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st: Interaction terms in 2SLS


From   Glenn Hoetker <ghoetker@uiuc.edu>
To   "Statalist@Hsphsun2. Edu" <statalist@hsphsun2.harvard.edu>
Subject   st: Interaction terms in 2SLS
Date   Sun, 13 Mar 2005 11:02:56 -0600

I am facing the following problem and hope someone can help me with it.
I have the following model, and do not believe Y1 is exogenous in the
second equation.

Y1=X1 + X2
Y2=X3 + Y1 + Y1*X3

This seems like a classic application for 2SLS, but I can't use a
prepackaged 2SLS routine, since estimating the second equation requires
calculating (Y1_hat*X3). One approach would seem to be doing 2SLS
manually by modeling

Y1_hat=X1 + X2 + X3

and use the results to then estimate the second equation as

Y2=X3 + Y1_hat + Y1_hat*X3.

Several questions:

1.  Is this approach valid in general?
2.  If so, how would one calculate the standard errors for the second
equation?
3A.  In terms of identification, do I have to count both Y1 and Y1*X3 as
endogenous variables?
3B.  If the answer to 3A is yes, can I follow the approach I outlined
above, or do I actually need to estimate two first stage equations
(recognizing that my simplified model has identification problems):

Y1_hat=X1 + X2 + X3
(Y1*X3)_hat=X1 + X2 + X3

with a second stage equation of

Y2=X3 +  Y1_hat + (Y1*X3)_hat ?

Any suggestions, references, or ideas for alternative modeling
approaches would be very, very appreciated.  Many thanks in advance.

Glenn

Glenn Hoetker
Assistant Professor of Strategy
College of Business
University of Illinois at Urbana-Champaign
217-265-4081
ghoetker@uiuc.edu




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