "Small-Sample Bias in GMM Estimation of Covariance Structures," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 353-66, July.
  12. Guido W. Imbens & Richard H. Spady & Phillip Johnson, 1998. "Information Theoretic Approaches to Inference in Moment Condition Models," Econometrica, Econometric Society, vol. 66(2), pages 333-358, March.
  13. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
  14. K. Newey, Whitney, 1985. "Generalized method of moments specification testing," Journal of Econometrics, Elsevier, vol. 29(3), pages 229-256, September.
  15. Yuichi Kitamura, 2001. "Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Econometrica, Econometric Society, vol. 69(6), pages 1661-1672, November.
  16. Patrik Guggenberger, 2008. "Finite Sample Evidence Suggesting a Heavy Tail Problem of the Generalized Empirical Likelihood Estimator," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 526-541.
  17. Raymond Kan & Cesare Robotti, 2009. "Model Comparison Using the Hansen-Jagannathan Distance," Review of Financial Studies, Society for Financial Studies, vol. 22(9), pages 3449-3490, September.
  18. Whitney Newey & Richard Smith, 2003. "Higher order properties of GMM and generalised empirical likelihood estimators," CeMMAP working papers CWP04/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  19. Hall, Alastair R. & Inoue, Atsushi, 2003. "The large sample behaviour of the generalized method of moments estimator in misspecified models," Journal of Econometrics, Elsevier, vol. 114(2), pages 361-394, June.
  20. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  21. Imbens, Guido W. & Spady, Richard, 2002. "Confidence intervals in generalized method of moments models," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 87-98, March.
  22. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
  23. Magdalinos, Michael A. & Symeonides, Spyridon D., 1996. "A reinterpretation of the tests of overidentifying restrictions," Journal of Econometrics, Elsevier, vol. 73(2), pages 325-353, August.
  24. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
  25. Ramalho, Joaquim J. S. & Smith, Richard J., 2002. "Generalized empirical likelihood non-nested tests," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 99-125, March.
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