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Minimum Divergence, Generalized Empirical Likelihoods, and Higher Order Expansions

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Author Info
Giuseppe Ragusa () (Department of Economics, University of California-Irvine)

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Abstract

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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Publisher Info
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
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Handle: RePEc:irv:wpaper:080906

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Related research
Keywords: Minimum divergence; GMM; Generalized empirical likelihood; Higher order efficiency; Misspecified models;

Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data

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  1. Rothenberg, Thomas J., 1984. "Approximating the distributions of econometric estimators and test statistics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 15, pages 881-935 Elsevier. [Downloadable!] (restricted)
  2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July. [Downloadable!] (restricted)
  3. Ron Mittelhammer & George Judge & Ron Schoenberg, 2003. "Empirical Evidence Concerning the Finite Sample Performance of EL-Type Structural Equation Estimation and Inference Methods," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series 945, Department of Agricultural & Resource Economics, UC Berkeley. [Downloadable!]
  4. 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, 01. [Downloadable!] (restricted)
    Other versions:
  5. Yoon-Jae Whang, 2003. "Smoothed Empirical Likelihood Methods for Quantile Regression Models," Econometrics 0310005, EconWPA. [Downloadable!]
    Other versions:
  6. 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.
    Other versions:
  7. Sargan, J D, 1974. "The Validity of Nagar's Expansion for the Moments of Econometric Estimators," Econometrica, Econometric Society, vol. 42(1), pages 169-76, January. [Downloadable!] (restricted)
  8. Bryan W. Brown & Whitney K. Newey, 1998. "Efficient Semiparametric Estimation of Expectations," Econometrica, Econometric Society, vol. 66(2), pages 453-464, March.
  9. Back, Kerry & Brown, David P, 1993. "Implied Probabilities in GMM Estimators," Econometrica, Econometric Society, vol. 61(4), pages 971-75, July. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
  11. Naoto Kunitomo & Yukitoshi Matsushita, 2003. "On Finite Sample Distributions of the Empirical Likelihood Estimator and the GMM Estimator," CIRJE F-Series CIRJE-F-200, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  12. Imbens, Guido W, 2002. "Generalized Method of Moments and Empirical Likelihood," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 493-506, October.
  13. Yuichi Kitamura, 2001. "Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Econometrica, Econometric Society, vol. 69(6), pages 1661-1672, November. [Downloadable!] (restricted)
  14. 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. [Downloadable!]
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  15. 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.
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