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A symptotic Bias for GMM and GEL Estimators with Estimated Nuisance Parameter

Author

Listed:
  • Whitney K. Newey

    (Department of Economics, M.I.T.)

  • Joaquim J.S. Ramalho

    (Department of Economics, University of Évora)

  • Richard J. Smith

    (Department of Economics, University of Warwick)

Abstract

This papers studies and compares the asymptotic bias of GMM and generalized empirical likelihood (GEL) estimators in the presence of estimated nuisance parameters. We consider cases in which the nuisance parameter is estimated from independent and identical samples. A simulation experiment is conducted for covariance structure models. Empirical likelihood offers much reduced mean and median bias, root mean squared error and mean absolute error, as compared with two-step GMM and other GEL methods. Both analytical and bootstrap bias-adjusted two-step GMM estima-tors are compared. Analytical bias-adjustment appears to be a serious competitor to bootstrap methods in terms of finite sample bias, root mean squared error and mean absolute error. Finite sample variance seems to be little affected.

Suggested Citation

  • Whitney K. Newey & Joaquim J.S. Ramalho & Richard J. Smith, 2003. "A symptotic Bias for GMM and GEL Estimators with Estimated Nuisance Parameter," Economics Working Papers 5_2003, University of Évora, Department of Economics (Portugal).
    • Handle: RePEc:evo:wpecon:5_2003
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    File URL: http://hdl.handle.net/10174/8401
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    References listed on IDEAS

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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. 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.
    3. Altonji, Joseph G & Segal, Lewis M, 1996. "Small-Sample Bias in GMM Estimation of Covariance Structures," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 353-366, July.
    4. Horowitz, J., 1996. "Bootstrap Critical Values For Tests Based On The Smoothed Maximum Score Estimator," SFB 373 Discussion Papers 1996,44, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. 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.
    6. 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.
    7. Guido W. Imbens & Richard H. Spady & Phillip Johnson, 1998. "Information Theoretic Approaches to Inference in Moment Condition Models," Econometrica, Econometric Society, vol. 66(2), pages 333-358, March.
    8. Guido W. Imbens, 1997. "One-Step Estimators for Over-Identified Generalized Method of Moments Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(3), pages 359-383.
    9. Joel L. Horowitz, 1996. "Bootstrap Critical Values for Tests Based on the Smoothed Maximum Score Estimator," Econometrics 9603003, University Library of Munich, Germany.
    10. Joel L. Horowitz, 1998. "Bootstrap Methods for Covariance Structures," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 39-61.
    11. Joel L. Horowitz, 1996. "Bootstrap Methods For Covariance Structures," Econometrics 9610003, University Library of Munich, Germany.
    12. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
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    14. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
    15. 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.
    16. Pagan, Adrian, 1984. "Econometric Issues in the Analysis of Regressions with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 221-247, February.
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    Citations

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    Cited by:

    1. Smith, Richard J., 2007. "Efficient information theoretic inference for conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 138(2), pages 430-460, June.
    2. 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.
    3. Jeffrey M. Wooldridge, 2004. "Estimating average partial effects under conditional moment independence assumptions," CeMMAP working papers CWP03/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Parente, Paulo M.D.C. & Smith, Richard J., 2011. "Gel Methods For Nonsmooth Moment Indicators," Econometric Theory, Cambridge University Press, vol. 27(1), pages 74-113, February.
    5. Esteban-Bravo, Mercedes & Vidal-Sanz, Jose M., 2007. "Worst-case estimation for econometric models with unobservable components," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3330-3354, April.
    6. Richard Smith, 2005. "Local GEL methods for conditional moment restrictions," CeMMAP working papers CWP15/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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    More about this item

    Keywords

    GMM; Empirical Likelihood; Exponential Tilting; Continuous Updating; Bias; Stochastic Expansions;
    All these keywords.

    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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