Yvonne,
Date sent: Thu, 14 Oct 2004 11:23:49 +0200
From: "" <[email protected]>
To: "" <[email protected]>
Subject: st: Reduced form specification for endogenous interaction variable
Send reply to: [email protected]
> Hi,
> This is a follow up to a response you gave on your website (on 26 August,
> 2004) to someone querying 'RE: Interaction with an instrumented variable -
> IV'.
>
> The person with the query has the following specification and query,
> "Y=b0 + b1*X1 + b2*X2 + b3*X3 + b4*X2*X3 + U
>
> X2 is the endogenous variable, which is instrumented with Z.
> X2 is itself interacted with X3.
> How does one model the interaction between an instrumented variable (X2
> instrumented with Z) and an exogenous variable (X3)?"
>
> And this was your response,
> "You've got two endogenous variables, just as if you had another endogenous
> variable X4 and you did not realize that X4=X2*X3. But if Z is a valid
> instrument, and X3 is truly exogenous, then Z*X3 is a valid instrument, too."
>
> However, its not clear from this how you go about estimating the reduced
> form. What would you use as your LHS variable in the reduced form.
>
> Would the specification for the reduced form for the endogenous interaction
> variable look as follows,
> X2*X3=b0 + Z*X3 + b1*X1 + b2*X2 + b3*X3 + u?
You forgot Z, the reduced form coefficient on Z*X3 is missing, and
you should use different symbols for your reduced form coefficients.
Say the b's are the structural coefficients, and a's are RF coeffs.
Then the RF is:
X2*X3=a0 + a1*Z + a2*Z*X3 + a3*X1 + a4*X2 + a5*X3 + u
--Mark
>
> Regards,
> Yvonne Mhango
> University of Cape Town
> South Africa
>
>
>
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Prof. Mark E. Schaffer
Director
Centre for Economic Reform and Transformation
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS UK
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