st: Fractional logit, selection and panel data

["Seliger Florian" <seliger@kof.ethz.ch>]

Dear Statalist,

There were several discussion on modeling proportions , e.g. http://www.stata.com/statalist/archive/2012-10/msg00241.html.

I've learnt that 
1. Tobit is not appropriate for proportions although it is widely used in practice
2. Fractional logit is the right method.
3. It can be implemented by glm

Just as in the old thread, my dependent variable is a sales share with certain products (0 - 100%).
I also have a selection equation where the dependent tells me whether firms introduced a product at all (binary coded).
On the right-hand side, I have more or less the same variables in both equations (except for an exclusion restriction that might be added in the selection equation).

I'm wondering if I can proceed as follows:

*Estimate selection equation with logit
logit newproduct x1 x2 x3
*Calculate inverse-mills ratio
predict inno_hat if e(sample), xb
gen pdflogit_inno=normalden(inno_hat)
gen cdflogit_inno=normal(inno_hat)
gen imr=pdflogit_inno/cdflogit_inno
*Estimate outcome equation with glm and include inverse mills ratio
glm salesshare_with_new_product/100 x1 x2 x3 imr, family(binomial) link(logit)

I have also noticed a command for estimation of one- and two-part fractional regression models called "frm" by Ramalho
http://evunix.uevora.pt/~jsr/FRM.htm

I don't have a clue what's appropriate in my case. Do any of you have experience with "frm" or with selection models  in this context?
Any help is appreciated!


For panel fractional data, there is a presentation of J. Wooldridge http://www.stata.com/meeting/chicago11/abstracts/#wooldridge
Although there is a command "xtgee" for panel data, Wooldridge seems to suggest (if I get him right) to use xtreg for unbalanced panel data.
Does anyone know why not to use xtgee and why xtreg appears to be appropriate for fractions?

Thank you for your consideration.

Best regards,
Florian





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