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: [email protected]
From: jean ries <[email protected]>
Subject: Re: st: 2SLS with Probit in the first-stage regression
Send reply to: [email protected]
> 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
>
> *
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> * 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
44-131-451-3485 CERT administrator
http://www.som.hw.ac.uk/cert
*
* For searches and help try:
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