Some finite sample properties of Zellner estimator in the context of m seemingly unrelated regression equations

Abstract

Abstract In m seemingly unrelated regression equations model the variance–covariance of Zellner estimator, the differences of the variance–covariance between Zellner estimator and the best linear unbiased estimator and between Zellner estimator and the least-squares estimator are given, respectively, under the assumptions that their disturbances are multivariate normal distribution and that among the m symmetric projection matrices on the space spanned by the column vectors of the matrices of m exogenous variables, any two matrices commute. The variance–covariance of Zellner estimator of any equation is discussed under the other conditions too.