GMM, GEL, serial correlation, and asymptotic bias


Anatolyev, Stanislav (2005) “GMM, GEL, serial correlation, and asymptotic bias”, Econometrica, Vol. 73, No. 3, pp. 983–1002


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.

Paper in RePEc:

Econometrica, 73:3, 983-1002

Paper in accepted version:


Presented at:

European Economic Association annual congress, Stockholm, Sweden, August 20-24, 2003
North American summer meeting of Econometric Society, Evanston, USA, June 26-29, 2003
Catholic University of Leuven, Belgium, April 3, 2003
Econometric Study Group annual conference, Bristol, UK, July 18–20, 2002
XII New Economic School research conference, Moscow, Russia, October 3-5, 2002

Cited by:

Guggenberger, P. & Ramalho, J.J.S. and Smith, R. (2012) "GEL statistics under weak identification", Journal of Econometrics, Vol. 170, pp. 331-349.
Gospodinov, N. & Otsu, T. (2012) "Local GMM estimation of time series models with conditional moment restrictions;, Journal of Econometrics, Vol. 170, pp. 476-490.
Allen, J., Gregory, A.W. and Shimotsu, K. (2011) "Empirical likelihood block bootstrapping", Journal of Econometrics, Vol. 161, pp. 110-121.
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Pierre Chaussé (2010) "Computing generalized method of moments and generalized empirical likelihood with R", Journal of Statistical Software, Vol. 34, pp. 1-35.
Francesco Bravo (2009) "Blockwise generalized empirical likelihood inference for non-linear dynamic moment conditions models", Econometrics Journal, Vol. 12, pp. 208-231.
Luis F. Martins and Vasco J. Gabriel (2009) "New Keynesian Phillips Curves and potential identification failures: A Generalized Empirical Likelihood analysis", Journal of Macroeconomics, Vol. 31, pp. 561-571.
Yuichi Kitamura (2009) "Empirical Likelihood Methods in Econometrics: Theory and Practice", in: "Advances in Economics and Econometrics, Theory and Applications, Ninth World Congress", by R. Blundell, W. Newey and T. Persson (eds.).
Fernanda P.M. Peixe, Alastair R. Hall, and Kostas Kyriakoulis (2006) "The mean squared error of the instrumental variables estimator when the disturbance has an elliptical distribution", Econometric Reviews, Vol. 25, pp. 117-138.
Ivan Fernandez-Val (2005) "Bias correction in panel data models with individual specific parameters", Manuscript, Boston University.
Pierre Chaussé (2005) "La Vraisemblance Empirique et la Méthode des Moments Généralisés: Survol de la Littérature et Extensions", Manuscript, Université du Québec à Montréal.
Alain Guay and Florian Pelgrin (2005) "The U.S. New Keynesian Phillips Curve: An Empirical Assessment", Manuscript, Université du Québec à Montréal.