Following on from my earlier problems with endogeneity and panel data, I
now have a question with regard to the choice of the instrumental variable.
I have the regression (panel data, fixed effects)
Y b1X1 b2X2 b3dummies
and I suspect that X2 might be endogenous. Is it possible to obtain an
instrument by first estimating
X2 c1X1
(where X1 is the same variable as the X1 in the first regression) and then
use the predicted values of X2 as the instrument for the first regression?