MULTICOLLINEARITY

Question 1

What is multicollinearity?

Answer 1

Multicollinearity is when there is an exact linear relation between regressors

Question 2

How do we detect multicollinearity? Five ways.

Answer 2

1. High R2 but many stat insignificant t-stats.
2. High pairwise correlation of explanatory variables (>=0.8)
3. High partial correlation between coefficients
4. Auxiliary regression producers sig F stat
5. High variance inflation factor or low tolerance factor.

Question 3

What is VIF?

Answer 3

VIF is a measure of the degrees to which the variance of the OLS estimator is inflated due to collinearity.

Question 4

What are the four consequences of multicollinearity?

Answer 4

1) OLS estimators are still BLUE
2) Large standard errors and small t-stats which make it more difficult to reject the null when we should
3) Can’t conduct reliable hypothesis-testing due to high R2 but insignificant p-values.
4) Coefficients are sensitive to small changes in data

Question 5

Stata output

Answer 5

High R2 but few significant variables. While the adjusted R2 isn’t too high it is stat significant at the 1% level. There is also a number of insignificant variables that would expect to be significant such as education.
There appears to be high collinearity, even the VIF mean is 2.73.