# Multicollinearity Using VIF and Condition Indeces

I am testing my dataset for multicollinearity using VIF and condition indices(CI).My dataset is cross-sectional macroeconomics data. I have 6 independent variables ($$x_1$$,$$x_2$$,$$x_3$$,$$x_4$$,$$x_5$$,$$x_6$$) plus 2 dummies ($$d_1,d_2$$) plus 2 interactions terms ($$d_1*x_1$$,$$d_2*x_1$$).

regression t-test : seven statistical significant variables F: statistical significant overall

VIF&CI

Mean VIF : 10.63 (with very high R-squared (>85%) in all dummies and interaction terms) CI : 48.3

When I remove dummies and interactions from the model the results are much more better (Mean VIF : 1.62 , CI: 19.34 R-squared <50%).

I am expecting -due to the nature of dummies and interaction terms- that my results would present multicollinearity.

Are the above results serious evidence for multicollinearity in my model?

## 2 Answers

"The variables with high VIFs are indicator (dummy) variables that represent a categorical variable with three or more categories. If the proportion of cases in the reference category is small, the indicator variables will necessarily have high VIFs, even if the categorical variable is not associated with other variables in the regression model."

taken from: When Can You Safely Ignore Multicollinearity? http://www.statisticalhorizons.com/multicollinearity

• Exactly, with categorical variables the VIFs do not have the same thresholds anymore. I would recommend you report the VIFs without any dummy or interaction, only numerical variables, then with dummies but no interactions, then with all the variables. This will make a stronger point that you don't have a problem (1.62 is very good). Feb 7 '17 at 11:58

The answer I got from my graduate econometrics course was that VIF above 6 signifies potential multicollinearity. There is no hard and fast rule however, and I've heard of people using 4 as their threshold as well.

I would argue that for econometrics, it becomes more of an issue when you believe from a conceptual framework perspective that some of your variables are components of another. You as the analyst have the responsibility at the end of the day of determining this from your conceptual knowledge of the data being studied.