Statalist The Stata Listserver


[Date Prev][Date Next][Thread Prev][Thread Next][Date index][Thread index]

st: Likelihood estimation of Bivariate probit with sample selection


From   André Paul <hcpats@hotmail.fr>
To   statalist@hsphsun2.harvard.edu
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: http://www.stata.com/capabilities/mlexample.html 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,
André

_________________________________________________________________
http://desktop.msn.fr/

*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/




© Copyright 1996–2020 StataCorp LLC   |   Terms of use   |   Privacy   |   Contact us   |   What's new   |   Site index