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st: Likelihood estimation of Bivariate probit with sample selection

From   André Paul <>
Subject   st: Likelihood estimation of Bivariate probit with sample selection
Date   Sun, 26 Mar 2006 19:46:16 +0200

Dear all,

Following one of my previous posts, I have been advised to specify my own likelihood function to estimate a bivariate probit model with sample selection (or censoring).
I saw the help file on Stata's web site: but I would need further guidance to do this...

y1 and y2 are our dummy variables:

z1 = b1'x1 + e1, y1=1 if z1>0
z2 = b2'x2 + e2, y2=1 if z1 >0
e1,e2 ~ BVN(0,0,1,1,r) [BVN= Bivariate Normal]
(y1,x1) is observed only when y2 = 1.

According to the exemple on the web site, there are two steps

1) write a programme to define the log likelihood function

ln[N2(X1b1, X2b2, r)] if y1 = 1 and y2=1
ln[N2(-X1b1, X2b2, -r)] if y1=0 and y2=1
ln[1-N(X2b2)] if y2=0

where N2 is the bivariate Normal cumulative distribution and N is the univariate Normal cumulative distribution. r=cov(e1,e2)

I am already stuck here, as I don't know:
- how to define the Normal and bivariate normal functions...
- how to extend the exemple on the web to a bivariate case (when we have y1 and y2 instead of "just" y)
-how to get the programme to maximize the function w.r.t. b1, b2 and r.

2) Run the maximitaztion with something like:

ml model lf name_of_the_programme (y=X)
ml maximize

Same problem as above, how to extend to a bivariate case and get two tables of estimates?

I would be really happy if someone could help me,
Thank you in advance,


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