The detection of multicollinearity in econometric models is usualy based on the so-called condition number (CN) of the data matrix X. However, the computation of the CN, which is the greater condition index, gives misleading results in particular cases and many commercial computer packages produce an inflated CN, even in cases of spurious multicollinearity, i.e. even if no collinearity exists when the explanatory variables are considered. And this is due to the very low total variation of some columns of the transformed data matrix, which is used to compute CN. On the other hand, we may have the problem of latent multocollinearity which can be revealed by additionally computing a revised CN. With all these in mind, we figure out the ill-conditioned situations, suggesting some practical rules of thumb to face such problems using a single diagnostic in a fairly simple procedure. It is noted that this procedure is not mentioned in the relevant literature.
condition index condition number eigenvalues multicollinearity (spurious, latent) singular value decomposition total variation