# st: ML model with sequential sample selection

 From "Geraldo Cerqueiro" To statalist@hsphsun2.harvard.edu Subject st: ML model with sequential sample selection Date Fri, 02 Mar 2007 19:02:21 +0100

```Dear all,

I'm estimating the following model:

I1*=Z1d1+e1
I2*=Z2d2+e2 (observed if I1*>0)
Y=Xb+u (observed if I1*>0 and I2*>0)

where (e1,e2,u) are trivariate normal. In terms of ML there are 3 contributions: P(e1<-Z1d1), P(e2<-Z2d2,e1<Z1d1) and f(Y|e1<Z1d1,e2<Z2d2)=P(e1<Z1d1,e2<Z2d2|u)*f(u)

First, I estimate this model using the Heckman's two-step approach and use the estimates as starting values for the full ML model
The problem is that the Ml is not accepting the starting values of the correlation parameters (it returns error r(491)). Also, the ML model is converging to very extreme  values of the correlation parameters.
Can anyone take a look at the program and tell me whether I disregarded something? Thanks a lot!

capture program drop experim_lf
program experim_lf
version 9.2
args lnf z1d1 z2d2 xb sigma rho12 rho1u rho2u
tempvar u cum1 cum2 rho
quietly {
scalar `rho12'=0
gen double `u'=\$ML_y3-`xb'
gen double `cum1'=((`z1d1'-`u'*`rho1u'/`sigma')/sqrt(1-`rho1u'^2))
gen double `cum2'=((`z2d2'-`u'*`rho2u'/`sigma')/sqrt(1-`rho2u'^2))
gen double `rho'=`rho12'-`rho1u'*`rho2u'

replace `lnf'=ln(normal(-`z1d1')) if \$ML_y1==0

replace `lnf'=ln(binormal(`z1d1',-`z2d2',-`rho12')) if \$ML_y2==0

replace `lnf'=ln(binormal(`cum1',`cum2',`rho'))+ln(normalden(`u',0,`sigma')) if \$ML_y2==1

}
end

Geraldo

*
*   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/
```