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st: Fractional Logit Model


From   Richard Bluhm <richard.bluhm@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Fractional Logit Model
Date   Sat, 20 Apr 2013 17:04:01 +0200

Hi Samuel,

I have some experience with these models and may have a few more
useful pointers for you. Regarding #4, you probably will want to
specify a probit link instead of a logit link. The models discussed in
Papke & Wooldridge 2008 use Correlated Random Effects (CRE) to account
for the presence of unobserved heterogeneity (the time averages + a
normally distributed term). Hence, the GLM/GEE estimator with CRE as
they propose it works with a probit link. Since you have a panel
problem you will also want to use cluster robust standard errors. The
normal  SEs will be much too large in the fractional probit/logit case
as Nicholas Cox points out. You can use something like "glm y x xbar,
fam(bin) link(probit) vce(cluster id)", where "*bar" means time
average and you cluster on your panel identifier. You may switch to
GEE but that will probably not make much of a difference for the final
results (see the example in their paper). All of the coefficients are
scaled and only the partial effects of time-varying variables are
identified, so "margins, dydx(x)" will be your friend for getting the
average partial effects after running your model.

In addition, for 1#-3#, note that these methods work only on balanced
panel data! For unbalanced panels, you'll have to make it balanced or
you'll have to take a look at Wooldridge's slides for the 2011 Chicago
Stata Users Group meeting (google it) or at the working paper
"Correlated Random Effects Models with Unbalanced Panels" currently on
his website. It get's a bit more complicated then and these models are
reasonably sophisticated, meaning you may want to tread carefully as a
newbie. I am in the process of writing a program to fit some of these
models for very unbalanced panels but it's not done yet (lacks a help
file and some debugging), so it won't be available for a few more
weeks.

Last but not least, Wooldridge explains these issues more in his
fantastic graduate textbook "Econometric Analysis of Cross Section and
Panel Data" (2010 edition, not the earlier one). The accompanying
slides are online somewhere at MIT Press and may give you a peak into
what's in the book (they also include some example code).

Hope this helps.

Richard

-- 
Richard Bluhm
PhD Fellow
UNU-MERIT/ MGSoG
www.maastrichtuniversity.nl
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