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On the finite-sample properties of conditional empirical likelihood estimators


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  • Crudu, Federico
  • Sándor, Zsolt


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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 34116.

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Date of creation: 23 Sep 2011
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Handle: RePEc:pra:mprapa:34116

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

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  1. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 14(3), pages 262-80, July.
  2. Richard Smith, 2005. "Efficient information theoretic inference for conditional moment restrictions," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP14/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. Jerry Hausman & Whitney Newey & Tiemen Woutersen & John Chao & Norman Swanson, 2007. "Instrumental variable estimation with heteroskedasticity and many instruments," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP22/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Fuller, Wayne A, 1977. "Some Properties of a Modification of the Limited Information Estimator," Econometrica, Econometric Society, Econometric Society, vol. 45(4), pages 939-53, May.
  5. Nikolay Gospodinov & Taisuke Otsu, 2008. "Local GMM Estimation of Time Series Models with Conditional Moment Restrictions," Working Papers, Concordia University, Department of Economics 08010, Concordia University, Department of Economics.
  6. Yuichi Kitamura & Gautam Tripathi & Hyungtaik Ahn, 2001. "Empirical Likelihood-Based Inference in Conditional Moment Restriction Models," CIRJE F-Series, CIRJE, Faculty of Economics, University of Tokyo CIRJE-F-124, CIRJE, Faculty of Economics, University of Tokyo.
  7. 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, Elsevier, vol. 138(2), pages 461-487, June.
  8. Manuel A. Domínguez & Ignacio N. Lobato, 2004. "Consistent Estimation of Models Defined by Conditional Moment Restrictions," Econometrica, Econometric Society, Econometric Society, vol. 72(5), pages 1601-1615, 09.
  9. Pascal Lavergne & Valentin Patilea, 2008. "Smooth Minimum Distance Estimation and Testing in Conditional Moment Restrictions Models: Uniform in Bandwidth Theory," Discussion Papers, Department of Economics, Simon Fraser University dp08-08, Department of Economics, Simon Fraser University.
  10. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, Econometric Society, vol. 48(4), pages 817-38, May.
  11. Patrik Guggenberger, 2008. "Finite Sample Evidence Suggesting a Heavy Tail Problem of the Generalized Empirical Likelihood Estimator," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 27(4-6), pages 526-541.
  12. Fiebig, Denzil G, 1985. "Evaluating Estimators without Moments," The Review of Economics and Statistics, MIT Press, MIT Press, vol. 67(3), pages 529-34, August.
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