What’s the best way to detect Multicollinearity?
I don’t quite remember what the CFAI says about that, but as an economic major who has done multiple courses in econometrics, I would say that if you add/remove independent variables to your model and it changes the values of your coefficients significantly, it may be a good sign. Also, if your model is highly significant as whole (F-test with low p-values) but your coefficients are not significants individually (t-tests with high p-values), it can also be a good sign.
Maple frog is right, the classic sign of multicollinearity is a highly significant f-stat and low (not statistically significant) slope coefficients. Another way to detect multicollinearity is looking at a correlation matrix of the regressions in your model. If there are very high pairwise correlations then it may be that multicollinearity is present. An example of a high pairwise correlation might be if you included both nominal interest rates and inflation as independent variables in a regression.
Correlation matrices are pretty much useless except in the case of two independent variables. It’s not uncommon for several variables to have low pairwise correlations but for multicollinearity to pose an issue in the analysis. Honestly, the CFA curriculum is absolutely garbage for the stats. In real life, MC can still be an issue without showing nonsignificant coefficient t-tests with a significant F-test. As maple mentioned, the coefficients can get a little wonky-- they may change quite a bit in direction and magnitude or from sample to sample. However, simply adding and dropping variables to notice changes in coefficients isn’t enough to conclude that MC is an issue, because coefficients may change dramatically due to a confounder being added to or removed from the model. Additionally, only the independent variables that are involved in the collinearity will be affected, which is something else I don’t recall the CFAI doing a decent job in pointing out. In other words, if X1, X2, and X3 are all in the model, and X1 and X2 are highly collinear, X3 won’t get mixed up in the issues that might present for the coefficients of X1 and X2. Also of note is that MC does not in any capacity make coefficients inconsistent or biased-- predictions and model fit (F-stat, R-square) are unharmed(something further that the CFAI doesn’t really address well).
The CFA Institute has yet to cover one of the simplest methods for assessing potential collinearity: the Variance Inflation Factor (VIF) or a tolerance value. These statistics essentially summarize the magnitude of the relationship of each independent variable with the remaining independent variables and these (either one, because one is a transformation of the other) are pretty helpful.
Hope this helps!
Grunch.
If the F-test is significant, R^2 is high and individual t-tests are not significant.
Affect? coefficients unreliable & standard errors too large.
Correct? Omit one or more independent variables
Per the CFAI books, sure, but this is far from a good rundown. They either don’t get it or are trying to hard to boil down the topic beyond where it should be for inclusion in the curriculum.
+1
The thing is that the cfai try to present econometrics in a cookbook black and white version while if you ever followed any real econometrics class you at least understand that it’s more complicated than that! But for the sake of the exam, the f-test whole model vs individual coefficient t-stat is probably what they are looking for!
+2 thanks guys!
I agree with you for the purposes of th exam. My issue is that the CFA Institute claims to provide an education, not a test prep service, so they should actually teach the material or summarize it well-- they do neither.
I completely agree with you-- you can probably find an old post of mine somewhere with me complaining that the CFAI makes stats appear as a cookbook topic, which it’s far from that (and they don’t seem to understand that well when I’ve contacted them about issues). They, along with many other people who don’t have a background in stats, seem to view it the same way that many people view mathematics as just a way to crunch numbers. Anyone with a decent background in stats (or mathematics) can tell you that’s very far from reality.