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

  • 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)

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.

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Paper provided by University of Évora, Department of Economics (Portugal) in its series Economics Working Papers with number 5_2003.

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Length: 41 pages
Date of creation: 2003
Date of revision:
Handle: RePEc:evo:wpecon:5_2003
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  1. Imbens, Guido W, 1997. "One-Step Estimators for Over-Identified Generalized Method of Moments Models," Review of Economic Studies, Wiley Blackwell, vol. 64(3), pages 359-83, July.
  2. Guido W. Imbens & Phillip Johnson & Richard H. Spady, 1995. "Information Theoretic Approaches to Inference in Moment Condition Models," NBER Technical Working Papers 0186, National Bureau of Economic Research, Inc.
  3. 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.
  4. Smith, Richard J, 1997. "Alternative Semi-parametric Likelihood Approaches to Generalised Method of Moments Estimation," Economic Journal, Royal Economic Society, vol. 107(441), pages 503-19, March.
  5. 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 262-80, July.
  6. Heckman, James J, 1979. "Sample Selection Bias as a Specification Error," Econometrica, Econometric Society, vol. 47(1), pages 153-61, January.
  7. Joel L. Horowitz, 1996. "Bootstrap Methods For Covariance Structures," Econometrics 9610003, EconWPA.
  8. 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 221-47, February.
  9. Whitney Newey & Richard Smith, 2003. "Higher order properties of GMM and generalised empirical likelihood estimators," CeMMAP working papers CWP04/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  10. Arulampalam, W. & Robin A. Naylor & Jeremy P. Smith, 2002. "University of Warwick," Royal Economic Society Annual Conference 2002 9, Royal Economic Society.
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