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st: RE: simultaneous system of probit models

From   "Pagan, jose" <>
To   <>
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:
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.

José A. Pagán
Robert Wood Johnson Health & Society Scholar
University of Pennsylvania
Colonial Penn Center
3641 Locust Walk
Philadelphia, PA 19104
Ph: (215) 746-2772
Fax: (215) 746-0397



-----Original Message-----
From: [] 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 J. Baumgartner 
DIW Berlin
Deutsches Institut für Wirtschaftsforschung
German Institute for Economic Research
Abt. Staat / Dept. Public Economics
Königin-Luise-Str. 5; 14195 Berlin; Germany  
Tel.: +49/30/89789-307; Fax.: +49/30/89789-114

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