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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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  • Stanislav Anatolyev, 2005. "GMM, GEL, Serial Correlation, and Asymptotic Bias," Econometrica, Econometric Society, vol. 73(3), pages 983-1002, May.
  • Handle: RePEc:ecm:emetrp:v:73:y:2005:i:3:p:983-1002
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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2005.00601.x
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    Cited by:

    1. Lee, Seojeong, 2016. "Asymptotic refinements of a misspecification-robust bootstrap for GEL estimators," Journal of Econometrics, Elsevier, vol. 192(1), pages 86-104.
    2. Chang, Jinyuan & Chen, Song Xi & Chen, Xiaohong, 2015. "High dimensional generalized empirical likelihood for moment restrictions with dependent data," Journal of Econometrics, Elsevier, vol. 185(1), pages 283-304.
    3. Alastair R. Hall & Yuyi Li & Chris D. Orme & Arthur Sinko, 2015. "Testing for Structural Instability in Moment Restriction Models: An Info-Metric Approach," Econometric Reviews, Taylor & Francis Journals, vol. 34(3), pages 286-327, March.
    4. Yoshihide Kakizawa, 2013. "Frequency domain generalized empirical likelihood method," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(6), pages 691-716, November.
    5. Allen, Jason & Gregory, Allan W. & Shimotsu, Katsumi, 2011. "Empirical likelihood block bootstrapping," Journal of Econometrics, Elsevier, vol. 161(2), pages 110-121, April.
    6. Anatolyev, Stanislav, 2008. "Method-of-moments estimation and choice of instruments: Numerical computations," Economics Letters, Elsevier, vol. 100(2), pages 217-220, August.
    7. PETER McADAM & ALPO WILLMAN, 2013. "Technology, Utilization, and Inflation: What Drives the New Keynesian Phillips Curve?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(8), pages 1547-1579, December.
    8. Alastair R. Hall, 2013. "Generalized Method of Moments," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 14, pages 313-333 Edward Elgar Publishing.
    9. 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.
    10. Hill, Jonathan B. & Prokhorov, Artem, 2016. "GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inference," Journal of Econometrics, Elsevier, vol. 190(1), pages 18-45.
    11. Yuichi Kitamura, 2006. "Empirical Likelihood Methods in Econometrics: Theory and Practice," CIRJE F-Series CIRJE-F-430, CIRJE, Faculty of Economics, University of Tokyo.
    12. Stanislav Anatolyev, 2007. "Optimal Instruments In Time Series: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 21(1), pages 143-173, February.
    13. Yoshitsugu Kitazawa, 2014. "Consistent estimation for the full-fledged fixed effects zero-inflated Poisson model," Discussion Papers 66, Kyushu Sangyo University, Faculty of Economics.
    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. 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.
    16. Kenneth West & Ka-fu Wong & Stanislav Anatolyev, 2009. "Instrumental Variables Estimation of Heteroskedastic Linear Models Using All Lags of Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 28(5), pages 441-467.
    17. 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.
    18. 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.
    19. Márcio Poletti Laurini & Luiz Koodi Hotta, 2016. "Generalized moment estimation of stochastic differential equations," Computational Statistics, Springer, vol. 31(3), pages 1169-1202, September.
    20. 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.
    21. 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.
    22. Alain Guay & Florian Pelgrin, 2007. "Using Implied Probabilities to Improve Estimation with Unconditional Moment Restrictions," Cahiers de recherche 0747, CIRPEE.
    23. Sowell, Fallaw, 2006. "The Empirical Saddlepoint Approximation for GMM Estimators," MPRA Paper 3356, University Library of Munich, Germany, revised May 2007.
    24. 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.
    25. Mardi Dungey & Vitali Alexeev & Jing Tian & Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91, pages 1-24, June.

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