Two-stage estimate of the parameters in seemingly unrelated regression model

For a general model of seemingly unrelated regression (SUR), this paper proposes a two-stage estimate of the parameters based on the covariance-improved approach due to Rao. Some advantages of this estimate include the conciseness of expression and the efficiency in making use of the sample information. Assume that the errors have normal distributions, the exact expression of the covariance matrix of the estimate is obtained and the superiority over the LSE (least squares estimate) is shown under some condition but without any constraint on the design matrix.