BRICKMAKING AND THE COLLINEAR ARTS - A CAUTIONARY TALE

In their model of induced unemployment and unemployment insurance bene fits Grubel, Maki, and Sax (1975) break the collinearity between two s ubsets of regressors by replacing one subset with the residuals from t he regression of that subset on the other. This note works out the sta tistical implications of this orthogonalization procedure in the gener al linear model. It is shown that a subset of estimators is always bia sed and inconsistent and that conventional inference is thereby invali dated. Furthermore, we demonstrate that orthogonalization can actually worsen collinearity if measured by its effect on estimated variances. The implications of these results for the model simplification proced ure used recently in Baba, Hendry, and Starr (1992) are also discussed .