# Re: st: 2SLS with Probit in the first-stage regression

 From "jake10002002" To statalist@hsphsun2.harvard.edu Subject Re: st: 2SLS with Probit in the first-stage regression Date Mon, 13 Sep 2004 17:09:50 -0000

```Thank you Mark and Jean! Your answers were very helpful for me.
Jake
--- In statalist@yahoogroups.com, "Mark Schaffer" <M.E.Schaffer@h...>
wrote:
> Jake,
>
> As Jean points out, you can use the two-step procedure described by
> Wooldridge, and the SEs will be correct.
>
> You can also use standard IV - the SEs with IV will also be
correct.
> The Wooldridge procedure is more efficient; the advantage of using
IV
> is that you can do overidentification test (using -ivreg2- or
> -overid-).
>
> Another possibility is to use Stata's -treatreg-.  This gives you
> either MLE or two-step estimation, and in both cases reports valid
> standard errors.  MLE is more efficient than two-step, which is
more
> efficient than the Wooldridge procedure, which is more efficient
than
> IV.
>
> FYI, this question comes up fairly frequently on Statalist: here's
an
> example from this past July:
>
> http://www.stata.com/statalist/archive/2004-07/msg00710.html
>
> Hope this helps.
>
> --Mark
>
> Date sent:      	Mon, 13 Sep 2004 15:23:54 +0200
> To:             	statalist@h...
> From:           	jean ries <ries@i...>
> Subject:        	Re: st: 2SLS with Probit in the first-stage
regression
>
> > Jake,
> >
> > Have a look at Wooldridge (2002), pages 623-625. He discusses the
> > situation you are facing. He suggests the following procedure:
> >
> > . probit w x1-xn z
> > . predict ghat
> > . ivreg y x1-xn (w = ghat)
> >
> > where:
> > y ==> outcome
> > x1-xn ==> exogenous variables
> > w ==> endogenous binary variable
> > z ==> instrument
> >
> > Wooldridge shows that in this procedure the 2SLS standard errors
> > remain valid. He also discusses the procedure you seem to have
used:
> >
> > . probit w x1-xn z
> > . predict ghat
> > . regress y x1-xn ghat
> >
> > and points to the problems that arise by doing so.
> >
> > Reference:
> > Jeffrey M. Wooldridge, Econometric Analysis of Cross Section and
Panel
> > Data, MIT Press, 2002.
> >
> >
> > best wishes,
> >
> > jean
> >
> > At 05:30 13/09/2004, you wrote:
> > >Hi,
> > >I'd like to do a 2SLS estimation where the first-stage
> > >regression is Probit.
> > >For example, the model is
> > >y = a + b1X1 + b2X2 + u
> > >where X1 is an endogenous binary variable.
> > >I'd like to instrument X1 with Z1 and Z2 where the
> > >first-stage regression is a Probit
> > >X1 = a + b1Z1 + b2Z2 + b3X2 + e
> > >I tried to use ivreg but it seems the first-stage
> > >regression ivreg does is OLS rather than Probit.
> > >Although I can do the first-stage Probit regression
> > >manually and then use the predicted X1 in the
> > >second-stage regression, I don't think it is accurate
> > >since the OLS standard errors of the second-stage
> > >regression will be incorrect in such a case.
> > >Does Stata has a procedure that does 2SLS with Probit
> > >in the first-stage?
> > >Any suggestions would be greatly appreciated!
> > >Thanks,
> > >Jake
> >
> > *
> > *   For searches and help try:
> > *   http://www.stata.com/support/faqs/res/findit.html
> > *   http://www.stata.com/support/statalist/faq
> > *   http://www.ats.ucla.edu/stat/stata/
>
> 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
> http://www.som.hw.ac.uk/cert
>
> *
> *   For searches and help try:
> *   http://www.stata.com/support/faqs/res/findit.html
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/

*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```