Dear statalist,
Using stata 8, I am trying to perform a model composed of three equations:
The first equation is:
y_1*=Z\gamma+\nu, y_1=1 if y_1*>0
with Z a vector of characteristics, \gamma the vector of coefficent and \nu the
error term
The second equation is:
y_2*=W\delta+Y\lambda+\eta, y_2=1 if y_2*>0
and the third equation is:
r=X\beta+\epsilon , where r a continuous variable observed if and only if
y_2=1
(\nu,\eta,\epsilon) are jointly normally distributed, with means 0.
The variance of \nu is 1, like the one of \eta (they are probit). The one of
\epsilon is \sigma^2. If someone wants to help me and have latex, the variance
covariance matrix is
$\left(\begin{array}{ccc}
1&\rho_{\nu,\eta}&\sigma_\epsilon\rho_{\nu,\epsilon}\\
\rho_{\nu,\eta}&1&\sigma_\epsilon\rho_{\eta,\epsilon}\\
\sigma_\epsilon\rho_{\nu,\epsilon}&\sigma_\epsilon\rho_{\eta,\epsilon}&\sigma_\epsilon^2\\
\end{array}\right)$. $\sigma_\epsilon$ is the standard
error of $\epsilon$ and $\rho_{i,j}$ the correlation
between $i$ and $j$.
I have been able to write the log likelihood of this model, using the Bayes rule
to avoid cumbersome cumulative trivariate normal distribution.
However, I am unable to programm it on STATA.
Are there any maximum likelihood experts who might be able to help? Or someone
who have already done a similar programm?
Thanks for your help.
Fabian
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