Goodness of fit for seemingly unrelated regressions

Abstract

This paper presents a measure of goodness of fit for Zellner's seemingly unrelated regressions. The measure is a monotonic transform of the appropriate (asymptotic) F-statistic, is bounded on [0, 1] and is maximized by Zellner's estimation technique. Glahn's composite correlation coefficient is shown to be a special case of this measure. It is also compared to Hooper's squared trace correlation coefficient. All three measures as well as some additional asymptotic summary test statistics are calculated for the two-equation example of Zellner. The applicability of the latter test statistics seems not to be recognized in applied work.