using probit as first stage in two-stage regression, and interacted variables

Hello Statalist,

I'm hoping someone might take the time to help me - it would be much appreciated!

I am trying to ascertain the treatment effect of being in a programme but as the assignment to the programme is fuzzy (in RD design terms) I want to use the predicted value of assignment as the treatment variable - using the following steps so as to account for standard errors:

> . probit w x1-xn z
> . predict ghat
> . ivreg y x1-xn (w = ghat)
>
> where:
> y ==> outcome
> x1-xn ==> exogenous variables
> w ==> endogenous binary variable
> z ==> instrument

My problem is that I want to also include interacted variables in order to ascertain heterogenous effects - I specified the following:

probit military age_c
predict ps
ivregress 2sls prej ps noncoeth##c.ps c.age_c##c.ps (military = ps), cluster(date)

and I get the following error: "equation not identified' must have at least as many instruments not in the regression as there are instrumented variables"

I have tried a number of variations of specification - can someone tell me what I am doing wrong?

I would rather not revert to OLS for the SE issue but am beginning to think this is the only way to capture the treatment effects of noncoeth and age_c given assignment.

many thanks in advance
x