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st: Estimate interaction effects with ivreg

Subject   st: Estimate interaction effects with ivreg
Date   Mon, 5 Dec 2011 22:23:44 +0100

Dear All,

I have estimated an OLS regression model with an interaction effect as follows

Y = b_0 + b_1*A + b_2*D + b_3*A*D + X'*b_4 + u

where D is a binary variable, X' are the remaining covariates and u is an error term.

The interaction effect is such that corr(Y,A)<0 if D=0 and corr(Y,A)=0 if D=1. The dummy further depends on the value of some moderator variable Z, namely D_i=1 if Z_i>median(Z) and D_i=0 otherwise. Thus, the association between Y and A critically depends on the value of Z. In particular, the interaction effect follows from the notion that corr(Z,A)<0 if D=0 and corr(Y,A)=0 if D=1.

Now I want to find a way to mitigate the endogeneity bias between Y and A in this model. Assuming that Z is not correlated with the error u, the above specification suggests that Z be used as partial IV for the endogenous variable A. So I think the following 2SLS model might be appropriate:

ivreg Y D X' (A = (1-D)*Z U V W)

where U V W are additional excluded instruments. Would this be a valid approach under the current IV theory?

Thanks for your help.

Best regards,
Andreas Zweifel
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