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Empirical Likelihood Methods in Econometrics: Theory and Practice

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    Abstract

    Recent developments in empirical likelihood (EL) methods are reviewed. First, to put the method in perspective, two interpretations of empirical likelihood are presented, one as a nonparametric maximum likelihood estimation method (NPMLE) and the other as a generalized minimum contrast estimator (GMC). The latter interpretation provides a clear connection between EL, GMM, GEL and other related estimators. Second, EL is shown to have various advantages over other methods. The theory of large deviations demonstrates that EL emerges naturally in achieving asymptotic optimality both for estimation and testing. Interestingly, higher order asymptotic analysis also suggests that EL is generally a preferred method. Third, extensions of EL are discussed in various settings, including estimation of conditional moment restriction models, nonparametric specification testing and time series models. Finally, practical issues in applying EL to real data, such as computational algorithms for EL, are discussed. Numerical examples to illustrate the efficacy of the method are presented.

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    File URL: http://cowles.econ.yale.edu/P/cd/d15b/d1569.pdf
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    Bibliographic Info

    Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1569.

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    Length: 66 pages
    Date of creation: Jun 2006
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    Publication status: Published in Richard Blundell, W.K. Newey, and T. Persson, eds., Advances in Economics and Econometrics: Theory and Applications, Ninth World Congress, vol. 3, Cambridge University Press, 2007, Ch. 7
    Handle: RePEc:cwl:cwldpp:1569

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    Related research

    Keywords: Convex analysis; Empirical distribution; GNP-optimality; Large deviation principle; Moment restriction models; Nonparametric test; NPMLE; Semiparametric efficiency; Weak dependence;

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    1. Francesco Bravo, 2005. "Blockwise empirical entropy tests for time series regressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(2), pages 185-210, 03.
    2. Yuichi Kitamura, 2001. "Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Econometrica, Econometric Society, vol. 69(6), pages 1661-1672, November.
    3. Cosslett, Stephen R, 1983. "Distribution-Free Maximum Likelihood Estimator of the Binary Choice Model," Econometrica, Econometric Society, vol. 51(3), pages 765-82, May.
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    Cited by:
    1. Xu, Ke-Li, 2009. "Empirical likelihood-based inference for nonparametric recurrent diffusions," Journal of Econometrics, Elsevier, vol. 153(1), pages 65-82, November.
    2. Stefan Boes, 2007. "Count Data Models with Unobserved Heterogeneity: An Empirical Likelihood Approach," SOI - Working Papers 0704, Socioeconomic Institute - University of Zurich.
    3. Yuichi Kitamura & Taisuke Otsu & Kirill Evdokimov, 2009. "Robustness, Infinitesimal Neighborhoods, and Moment Restrictions," Cowles Foundation Discussion Papers 1720, Cowles Foundation for Research in Economics, Yale University.
    4. Lehmann, Bruce N., 2009. "The role of beliefs in inference for rational expectations models," Journal of Econometrics, Elsevier, vol. 150(2), pages 322-331, June.
    5. Canay, Ivan A., 2010. "EL inference for partially identified models: Large deviations optimality and bootstrap validity," Journal of Econometrics, Elsevier, vol. 156(2), pages 408-425, June.
    6. Zhiguo Xiao, 2011. "Efficient Estimation of Moment Condition Models with Heterogenous Populations," Annals of Economics and Finance, Society for AEF, vol. 12(1), pages 89-107, May.
    7. Xiao, Zhiguo, 2010. "The weighted method of moments approach for moment condition models," Economics Letters, Elsevier, vol. 107(2), pages 183-186, May.
    8. Devereux, Paul J. & Tripathi, Gautam, 2009. "Optimally combining censored and uncensored datasets," Journal of Econometrics, Elsevier, vol. 151(1), pages 17-32, July.

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