The Exact Distribution of Zellner's SUR
This paper derives the exact ﬁnite sample distribution of the two-stage GLS (generalized least squares) estimator in a multivariate linear model with general linear parameter restrictions. This includes the seemingly unrelated regression (SUR) model as a special case and generalizes presently known exact results for the latter system. The usual classical assumptions are made concerning nonrandom exogenous variables and normally distributed errors.
Phillips, Peter C.B., "The Exact Distribution of Zellner's SUR" (1983). Cowles Foundation Discussion Papers. 913.