Some overall properties of seemingly unrelated regression models

Seemingly unrelated regression models are extensions of linear regression models which allow correlated errors between equations. Estimations and inferences of singular seemingly unrelated regression models involve some complicated operations of the given matrices in the models and their generalized inverses. In this study, we characterize the consistency, natural restrictions, estimability of parametric functions under a singular seemingly unrelated regression model using the matrix rank method. We also derive necessary and sufficient conditions for the ordinary least squares estimators and the best linear unbiased estimators of parametric functions to be equal under seemingly unrelated regression models. Copyright Springer-Verlag Berlin Heidelberg 2014