An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias

TLDR

The paper proposes using Aitken’s generalized least‑squares on the entire system of equations to estimate parameters of seemingly unrelated regressions. The method applies Aitken’s GLS to the full system and includes tests of equality of coefficient vectors using micro and macro data, with the procedure illustrated on 1935–1954 investment data for two firms. The estimators are asymptotically at least as efficient as ordinary least squares, with substantial gains when regressors are weakly correlated across equations and disturbances are highly correlated, and the equality test confirms no aggregation bias when the hypothesis holds.

Abstract

Abstract In this paper a method of estimating the parameters of a set of regression equations is reported which involves application of Aitken's generalized least-squares [1] to the whole system of equations. Under conditions generally encountered in practice, it is found that the regression coefficient estimators so obtained are at least asymptotically more efficient than those obtained by an equation-by-equation application of least squares. This gain in efficiency can be quite large if "independent" variables in different equations are not highly correlated and if disturbance terms in different equations are highly correlated. Further, tests of the hypothesis that all regression equation coefficient vectors are equal, based on "micro" and "macro" data, are described. If this hypothesis is accepted, there will be no aggregation bias. Finally, the estimation procedure and the "micro-test" for aggregation bias are applied in the analysis of annual investment data, 1935–1954, for two firms.