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Empirical Likelihood Methods in Econometrics: Theory and Practice

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  • Yuichi Kitamura

    (Department of Economics, Yale University)

Abstract

Recent developments in empirical likelihood (EL) methods are reviewed. First, to put the method inperspective, 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," CIRJE F-Series CIRJE-F-430, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2006cf430
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    4. Thanasis Stengos & Ximing Wu, 2010. "Information-Theoretic Distribution Test with Application to Normality," Econometric Reviews, Taylor & Francis Journals, vol. 29(3), pages 307-329.
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    6. Xiao, Zhiguo, 2010. "The weighted method of moments approach for moment condition models," Economics Letters, Elsevier, vol. 107(2), pages 183-186, May.
    7. Liao, Yuan & Jiang, Wenxin, 2011. "Posterior consistency of nonparametric conditional moment restricted models," MPRA Paper 38700, University Library of Munich, Germany.
    8. 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.
    9. J. Arismendi-Zambrano & R. Azevedo, 2020. "Implicit Entropic Market Risk-Premium from Interest Rate Derivatives," Economics Department Working Paper Series n303-20.pdf, Department of Economics, National University of Ireland - Maynooth.
    10. 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.
    11. Prosper Dovonon, 2016. "Large Sample Properties of the Three-Step Euclidean Likelihood Estimators under Model Misspecification," Econometric Reviews, Taylor & Francis Journals, vol. 35(4), pages 465-514, April.
    12. Almeida, Caio & Freire, Gustavo, 2022. "Pricing of index options in incomplete markets," Journal of Financial Economics, Elsevier, vol. 144(1), pages 174-205.
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    15. Caio Almeida & René Garcia, 2017. "Economic Implications of Nonlinear Pricing Kernels," Management Science, INFORMS, vol. 63(10), pages 3361-3380, October.
    16. Xu, Ke-Li, 2020. "Inference of local regression in the presence of nuisance parameters," Journal of Econometrics, Elsevier, vol. 218(2), pages 532-560.
    17. Jun Ma & Zhengfei Yu, 2020. "Empirical Likelihood Covariate Adjustment for Regression Discontinuity Designs," Papers 2008.09263, arXiv.org, revised May 2022.
    18. 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.
    19. Yuan, Ao & He, Wenqing & Wang, Binhuan & Qin, Gengsheng, 2012. "U-statistic with side information," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 20-38.
    20. 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.
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