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Empirical Likelihood Methods in Econometrics: Theory and Practice

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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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
Date of revision:
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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  1. Yuichi Kitamura, 2001. "Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Econometrica, Econometric Society, vol. 69(6), pages 1661-1672, November.
  2. Cosslett, Stephen R, 1983. "Distribution-Free Maximum Likelihood Estimator of the Binary Choice Model," Econometrica, Econometric Society, vol. 51(3), pages 765-82, May.
  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, 03.
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