Hello everybody,


I please need your help, since I don't know how to proceed with my research.

I'm estimating an inverted U-shape relationship between my outcome variable and my regressor and in a second step a moderating effect on this u-curve with a binary variable. This is done with a fixed effects estimator an implemented in stata as follows:

Code:
 xtreg y c.x#c.x##i.dummy controls i.year, fe vce(cluster ID)
The controls include lagged variables.

Now I have reason to think that the dummy variable is endogenous, and I have two instrumental variables created for it.

But how do I implement an instrumental variable regression with a binary endogenous variable, and that many interaction terms? And is there any way to keep the fixed effects estimator?

Your help would be highly highly appreciated!