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

From   "Mark Schaffer" <[email protected]>
To   [email protected]
Subject   Re: st: 2SLS with Probit in the first-stage regression
Date   Mon, 13 Sep 2004 14:34:04 +0100


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 

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 

FYI, this question comes up fairly frequently on Statalist: here's an 
example from this past July:

Hope this helps.


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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Prof. Mark E. Schaffer
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

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