Key points are not available for this paper at this time.
A. S. Goldberger, A. L. Nagar, H. S. Odeh, The Covariance Matrices of Reduced-Form Coefficients and of Forecasts for a Structural Econometric Model, Econometrica, Vol. 29, No. 4 (Oct., 1961), pp. 556-573
Goldberger et al. (Sun,) studied this question.