Dear Stata Users,

I have two questions regarding 2-stage models and interaction terms:


1. Assume model (1) y = a1x1 + a2x2 + a3(x1*x2)

with x1 endogenous and x2 exogenous variables. If I have an instrument z1 for x1 can I run the first stage without the interaction term (x1*x2), calculate the prediction of x1 (name it x1hat) and then run a 2-stage for model (1) with instruments z1 and x1hat*x2 and correct the standard errors with bootstrapping? Or using straight z1 and z1*x2 as instruments is also correct?

2. Also assuming the same model with both x1 and x2 being endogenous and that I have two instruments z1 and z2 for each one of them. Can I use z1*z2 as a third instrument and run a 2-stage model with three endogenous variables x1, x2 and x1*x2 and three instruments z1, z2 and z1*z2?

I looked it up and found quite a few threads that suggested different approaches.

Any suggestions are highly appreciated.

Emmanouil

Emmanouil Avgerinos, Ph.D.
Assistant Professor in Decision Sciences
Operations & Technology Area
IE Business School (Instituto de Empresa)
María de Molina, 12 - 5th Floor
28006 Madrid