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st: Instrumental Variables: discrete endogenous & continuous outcome

From   Phanwin Yokying <>
Subject   st: Instrumental Variables: discrete endogenous & continuous outcome
Date   Mon, 1 Apr 2013 11:49:45 -0400

Dear Statalisters,

      I am running a regression with several binary endogenous variables and a continuous outcome using the IV approach. 

  Y = aX1 + bX2 +  c X3+ dX2*X1 +eX2*X3 + controls 
Y is continuous
X1 is discrete exogenous variable (demographic characteristics)
X2 is discrete endogenous variable 
X3 is discrete exogenous variables (e.g demographic characteristics) 

Y also suffers from selection bias, which implies that Heckman selection bias method might be necessary also.

Question1: If I were to run this "by hand," what steps would you suggest I should take? I have taken the following steps:
1. X2 = Z + controls
2. predict ghat
3. ivregress = controls (X2 = ghat) >>>> how do I incorporate the interaction terms and correction bias here? Could you advice?

Question 2: ivregress gmm Y controls (X2 X2*X1 = Z Z*X1)  >>> would this be the correct way to approach this? how can I take into consideration the selection bias that exists in Y? 

Your help and advise would be much appreciated. 

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