ON THE ASYMPTOTIC EFFICIENCY OF GMM MARINE CARRASCO

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 ker-nel 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 clo-sure 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 ob-servations are known to be Markov and satisfy a conditional moment restriction. We show that it coincides with the asymptotic variance of the optimal GMM esti-mator, 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. 1