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On the finite-sample properties of conditional empirical likelihood estimators

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  • Crudu, Federico
  • Sándor, Zsolt

Abstract

We provide Monte Carlo evidence on the finite sample behavior of the conditional empirical likelihood (CEL) estimator of Kitamura, Tripathi, and Ahn (2004) and the conditional Euclidean empirical likelihood (CEEL) estimator of Antoine, Bonnal, and Renault (2007) in the context of a heteroskedastic linear model with an endogenous regressor. We compare these estimators with three heteroskedasticity-consistent instrument-based estimators in terms of various performance measures. Our results suggest that the CEL and CEEL with fixed bandwidths may suffer from the no-moment problem, similarly to the unconditional generalized empirical likelihood estimators studied by Guggenberger (2008). We also study the CEL and CEEL estimators with automatic bandwidths selected through cross-validation. We do not find evidence that these suffer from the no-moment problem. When the instruments are weak, we find CEL and CEEL to have finite sample properties --in terms of mean squared error and coverage probability of confidence intervals-- poorer than the heteroskedasticity-consistent Fuller (HFUL) estimator. In the strong instruments case the CEL and CEEL estimators with automatic bandwidths tend to outperform HFUL in terms of mean squared error, while the reverse holds in terms of the coverage probability, although the differences in numerical performance are rather small.

Suggested Citation

  • Crudu, Federico & Sándor, Zsolt, 2011. "On the finite-sample properties of conditional empirical likelihood estimators," MPRA Paper 34116, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:34116
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    File URL: https://mpra.ub.uni-muenchen.de/34116/1/MPRA_paper_34116.pdf
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    References listed on IDEAS

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    1. Fiebig, Denzil G, 1985. "Evaluating Estimators without Moments," The Review of Economics and Statistics, MIT Press, vol. 67(3), pages 529-534, August.
    2. Manuel A. Domínguez & Ignacio N. Lobato, 2004. "Consistent Estimation of Models Defined by Conditional Moment Restrictions," Econometrica, Econometric Society, vol. 72(5), pages 1601-1615, September.
    3. Antoine, Bertille & Bonnal, Helene & Renault, Eric, 2007. "On the efficient use of the informational content of estimating equations: Implied probabilities and Euclidean empirical likelihood," Journal of Econometrics, Elsevier, vol. 138(2), pages 461-487, June.
    4. Fuller, Wayne A, 1977. "Some Properties of a Modification of the Limited Information Estimator," Econometrica, Econometric Society, vol. 45(4), pages 939-953, May.
    5. 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.
    6. Pascal Lavergne & Valentin Patilea, 2008. "Smooth Minimum Distance Estimation and Testing in Conditional Moment Restrictions Models: Uniform in Bandwidth Theory," Discussion Papers dp08-08, Department of Economics, Simon Fraser University.
    7. 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.
    8. Yuichi Kitamura & Gautam Tripathi & Hyungtaik Ahn, 2004. "Empirical Likelihood-Based Inference in Conditional Moment Restriction Models," Econometrica, Econometric Society, vol. 72(6), pages 1667-1714, November.
    9. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    10. Smith, Richard J., 2007. "Efficient information theoretic inference for conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 138(2), pages 430-460, June.
    11. 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.
    12. Gospodinov, Nikolay & Otsu, Taisuke, 2012. "Local GMM estimation of time series models with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 170(2), pages 476-490.
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    Keywords

    Conditional empirical likelihood; conditional Euclidean likelihood; heteroskedasticity; weak instruments; cross-validation;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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