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,