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

[jean ries <ries@ires.ucl.ac.be>]

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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