The problem of near-multicollinearity revisited: erratic vs systematic volatility

摘要

The main argument of the paper is that the traditional discussion of near-multicollinearity 'boils down' to two rather different issues which are often conflated: (a) a structural issue (high correlation among regressors) which, under certain conditions, gives rise to systematic volatility, and (b) a numerical issue (the regressor data matrix (X~TX) is ill-conditioned) which gives rise to erratic volatility. We call into question the traditional account concerning the effects of increasing the correlation among the regressors, and we put forward a revised account of systematic volatility. The main conclusion is that the precision of the coefficient estimators and the associated t-ratios do not necessarily decrease as the correlation among regressors increases. We also question the traditional methods of detecting erratic volatility and propose norm bounds for quantifying the potential problem.