st: RE: Can I put different variables in the two stages of ivregress 2sls?

["Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>]

Xiaofei,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
> statalist@hsphsun2.harvard.edu] On Behalf Of XIAOFEI XING
> Sent: 13 January 2014 03:00
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Can I put different variables in the two stages of ivregress 2sls?
> 
> Dear Statalist,
> 
> If I run the following IV regression by Stata:
> 
> ivregress 2sls rent pcturban region (hsngval = faminc), first
> 
> Stata will show the two stages of the regression as follows:
> 
> The first step is
> hsngval = a1*pcturban + a2*region + a3*faminc
> 
> The second step is
> rent=b1*hsngval + b2*pcturban + b3*region
> 
> My question is: can I exclude pcturban from first step. In other words, can I
> put different variables in the two steps? For example, if my models are
> shown as follows (faminc is still the instrument variable):
> 
> The first step:
> hsngval = a1*region + a2*faminc
> 
> The second step:
> rent=b1*hsngval + b2*pcturban + b3*region
> 
> Can I do it by "ivregress" ?

No, you can't, and it's because of the definition of the IV/2SLS estimator.  It is a single-equation limited-information estimator, and the definition of the estimator implies that if you use the (rather old-fashioned) 2-stage method of calculating it, you must include *everything* exogenous in the first step.

Another way to put it is that you don't want to do single-equation limited-information estimation at all.  In standard IV/2SLS, the first stage is just a calculation step - it doesn't necessarily have a structural interpretation.  But you want the "first stage" to be a structural equation and exclude an exogenous regressor from it because your model says it shouldn't be there.  In that case, you want to use a system estimator such as Stata's -reg3- or -sem- so that you can estimate both of your structural equations.

There is a Statalist FAQ on this point here:

http://www.stata.com/support/faqs/statistics/instrumental-variables-regression/

And FYI the question comes up on Statalist from time to time:

http://www.stata.com/statalist/archive/2009-06/msg00653.html

HTH,
Mark

> Thanks a lot.
> 
> Best wishes,
> 
> Xiaofei
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