Robust Conjecture as a Solution of the Implausible Coefficients Under Multicollinearity

Abstract:     
Despite the long and frustrating history of struggling with the implausible coefficients under multicollinearity and all the sophisticated and creative methods that have been developed to deal with this problem, it turns out that the problem can be solved in a surprisingly simple way. This paper presents a simple approach that assures both statistically sound and theoretically consistent coefficients under multicollinearity. The approach is simple in the sense that it requires nothing but basic statistical methods plus a piece of a priori knowledge. In addition, the approach is robust even to the extreme case when the a priori knowledge is "wrong". This approach also has the potential to arm the Bayesian with objective robustness to avoid most of the controversy around the latter in a more general context than just the multicollinearity.

Keywords: confidence region, goodness of fit, restricted regression, hypothesis test, a priori knowledge, extraneous information, Bayesian

JEL Classifications: C2

Working Paper Series