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st: Simultaneous probit model

From   Danny Dan <>
Subject   st: Simultaneous probit model
Date   Sat, 11 Jun 2011 21:28:57 -0500


I am estimating a simultaneous equation probit model with two
equations as following:


where both Y1 and Y2 are binary. Y1 and Y2 are related and endogenous.

Y1  = 1 if Y1**>0
      = 0 otherwise.

Y2  = 1 if Y2**>0
      = 0 otherwise.

We can only observe Y1** and Y2**.

X1 and X2 are sets of exogenous variables and e1 and e2 error terms.
X1 and X2 may have some common variables, but not all the variables
are common. There are some unique variables in both X1 and X2 in order
to satisfy the identification condition.

There is a method described in Madalla (1983) (model 6,
Ch#8,Page#246-247) in order to estimate this type of models. But I do
not know how to compute the variance-covariance matrix using the same.
My questions are:

(i) Can any one provide me with any reference where the calculation
for variance-covariance matrix is described in detail.
(ii) Is there any code in Stata which can help estimating this model?
(iii) Can I use 'biprobit' in order to estimate this model?

Please help.

Thank you in advance.

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