A system identification method for errors-in-variables problems based on covariance matching was recently proposed. In the first step, a small amount of covariances of noisy input-output data are computed, and then a parametric model is fitted to these covariances. In this paper, the method is further analyzed and the asymptotic accuracy of the parameter estimates is derived. An explicit algorithm for computing the asymptotic covariance matrix of the parameter estimates is given, and the identification method is shown to be asymptotically statistically efficient assuming that the given information is the computed covariances. As an important byproduct, an efficient algorithm is presented for computing the covariance matrix of the computed input-output covariances. (C) 2010 Elsevier Ltd. All rights reserved.