Abstract
In their model of induced unemployment and unemployment insurance benefits Grubel, Maki, and Sax (1975) break the collinearity between two subsets of regressors by replacing one subset with the residuals from the regression of that subset on the other. This note works out the statistical implications of this orthogonalization procedure in the general linear model. It is shown that a subset of estimators is always biased and inconsistent and that conventional inference is thereby invalidated. 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 procedure used recently in Baba, Hendry, and Starr (1992) are also discussed.
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