Carrasco, Marine and Florens, Jean-Pierre (2014) On the Asymptotic Efficiency of GMM. Econometric Theory, 30 (2). pp. 372-406.

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Identification Number : 10.1017/S0266466613000340


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.

Item Type: Article
Language: English
Date: April 2014
Refereed: Yes
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 09 Jul 2014 17:45
Last Modified: 02 Apr 2021 15:48
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