The Perils of Multicollinearity: A Reassessment

Multicollinearity is typically thought of as a problem of large standard errors resulting from the near linear dependence of independent variables. One solution is to have more informative data, possibly in the form of a larger sample. In this paper I argue that this understanding of multicollinearity is only partially correct. The near collinearity of independent variables results in regression estimates being potentially quite sensitive to small degrees of model misspecification. I examine the assumption that the independent variables and error are uncorrelated and show that when there is multicollinearity, small deviations from this assumption can lead large changes in estimates. I then present a new estimator based on Bayesian methods that extends the classical OLS estimator by specifying a prior on the correlation between X and e. I show how this estimator can be used to calculate confidence intervals that reflect both sampling error and uncertainty with respect to the model specification.