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:
Paper in accepted version:
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
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