Given a set of continuous variables with missing data, we prove in this paper that the iterative application of a "least-squares estimation/multivariate normal imputation" procedure produces an efficient parameters estimator and is therefore an optimal parametric technique for imputation of missing data. There are two main assumptions behind our proof: (1) data are missing at random (MAR); (2) the data generating process is a multivariate normal linear regression. Disentangling the problem of convergence of the iterative procedure, we show that the estimator is a "method of simulated scores" (a particular case of McFadden's "method of simulated moments"), thus equivalent to maximum likelihood if the number of replications is conveniently large.