fractional probit with sample selection using CMP

[Guest]

Hello everyone!
I am planning to run a fractional response model with sample selection. I wonder if it is possible to do so with a CMP command by David Roodman ?
In a thread https://www.statalist.org/forums/for...l-added-to-cmp , it is mentioned that fractional model has been added to cmp. And in the original paper(Fitting fully observed recursive mixed-process models with cmp) by the author , commands for various probit models with heckman are given. My questions are:
1)can they be extended to frcational response model?
is a command like this correct?:
cmp (part = EDU DISTANCE GENDER i.Year* ) (SHARE= EDU GENDER i.Year* ), ind( $cmp_probit $cmp_frac )
where DISTANCE is the exclusion restriction for the model?
2) If the command is correct, can it be used in panel data by adding 'cluster(id)'?
Thanks

[David Roodman]

Yes you can do all that. But probably it should be "$cmp_frac*part" instead of "$cmp_frac". See the selection examples in the help file.

[Guest]

Thanks for the reply David Roodman

[Guest]

David Roodman I would be really grateful to you if you could answer one more doubt in this context.
I used the command and it works fine. But the number of observations (in the initial fitting of the models) is more for SHARE and less for part . And after the whole model is fitted then also it shows the total number of observations as that of SHARE. Can you please explain how is this possible ?

[David Roodman]

In a selection model, different equations have different numbers of observations. How then should the "number of observations" be defined for the model as a whole? For that purpose, cmp counts any observation that is in at least one equation. The return values e(N1), e(N2),... record numbers in each equation.

[Guest]

David Roodman i mean shouldn't the number of observations be less for SHARE (as SHARE is estimated for only those who have part==1)?

[David Roodman]

You can use whichever number you think is appropriate. cmp is a general tool. It doesn't "know" you are doing a selection model.

[Guest]

David Roodman
Is it possible to accommodate endogeneity (due to simultaneity) in such a model? For instance EDU affects part and SHARE, and part and SHARE also affect EDU . I know I am asking for too much in a model. But any way to do that, given that i have instruments?