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st: "Forbidden Regressions"

From   Erasmo Giambona <>
To   statalist <>
Subject   st: "Forbidden Regressions"
Date   Thu, 2 Apr 2009 14:31:44 +0200

Dear Statalist,

I have the following model: y = a +bX+cZ+d(X*Z) + fK + e. Both X and Z
are endogenous making X and Z also endogenous. K is exogenous. I am
fitting the model using IV methods. I instrument X and Z respectively
with X1 and Z1, and I use X1*Z1 to instrument X*Z.

I understand from a STATA thread
( that a
natural instrument for X*Z would also be the the product of the
predicted values of Xp and Zp from the first stage regressions (i.e.,

Would the following also be plausible instruments for X*Z: X1*Xp,
Xp^2, (Xp*Zp)^2, etc..?

I hope to hear some comments on this issue.


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