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GMM, GEL, Serial Correlation, and Asymptotic Bias

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  • Stanislav Anatolyev

Abstract

For stationary time series models with serial correlation, we consider generalized method of moments (GMM) estimators that use heteroskedasticity and autocorrelation consistent (HAC) positive definite weight matrices and generalized empirical likelihood (GEL) estimators based on smoothed moment conditions. Following the analysis of Newey and Smith (2004) for independent observations, we derive second order asymptotic biases of these estimators. The inspection of bias expressions reveals that the use of smoothed GEL, in contrast to GMM, removes the bias component associated with the correlation between the moment function and its derivative, while the bias component associated with third moments depends on the employed kernel function. We also analyze the case of no serial correlation, and find that the seemingly unnecessary smoothing and HAC estimation can reduce the bias for some of the estimators. Copyright The Econometric Society 2005.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 73 (2005)
Issue (Month): 3 (05)
Pages: 983-1002

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Handle: RePEc:ecm:emetrp:v:73:y:2005:i:3:p:983-1002

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Cited by:
  1. Seojeong Lee, 2014. "Asymptotic Refinements of a Misspecification-Robust Bootstrap for GEL Estimators," Discussion Papers 2014-02, School of Economics, The University of New South Wales.
  2. Yoshitsugu Kitazawa, 2014. "Consistent estimation for the full-fledged fixed effects zero-inflated Poisson model," Discussion Papers 66, Kyushu Sangyo University, Faculty of Economics.
  3. Martins, Luis F. & Gabriel, Vasco J., 2009. "New Keynesian Phillips Curves and potential identification failures: A Generalized Empirical Likelihood analysis," Journal of Macroeconomics, Elsevier, vol. 31(4), pages 561-571, December.
  4. Anatolyev, Stanislav, 2008. "Method-of-moments estimation and choice of instruments: Numerical computations," Economics Letters, Elsevier, vol. 100(2), pages 217-220, August.
  5. McAdam, Peter & Willman, Alpo, 2011. "Technology, utilization and inflation: what drives the New Keynesian Phillips Curve?," Working Paper Series 1369, European Central Bank.
  6. Guggenberger, Patrik & Ramalho, Joaquim J.S. & Smith, Richard J., 2012. "GEL statistics under weak identification," Journal of Econometrics, Elsevier, vol. 170(2), pages 331-349.
  7. Paul Levine & Luis F. Martins & Vasco J. Gabriel, 2006. "Robust Estimates of the New Keynesian Phillips Curve," School of Economics Discussion Papers 0206, School of Economics, University of Surrey.
  8. Alain Guay & Jean-Francois Lamarche, 2005. "The Information Content of Implied Probabilities to Detect Structural Change," Working Papers 0804, Brock University, Department of Economics, revised Oct 2008.
  9. Allen, Jason & Gregory, Allan W. & Shimotsu, Katsumi, 2010. "Empirical Likelihood Block Bootstrapping," Discussion Papers 2010-01, Graduate School of Economics, Hitotsubashi University.
  10. Nikolay Gospodinov & Taisuke Otsu, 2008. "Local GMM Estimation of Time Series Models with Conditional Moment Restrictions," Working Papers 08010, Concordia University, Department of Economics.
  11. Iglesias, Emma M. & Phillips, Garry D.A., 2008. "Asymptotic bias of GMM and GEL under possible nonstationary spatial dependence," Economics Letters, Elsevier, vol. 99(2), pages 393-397, May.
  12. Stanislav Anatolyev, 2005. "Optimal Instruments in Time Series: A Survey," Working Papers w0069, Center for Economic and Financial Research (CEFIR).
  13. Vasco Gabriel & Paul Levine & Christopher Spencer & Bo Yang, 2008. "On the (ir)relevance of direct supply-side effects of monetary policy," School of Economics Discussion Papers 0408, School of Economics, University of Surrey.
  14. Damba Lkhagvasuren, 2009. "Large Locational Differences in Unemployment Despite High Labor Mobility: Impact of Moving Cost on Aggregate Unemployment and Welfare," Working Papers 09009, Concordia University, Department of Economics, revised Mar 2010.
  15. Alain Guay & Florian Pelgrin, 2007. "Using Implied Probabilities to Improve Estimation with Unconditional Moment Restrictions," Cahiers de recherche 0747, CIRPEE.
  16. Yuichi Kitamura, 2006. "Empirical Likelihood Methods in Econometrics: Theory and Practice," CIRJE F-Series CIRJE-F-430, CIRJE, Faculty of Economics, University of Tokyo.
  17. Sowell, Fallaw, 2006. "The Empirical Saddlepoint Approximation for GMM Estimators," MPRA Paper 3356, University Library of Munich, Germany, revised May 2007.

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