In large demand systems, when the unknown error covariance matrix is approximated by its usual maximum likelihood estimator, the coefficient estimates are known to suffer from two problems: (1) the asymptotic standard errors severely understate the sampling variability of the estimates and (2) the efficiency of the maximum likelihood coefficient estimates is greatly impaired. In this paper, the author proposes an alternative estimator for the covariance matrix and evaluates its performance. Using time-series data for OECD countries, the author finds that there is a spectacular improvement. Copyright 1991 by MIT Press.