A Note on the Harmful Effects of Multicollinearity

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 R in the predictor matrix that is of the same order of magnitude as the R of the model overall. An empirical examination of this “rule-of-thumb”, in a stylized Monte Carlo study, is the purpose of this communication.