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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
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Goldberger et al. (1961) studied this question.
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