# Re: st: interaction with non-random treatment

 From "Mark Schaffer" To statalist@hsphsun2.harvard.edu Subject Re: st: interaction with non-random treatment Date Fri, 12 Mar 2004 09:37:51 -0000

```Amrita,

Subject:        	st: interaction with non-random treatment
Date sent:      	Fri, 12 Mar 2004 04:09:27 -0500
From:           	"Nain, Amrita" <anain@bus.umich.edu>
To:             	<statalist@hsphsun2.harvard.edu>

>
> Hello all,
>
> Here's a question that's giving me a headache. I am estimating a
> model of firm value V, V= beta1 * X + beta2*T + beta3*T * Y + u
> where X are firm-level exogenous variables, T is a some treatment
> the firm is subjected to and Y is a continuous exogenous
> industry-level variable and u is the error term. Firms that
> receive treatment T are not a random sample of firms - factors
> that lead to a firm being given a treatment are correlated with
> firm value. In the absence of an interaction term of T withY, I
> would use the treatreg command in Stata to deal with the potential
> correlation between T and u. But how do I get consistent estimates
> of beta2 and beta3? Thank for helping. Amrita

V= beta1 * X + beta2*T + u

and you had excluded variables correlated with T and not u, then you
could use -treatreg- to estimation your equation *and* the T
equation, i.e., you could estimate the system.  -treatreg- won't
handle more than one treatment effect, though, so if you want to
estimate your full system then you're stuck (unless some Stata user
out there has written a program to do what you want).

But - if you are interested in only the V equation, then you can get
consistent estimates of the parameters using -ivreg- (or our
-ivreg2-), assuming again that you have enough (valid and relevant)
excluded variables.  The estimates won't be efficient, because you
would be using a single-equation estimation method - for efficiency
you would need to estimate the full system a la -treatreg- - but they
will be consistent (again assuming the excluded instruments are valid
and relevant).

Hope this helps.

--Mark

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
44-131-451-3008 fax