I am using panel data, running a fixed effects regression using
xtreg Y X1 X2 X3, fe. I suspect, however, that past values of
Y are correlated with future values of one of the regressors e.g.
X1. This means that the strict exogeneity assumption of fixed effects regression will be violated.
To correct for this, can I use an IV? I have another variable
Z1 which is correlated with
X1 but uncorrelated with
Y once all other regressors are controlled for.
Could I, for example, run
ivreg Y X2 X3 ... Xn (X1=Z1)? How would I interpret my results?