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st: Fractional Probit with Fractional Endogenous Variable

Subject   st: Fractional Probit with Fractional Endogenous Variable
Date   Tue, 11 Feb 2014 12:38:14 -0500

I am working on a fractional probit model with an endogenous fractional
variable. I am trying to use a two stage procedure for the analysis. Both
the first stage and the second stage dependent variables are fractional
values ranging from 0 to 1. The first stage equation variables lead the
second stage variables by one period.  Our dataset is an unbalanced panel
dataset (the number of observations ranges from 2-6, with an average of
2.86 observations per firm).

If I estimate the analysis using two stage least squares, the predicted y
values lie outside the bounds of 0 and 1.

I am a bit uncertain how to estimate the fractional logit with a
fractional endogenous variable. Would it be correct to:
1) estimate the first stage using glm y x xbar z zbar timedummies, fa(bin)
link(probit) cluster(id)
2) estimate the inverse mills ratio using
predict double fracxb, xb
gen pdffrac = normalden(fracxb)
gen cdffrac = normprob(fracxb)
gen imr = pdffrac/cdffrac

3) by id: g lag_imr=imr[_n-1]
4) estimate the second stage using glm y x xbar lag_imr timedummies,
fa(bin) link(probit) cluster(id)
5) use bootstrapping and calculate the average partial effects

I would greatly appreciate any feedback or guidance.


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