Multicollinearity

Question 1

What does multicollinearity look at

Answer 1

Effects of estimation when explanatory variables are highly correlated, but not exactly (perfect) correlated.

E.g nominal and real interest rates are highly correlated so when testing individual significance they may seem insignificant because it does little additional explantory power since the other rate is included in the model too!

So solution would be to only use one interest rate since the second looks redundant

Question 2

So does multicollinearity violate OLS?

Answer 2

No, since strongly correlated, but not perfectly correlated so it is fine

Question 3

Consequences of multicollinearity

Answer 3

Still BLUE (unbias and lowest variance)

But just because best doesn’t mean good.

Question 4

4 Signals to identify multicollinearity is present in a model

Answer 4

1. Parameters have large variances and SE. Makes T statistics (B/SE) are likely to be small since rmb t=β₁-δ/SE, and so we are likely to not reject and conclude variables are insignificant.
2. Even if several insignificant variables (based off the t-statistic mentioned above) , R² can be high suggesting model is significant, so t statistic and R² contradict each other (sign of multicollinearity!)
3. Coefficients β may have the wrong sign
4. If data values were to change by a small amount, OLS estimates may change by a large amount (e.g adding 1 year to a 50year analysis and having a big change in results is a sign)

Question 5

So once we see those signals of potential multicollinearity, how do we actually detect multicollinearity (3)

Answer 5

Continue OLS estimation, see if t values are insignficant yet R² high i.e contradictory.

Look at correlation coefficients between variables (obviously since the definition of multicollinearity is strongly correlated but not perfectly!)

Run additional regressions

Question 6

Dealing with multicollinearity (4 eval of first 2 and 4th)

Answer 6

1.Drop one of the variables (e.g real and nominal interest rates, they’ll mirror each other so drop one)

Eval : However leads to estimates to be biased.

2. Try a different sample. And Bigger the better! (However data hard to come by)
3. Changing form of model e.g to log.
4. If study has literature, can use previous estimates.

Eval: may be incorrect, may not hold under your sample.