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ON THE ASYMPTOTIC EFFICIENCY OF GMM

Published online by Cambridge University Press:  23 October 2013

Marine Carrasco  and
Jean-Pierre Florens
Marine Carrasco*
Affiliation:
Université de Montréal CIREQ and CIRANO
Jean-Pierre Florens
Affiliation:
Toulouse School of Economics
*
*Address correspondence to Marine Carrasco, University of Montreal, Departement de Sciences Economiques, CP 6128, succ Centre Ville, Montreal, QC H3C3J7, Canada; e-mail:marine.carrasco@umontreal.ca.
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Abstract

The efficiency of the generalized method of moment (GMM) estimator is addressed by using a characterization of its variance as an inner product in a reproducing kernel Hilbert space. We show that the GMM estimator is asymptotically as efficient as the maximum likelihood estimator if and only if the true score belongs to the closure of the linear space spanned by the moment conditions. This result generalizes former ones to autocorrelated moments and possibly infinite number of moment restrictions. Second, we derive the semiparametric efficiency bound when the observations are known to be Markov and satisfy a conditional moment restriction. We show that it coincides with the asymptotic variance of the optimal GMM estimator, thus extending results by Chamberlain (1987, Journal of Econometrics 34, 305–33) to a dynamic setting. Moreover, this bound is attainable using a continuum of moment conditions.

Type
ARTICLES
Information
Econometric Theory , Volume 30 , Issue 2 , April 2014 , pp. 372 - 406
Copyright
Copyright © Cambridge University Press 2013 

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