Endogeneity in longitudinal regression analysis

Hi all,

I'm doing regression analysis on panel data. I control for omitted variables using a fixed-effects model.

However, it seems that my independent variables are also causally interrelated, that is, they are not independent but correlated.

Is it so that FE does not correct the problem of this form of endogeneity? If so, how can I circumvent the problem? Is there a way beyond choosing the IVs so that they are independent and uncorrelated with the error terms?

Also, if someone knows a test that determines whether endogeneity is a problem I would be keen to know (the above questions are more urgent, though :)