# st: RE: simultaneous system of probit models

 From "Pagan, jose" <[email protected]> To <[email protected]> Subject st: RE: simultaneous system of probit models Date Fri, 12 Dec 2003 14:14:41 -0500

```Hi Hans,

I'm analyzing a similar system and a paper by Greene (1998) argues that the likelihood function of a recursive simultaneous-equations probit is the same as that of a bivariate probit model. As such, you can just estimate the models using biprobit. You can download the paper via this link:
http://www.indiana.edu/~econed/issues/v29_4/1.htm
This is also summarized in Greene's Econometric Analysis (5th ed) in an example and in the discussion of the bivariate probit model, I think.

Knapp and Seaks argue that a likelihood-ratio test of the correlation coefficient of the residuals (rho) can be used as an endogeneity test. This is what the 'biprobit' command reports at the bottom of the results' table.

Knapp, Laura Greene and Terry G. Seaks (1998), "A Hausman test for a dummy variable in probit," Applied Economic Letters, vol 5, 321-323.

Good luck, Jose.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Jos� A. Pag�n
Robert Wood Johnson Health & Society Scholar
University of Pennsylvania
Colonial Penn Center
3641 Locust Walk

Ph: (215) 746-2772
Fax: (215) 746-0397
[email protected]

-----Original Message-----
From: [email protected] [mailto:[email protected]] On Behalf Of Hans J. Baumgartner
Sent: Friday, December 12, 2003 1:03 PM
To: statalist
Subject: st: simultaneous system of probit models

Hi stata-listers,

which command allows me to estimate a simultaneous system of probit models

y1* = X1b1 + u1
y2* = y1b2 + X2b3 + u2

where y1* is a latent variable and y1 = 1 if y1* > 0.3

Maddala (1983, p. 122) says that this system can be estimated in two
steps if E(u1, u2) = 0. But if E(u1, u2) = d, then the coefficients in
the second equation are not identified. I have doubts that in my sample
E(u1, u2) = 0. Thus, I would be very grateful if somebody could point me
to a test for this problem, too.

Best wishes
Hans

--
Hans J. Baumgartner
DIW Berlin
Deutsches Institut f�r Wirtschaftsforschung
German Institute for Economic Research
Abt. Staat / Dept. Public Economics
K�nigin-Luise-Str. 5; 14195 Berlin; Germany
Tel.: +49/30/89789-307; Fax.: +49/30/89789-114
http://www.diw.de
http://www.hansbaumgartner.de

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