# Highly correlated (independent) variables

I have a question that, for most of you, will look rather basic. I regress y on a set of control variables. Then I add my variables of interest, one after the other (so add one, run regression, remove it, add another one, run regression, etc.). I use different types of regressions: (P)OLS, FE, 2SLS and GMM. All regressions show a similar set of variables of interest that are statistically significant. However, these variables of interest are highly correlated (sometimes > 0.8), and this pertains to both the variables that are statistically significant and to those that are not.

How do I interpret this? So to recap: allthough the variables of interest are all highly correlated, some are always statiscally significant, whilest other are not. What does this mean?

Thank you for you help,

W.

• To me it sounds like y and all your control variables have more or less correlation with each other. Some of these correlations are statistically significant and some aren't. – Heikki Pulkkinen Aug 23 '18 at 11:37

## 1 Answer

You should remove some of the control variables that are correlated with each other. You may find then that a variable that was insignificant will become (more) significant because it no longer has collinearity with some other variable that was showing up as significant.
Ultimately the principle of parsimony (simplicity) says that you should try to build the simplest model possible. You can probably remove some or even many of the controls and get to the same or similar results without concerns about unpredictable and incorrect results due to those correlations.

• Maybe I was not being clear enough. It's not the control variables which are correlated, but the different 'variables of interest' (in this case, different measures to capture consumer confidence). – Student0909 Aug 23 '18 at 11:52
• ok. so, it is possible that you are discovering something through statistical modeling that was not evident from simple correlation. I wouldn't jump to that conclusion but that is the point of doing this. Having a 0.8 correlation is high but that doesn't mean two of your variables of interest will be equally highly correlated with the dependent variable, much less to have a statistically significant relationship in the presence of the controls. Do you have reason to believe that some variables are significant and others are not? Is that the goal? – Chris Umphlett Aug 23 '18 at 12:21