Define intruments when interaction dummy with endogenous

[felp]

I have a 2 equation system I want to estimate with TSLS. I wonder how I should define intrument for a dummy when it interacts with endogenous variable. A simplified example shows my problem where Y1 and Y2 are endogenous:

log(Y1)=C(1)*log(X1) + C(2)*log(Y2) + C(3)*dummy*log(Y2)
log(Y2)=C(4)*log(X2) + C(5)*log(Y1)

@inst log(X1) log(X2) dummy*log(Y2)

The problem i that Y2 is endogenous, and when I define dummy*log(Y2) I assume actual Y2 observations are used in stead og predicted values from equation 2. Could I just write:
"@inst log(X1) log(X2) dummy" and skip the "*log(Y2)" part? I only notice that it matters a lot what you do, but am not sure what's right?

[startz]

As you suggest, you should leave log(y2) out of the instrument list entirely.

[felp]

I agree, but my problem is how can I be sure that Eviews take care of this properly. As you see we have a model that is non-linear in variables and after doing some algebra the reduced form equations are:

log(y1) = [c1/(1- c2*c5-c3*c5*dummy)]log(x1) + [(c2*c4 +c3*c4*dummy)/(1- c2*c5-c3*c5*d)]log(x2)
log(y2) = [(c1*c5)/(1- c2*c5-c3*c5*dummy)]log(x1) + [c4/(1- c2*c5-c3*c5*d)]log(x2)

If I only use the log(x1) and log(x2) in the instrument list, will Eviews use these equations as reduced form or am I forced to do the two stages manually?

[startz]

I'm pretty sure that EViews will get it right. But you could always try it both ways. Note that if you do two stages manually the standard errors and t-stats reported in the second stage will be incorrect and require correction.

[felp]

I'm not able to find out what Eviews does by doing the two stages manually. When you say that you are sure Eviews get it right, do you mean that the reduced form equation of the first stage is estimated with non-linear methods when using "@inst log(x1) log(x2) dummy" as intrument list. The dumy takes the value 0 or 1 for different periods. Thus, using this as slope dummy on the endogenous variable makes reduced form equations non-linear in variables as you see in my previous post.

[startz]

I'm pretty sure that both log(y2) and dummy*log(y2) are separately regressed on all the instruments and that that's the right thing to do. A for sure answer would have to come from someone at EViews.