A Note on The Harmful Effects of Multicollinearity

Abstract

Assessing the harmful effects of multicollinearity in a regression model with multiple predictors has always been one of the great problems in applied econometrics. As correlations amongst predictors are almost always present to some extent (especially in time-series data generated by natural experiments), the question is at what point does inter-correlation become harmful. Despite receiving quite a bit of attention in the 1960s and 1970s (but only limited since), a fully satisfactory answer to this question has yet to be developed. My own thoughts on the issue have always been that multicollinearity becomes "harmful" when there is an R2 in the predictor matrix that is of the same order of magnitude as the R2 of the model overall. An empirical examination of this "rule-of-thumb," in a stylized Monte Carlo study, is the purpose of this communication.