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Re: st: simultaneous probit model

From   Partha Deb <>
Subject   Re: st: simultaneous probit model
Date   Thu, 08 Oct 2009 09:41:55 -0400

Notation is important here. The model you have written down is not quite model 6 in Maddala. Model 6 has

(1) Y1* = a*Y2* + b*X1 + e1
(2) Y2* = b*Y1* + c*X2 + e2

i.e., the endogenous regressors on the RHS are the latent indices underlying Y1 and Y2, not the binary indicators themselves. If this is the model you want, Maddala, on the pages you've cited, outlines a 2-step plug in method. That's straightforward to implement. Standard errors are more complicated, but you could just bootstrap it all to get consistent standard errors.



Marie-Benoit MAGRINI wrote:

I am looking for a program allowing me to implement the « model 6 » in the book of Maddala (1983, “Limited dependent and qualitative variables in econometrics”, chapter 8 about the two-stage estimation methods, page 246).

That is, I am trying to estimate the following simultaneous probit model :

(1) Y1 = a*Y2 + b*X1 + e1

(2) Y2 = b*Y1 + c*X2 + e2

where Y1 and Y2 are two endogeneous binary variables; X1 and X2 are two sets of exogenous variables of Y1 and Y2 respectively; e1 and e2 the error terms.

Y1 and Y2 are endogenously determined by each other.

I have looked at the ‘cdsimeq’ program but I understand that it corresponds to the model where one dependent variable is continuous and the other binary. So it cannot be used in my case.

I have also looked at the ‘biprobit’ procedure but I understand that it is adapted only for recursive model that is only one dependent variable is an explicative of the other one (the model 6 I’ve been trying to estimate is not recursive).

Could someone tell me if this simultaneous probit model can be estimated with STATA ?

best regards,

mb magrini

using Stata 10

Marie-Benoît MAGRINI
PhD in Economics
INRA - French National Institute for Agricultural Research
BP 52627
31326 Castanet Tolosan
Phone: 33 (0)5 61 28 54 22
Fax: 33 (0)5 61 73 20 77

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Partha Deb
Professor of Economics
Hunter College
ph:  (212) 772-5435
fax: (212) 772-5398

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