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Minimum Divergence, Generalized Empirical Likelihoods, and Higher Order Expansions

  • Giuseppe Ragusa

    ()

    (Department of Economics, University of California-Irvine)

This paper studies the Minimum Divergence (MD) class of estimators for econometric models specified through moment restrictions. We show that MD estimators can be obtained as solutions to a computationally tractable optimization problem. This problem is similar to the one solved by the Generalized Empirical Likelihood estimators of Newey and Smith (2004), but it is equivalent to it only for a subclass of divergences. The MD framework provides a coherent testing theory: tests for overidentification and parametric restrictions in this framework can be interpreted as semiparametric versions of Pearson-type goodness of fit tests. The higher order properties of MD estimators are also studied and it is shown that MD estimators that have the same higher order bias as the Empirical Likelihood (EL) estimator also share the same higher order Mean Square Error and are all higher order efficient. We identify members of the MD class that are not only higher order efficient, but, unlike the EL estimator, well behaved when the moment restrictions are misspecified.

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File URL: http://www.economics.uci.edu/files/docs/workingpapers/2008-09/ragusa-06.pdf
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Paper provided by University of California-Irvine, Department of Economics in its series Working Papers with number 080906.

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Length: 45 pages
Date of creation: May 2008
Date of revision:
Handle: RePEc:irv:wpaper:080906
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  1. 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.
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  4. Mittelhammer, Ronald C. & Judge, George G. & Schoenberg, Ron, 2003. "Empirical evidence concerning the finite sample performance of El-type structural equation estimation and inference methods," CUDARE Working Paper Series 945, University of California at Berkeley, Department of Agricultural and Resource Economics and Policy.
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  14. Back, Kerry & Brown, David P, 1993. "Implied Probabilities in GMM Estimators," Econometrica, Econometric Society, vol. 61(4), pages 971-75, July.
  15. Yuichi Kitamura, 2001. "Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Econometrica, Econometric Society, vol. 69(6), pages 1661-1672, November.
  16. Chen, Song Xi & Cui, Hengjian, 2007. "On the second-order properties of empirical likelihood with moment restrictions," Journal of Econometrics, Elsevier, vol. 141(2), pages 492-516, December.
  17. Srinivasan, T N, 1970. "Approximations to Finite Sample Moments of Estimators Whose Exact Sampling Distributions are Unknown," Econometrica, Econometric Society, vol. 38(3), pages 533-41, May.
  18. Susanne M. Schennach, 2007. "Point estimation with exponentially tilted empirical likelihood," Papers 0708.1874, arXiv.org.
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