Testing for incremental information content in the presence of collinearity

A number of recent research papers use two-stage procedures in lieu of a single multiple regression, in some cases purportedly as a solution to colinearity among independent variables. We demonstrate that, since collinearity is inherently a data problem rather than a statistical problem, no partitions of dependent or independent variables, orthogonal or otherwise, can provide insights into the relative influence of collinear variables. For the class of linear unbiased estimators this follows directly from the Gauss-Markov Theorem, but we demonstrate some of the results in detail as an aid to interpreting particular papers.