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Combining empirical likelihood and generalized method of moments estimators: Asymptotics and higher order bias

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  • Israelov, Roni
  • Lugauer, Steven

Abstract

This paper proposes an estimator combining empirical likelihood (EL) and the generalized method of moments (GMM) by allowing the sample average moment vector to deviate from zero and the sample weights to deviate from n-1. The new estimator may be adjusted through free parameter [delta][set membership, variant](0,1) with GMM behavior attained as [delta][long right arrow]0 and EL as [delta][long right arrow]1. When the sample size is small and the number of moment conditions is large, the parameter space under which the EL estimator is defined may be restricted at or near the population parameter value. The support of the parameter space for the new estimator may be adjusted through [delta]. The new estimator performs well in Monte Carlo simulations.

Suggested Citation

  • Israelov, Roni & Lugauer, Steven, 2011. "Combining empirical likelihood and generalized method of moments estimators: Asymptotics and higher order bias," Statistics & Probability Letters, Elsevier, vol. 81(9), pages 1339-1347, September.
  • Handle: RePEc:eee:stapro:v:81:y:2011:i:9:p:1339-1347
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    References listed on IDEAS

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    1. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    2. Antoine, Bertille & Bonnal, Helene & Renault, Eric, 2007. "On the efficient use of the informational content of estimating equations: Implied probabilities and Euclidean empirical likelihood," Journal of Econometrics, Elsevier, pages 461-487.
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    5. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
    6. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-280, July.
    7. Susanne M. Schennach, 2007. "Point estimation with exponentially tilted empirical likelihood," Papers 0708.1874, arXiv.org.
    8. Giuseppe Ragusa, 2011. "Minimum Divergence, Generalized Empirical Likelihoods, and Higher Order Expansions," Econometric Reviews, Taylor & Francis Journals, vol. 30(4), pages 406-456, August.
    9. Guido W. Imbens, 1997. "One-Step Estimators for Over-Identified Generalized Method of Moments Models," Review of Economic Studies, Oxford University Press, vol. 64(3), pages 359-383.
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