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Regularized Empirical Likelihood as a Solution to the No Moment

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  • Pierre Chausse

    (Department of Economics, University of Waterloo)

Abstract

In this paper, we explore the finite sample properties of the generalized empirical likelihood for a continuum, applied to a linear model with endogenous regressors and many discrete moment conditions. In particular, we show that the estimator from this regularized version of GEL has finite moments. It therefore solves the issue regarding the no moment problem of empirical likelihood. We propose a data driven method to select the regularization parameter based on a cross validation criterion, and show that the method outperforms many existing methods when the number of instruments exceeds 20.

Suggested Citation

  • Pierre Chausse, 2017. "Regularized Empirical Likelihood as a Solution to the No Moment," Working Papers 1708, University of Waterloo, Department of Economics, revised Nov 2017.
  • Handle: RePEc:wat:wpaper:1708
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    References listed on IDEAS

    as
    1. 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, January.
    2. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
    3. Jerry A. Hausman & Whitney K. Newey & Tiemen Woutersen & John C. Chao & Norman R. Swanson, 2012. "Instrumental variable estimation with heteroskedasticity and many instruments," Quantitative Economics, Econometric Society, vol. 3(2), pages 211-255, July.
    4. Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, vol. 16(06), pages 797-834, December.
    5. Carrasco, Marine & Kotchoni, Rachidi, 2017. "Efficient Estimation Using The Characteristic Function," Econometric Theory, Cambridge University Press, vol. 33(02), pages 479-526, April.
    6. Patrik Guggenberger, 2008. "Finite Sample Evidence Suggesting a Heavy Tail Problem of the Generalized Empirical Likelihood Estimator," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 526-541.
    7. Jinyong Hahn & Jerry Hausman & Guido Kuersteiner, 2004. "Estimation with weak instruments: Accuracy of higher-order bias and MSE approximations," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 272-306, June.
    8. Hausman, Jerry & Lewis, Randall & Menzel, Konrad & Newey, Whitney, 2011. "Properties of the CUE estimator and a modification with moments," Journal of Econometrics, Elsevier, vol. 165(1), pages 45-57.
    9. Donald, Stephen G & Newey, Whitney K, 2001. "Choosing the Number of Instruments," Econometrica, Econometric Society, vol. 69(5), pages 1161-1191, September.
    10. Carrasco, Marine & Tchuente, Guy, 2015. "Regularized LIML for many instruments," Journal of Econometrics, Elsevier, vol. 186(2), pages 427-442.
    11. Carrasco, Marine, 2012. "A regularization approach to the many instruments problem," Journal of Econometrics, Elsevier, vol. 170(2), pages 383-398.
    12. Smith, Richard J, 1997. "Alternative Semi-parametric Likelihood Approaches to Generalised Method of Moments Estimation," Economic Journal, Royal Economic Society, vol. 107(441), pages 503-519, March.
    13. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-280, July.
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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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