I am currently looking into the correlation between academic freedom (my independant variable) and university rankings (my dependant variable) using OLS.
I find a negative significant correlation, but since I only have one dependant variable, this results suffers from omitted variable bias. In order to take this into account, I want to introduce some control variables into my model (that are both correlated with my independant and dependant variable).
One of these controls is the presence of democracy/civil liberties (as measured by the Freedom House dataset) in the country. When I regress academic freedom on these variables, I find a very high correlation (the coefficient for both democracy and civil liberties is 0.95).
Because of this high correlation, I was wondering if it was a good idea to use democracy/civil liberties as a control variable to isolate the effect of academic freedom. Is there a risk of a biased coefficient because of this high correlation ? If there is a risk, would the use of proxies for qualities of institutions that are less correlated with academic freedom be a solution to still control for democracy in my model ?