Multicollinearity

A former student from my graduate applied econometrics course came by my office yesterday to talk about multicollinearity, which is the name for the situation where one estimates an econometric model of some sort and two or more of the independent variables are intercorrelated enough to make it hard to estimate their separate effects.

The example I use in my undergraduate course - the topic does not come up in my graduate course - is a regression of earnings on two measures of college quality, namely mean SAT score of the entering class and expenditures per student as well as a long list of characteristics of the individual measured prior to the time of their starting college. The two college characteristics are relatively highly correlated, but far from perfectly correlated. The result is that one can estimate the effects of one conditional on the other, but the estimates are not as precise as one might want in samples of reasonable size. This hints at why the late econometrician Art Goldberger at Wisconsin jokingly called multicollinearity micronumerosity instead.

The interesting thing about our conversation is that the student, who is not in the economics program, and his committee members, also not in economics, were very worried about the potential effect of multicollinearity not just on their estimates but on the matrix inversion underlying the estimator they were using. So we talked about condition numbers and such like, things that in applied econometrics essentially never get talked about. The conversation was interesting because it illustrated the extent to which applied literatures in different fields (or even sub-fields within, say, economics) can wander off and become preoccupied with issues that other fields largely ignore.

Thinking more about this, along with a follow-up email exchange, led to this post and this other post on multi-collinearity at David Giles' blog. both are worth a look if you are into such things.