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Re: st: How to instrument for an interaction term in the ivreg2


From   "Mark Schaffer" <M.E.Schaffer@hw.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: How to instrument for an interaction term in the ivreg2
Date   Thu, 05 May 2005 11:20:10 +0100

Binzhen,

Date sent:      	Thu, 05 May 2005 00:28:06 -0500
From:           	BINZHEN WU <binzhenwu@students.wisc.edu>
Subject:        	st: How to instrument for an interaction term in the ivreg2
To:             	statalist@hsphsun2.harvard.edu
Send reply to:  	statalist@hsphsun2.harvard.edu

> Dear Statalist,
> 
> I have a problem in a linear regression analogue to the difference-in-
> difference method. The regression runs as the following.
> 
> Y=aT+bZ+cTZ+dX,
> Here,  TZ=T*Z is the interaction term, T is the time dummy (=1 after
> the policy change), and Z are the continuous endogenous treatments, X
> are exogenous variables.
> 
> The instruments for Z is W and V. TW and TV are considered as 
> instruments for T*Z.

This is a misleading way of thinking about IV/2SLS.  The endogenous 
regressors are projected on all the instruments.  If you want to 
impose constraints (e.g., TW doesn't influence Z), you would need to 
use a system estimator.

> I am think about the following procedure:
> 1) predict Z from W, V, TW, TV, T, and X, denoted as Z'
> 2) let TZ'=T*Z'.
> 3) run regression of Y on Z', TZ', T, and X.

This is called a "forbidden regression".  See e.g. Wooldridge (2000), 
Econometric Analysis of Cross Section and Panel Data, 
section 9.5, esp. pp. 236-7.  This has come up before on Statalist:

http://www.stata.com/statalist/archive/2003-11/msg00795.html

> 
> However, it seems that I cannot implement the procedure by ivreg2.
> 
> "ivreg2 Y T X (TZ Z=W V TW TV)" is doing the following procedure: 1)
> predict TZ from W, V, TW, TV,T, and X, denoted as (TZ)' 2) predict Z
> from W, V, TW, TV, T, and X, denoted as Z' 3) run regression of Y on
> Z', (TZ)', T, and X.

ivreg2 does this in one step, but intuitively you have described it 
correctly.  Unlike your suggestion above, it will generate consistent 
estimates of the parameters and SEs (with the usual extra 
assumptions, of course).

Hope this helps.

Cheers,
Mark

> Can anyone tell me which procedure is better? Is there a 
> command/syntax to implement the first procedure and adjust the 
> standard errors at the same time.
> 
> Thank you in advance.
> 
> Binzhen 
> 
> 
> *
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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
44-131-451-3494 direct
44-131-451-3296 fax
44-131-451-3485 CERT administrator
http://www.sml.hw.ac.uk/cert

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