This note considers how hypotheses of invariance and super exogeneity may be formulated and tested in elliptical linear regression models. It is demonstrated that for jointly elliptical random variables super exogeneity will only hold under normality.

In the presence of heteroskedasticity of unknown form, the Ordinary Least Squares parameter estimator becomes inefficient, and its covariance matrix estimator inconsistent. Eicker (1963) and White (1980) were the first to propose a robust consistent covariance matrix estimator, that permits...

Decisions based on econometric model estimates may not have the expected effect if the model is misspecified. Thus, specification tests should precede any analysis. Bierens' specification test is consistent and has optimality properties against some local alternatives. A shortcoming is that the...