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

 From "Mark Schaffer" 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

> 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.

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.
>
>
> 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