The VIF Score. What is it Good For? Absolutely Nothing

Abstract

Variance inflation factors (VIF scores) are regression diagnostics commonly invoked throughout the social sciences. Researchers typically take the perspective that VIF scores below a numerical rule-of-thumb threshold act as a “silver bullet” to dismiss any and all multicollinearity concerns. Yet, no valid logical basis exists for using VIF thresholds to reject the possibility of multicollinearity-induced type 1 errors. Reporting VIF scores below a threshold does not in any way add to the credibility of statistically significant results among correlated variables. In contrast to this “threshold perspective,” our analysis expands the scope of a perspective that has considered multicollinearity and misspecification. We demonstrate analytically that a regression omitting a relevant variable correlated with included variables that exhibit multicollinearity is susceptible to endogeneity-induced bias inflation and beta polarization, leading to the possible co-existence of type 1 errors and low VIF scores. Further, omitting variables explicitly reduces VIF scores. We conclude that the threshold perspective not only lacks any logical basis but also is fundamentally misleading as a rule-of-thumb. Instrumental variables represent one clear remedy for endogeneity-induced bias inflation. If exogenous instruments are unavailable, we encourage researchers to test only straightforward, unambiguous theory when using variables that exhibit multicollinearity, and to ensure that correlated co-variates exhibit the expected signs.