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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.

Suggested Citation

  • Yuichi Kitamura, 2006. "Empirical Likelihood Methods in Econometrics: Theory and Practice," Cowles Foundation Discussion Papers 1569, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1569
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d15/d1569.pdf
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    1. Cosslett, Stephen R, 1983. "Distribution-Free Maximum Likelihood Estimator of the Binary Choice Model," Econometrica, Econometric Society, vol. 51(3), pages 765-782, May.
    2. Yuichi Kitamura, 2001. "Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Econometrica, Econometric Society, vol. 69(6), pages 1661-1672, November.
    3. Francesco Bravo, 2005. "Blockwise empirical entropy tests for time series regressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(2), pages 185-210, March.
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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. Caio Almeida & René Garcia, 2017. "Economic Implications of Nonlinear Pricing Kernels," Management Science, INFORMS, vol. 63(10), pages 3361-3380, October.
    3. Xu, Ke-Li, 2020. "Inference of local regression in the presence of nuisance parameters," Journal of Econometrics, Elsevier, vol. 218(2), pages 532-560.
    4. Devereux, Paul J. & Tripathi, Gautam, 2009. "Optimally combining censored and uncensored datasets," Journal of Econometrics, Elsevier, vol. 151(1), pages 17-32, July.
    5. Gishan Dissanaike & Amir Amel-Zadeh, 2007. ""Discussion of" Venture Capitalists, Business Angels, and Performance of Entrepreneurial IPOs in the UK and France," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 34(3-4), pages 529-540.
    6. Yuichi Kitamura & Taisuke Otsu & Kirill Evdokimov, 2013. "Robustness, Infinitesimal Neighborhoods, and Moment Restrictions," Econometrica, Econometric Society, vol. 81(3), pages 1185-1201, May.
    7. 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.
    8. 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.
    9. Xiao, Zhiguo, 2010. "The weighted method of moments approach for moment condition models," Economics Letters, Elsevier, vol. 107(2), pages 183-186, May.
    10. George A Vamvoukas, 2012. "Panel data modelling and the tax-spend controversy in the euro zone," Applied Economics, Taylor & Francis Journals, vol. 44(31), pages 4073-4085, November.
    11. 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.
    12. Stefan Boes, 2007. "Count Data Models with Unobserved Heterogeneity: An Empirical Likelihood Approach," SOI - Working Papers 0704, Socioeconomic Institute - University of Zurich.

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    More about this item

    Keywords

    Convex analysis; Empirical distribution; GNP-optimality; Large deviation principle; Moment restriction models; Nonparametric test; NPMLE; Semiparametric efficiency; Weak dependence;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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