st: ivreg2 and interaction terms

["Gars, Jared E" <jgars@purdue.edu>]

Statalist, 
                This issue has been brought up before but I have not found a sufficient answer either theoretically or technically. Hopefully we can get a clear answer for people in the future that search the list. 

I am regressing lnwage on a set of human capital characteristics (BMI, education, etc) where BMI is my endogenous variable. 

Lnwage = a + b(BMI) + c(BMI*dum) + d(dum) + g(X) + e, where X is a set of exogenous regressors and dum is a binary variable to proxy the type of firm that the worker is in. (we are ignoring the endogenous choice of firm choice because there is very little evidence that it is indeed endogenous) 

My intention is to capture whether returns to human capital vary across firm management in a transitional economy. So here I am allowing for a different intercept and slope for workers in more competitive firms.

Issues: I am using ivreg2, here is my input
xi: ivreg2 lnwage (lnBMI  lnBMI*dum = IV1 IV2  dum*IV1 dum*IV2 )   dum imr X    (IV1 and IV2 are my instruments) 

So I believe the appropriate thing to do is to interact my exogenous dummy on the instruments in the first stage. Is this the correct approach in theory and/or practice? It seems to suck out the significance of my instruments. The F stats drop to around 5 for each.  
 
I am not sure that this approach is correct or even really appropriate. Before you suggest just splitting them up, I am also doing that. However, the strength of my instruments diminishes significantly when the sample size becomes more limited.  I would like to be able to maintain the effectiveness of the instruments. 


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