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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.

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Bibliographic Info

Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 81 (2011)
Issue (Month): 9 (September)
Pages: 1339-1347

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Handle: RePEc:eee:stapro:v:81:y:2011:i:9:p:1339-1347

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Keywords: Generalized method of moments Empirical likelihood;

References

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  1. 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.
  2. Susanne M. Schennach, 2007. "Point estimation with exponentially tilted empirical likelihood," Papers 0708.1874, arXiv.org.
  3. 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 262-80, July.
  4. 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.
  5. Guido W Imbens, Phillip Johnson & Richard H Spady, . "Information theoretic approaches to inference in moment condition model," Economics Papers W12., Economics Group, Nuffield College, University of Oxford.
  6. Imbens, G.W. & Johnson, P. & Spady, R.H., 1995. "Information Theoretic Approaches to Inference in Movement Condition Models," Economics Papers 99, Economics Group, Nuffield College, University of Oxford.
  7. 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.
  8. Imbens, Guido W, 1997. "One-Step Estimators for Over-Identified Generalized Method of Moments Models," Review of Economic Studies, Wiley Blackwell, vol. 64(3), pages 359-83, July.
  9. Giuseppe Ragusa, 2008. "Minimum Divergence, Generalized Empirical Likelihoods, and Higher Order Expansions," Working Papers 080906, University of California-Irvine, Department of Economics.
  10. 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.
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