Fractional logit model - unbalanced panel - two-way fixed effects

[Katharina Koe]

Hello,

I am using panel data, my panel is unbalanced.
I observe N=773 cohorts over T=39 time periods.
the number of observations is 5090 and on average each cohort is observed 6.6 times.

My dependent variable is fractional (0-1)
my independent variables are mostly continuous, one is also fractional (0-1).

I am interested in the effects of the IV on the DV while holding time and country fixed
The cohorts are created based on individuals who have the year of birth & country in common.

I suspect my model could suffer from heteroskedasticity.

Searching the internet, I found two commands:

1. following the paper Papke & Wooldridge
http://people.stern.nyu.edu/wgreene/Econometrics/Papke-Wooldridge-FractionalResponse.pdf

glm DV IVs i.country i.year i.oldcountry##c.year, fam(bin) link(logit) robust


2. using a population-averaged model

xtgee DV IVs i.country i.year i.country##c.year, family(bin) link(logit) corr(independent) i(idcode) t(timevar) vce(robust)

My question is:
1. from my understanding, (1) only applies to balanced panels, is there an extension / similar approach for unbalanced panels?
2. I am not sure whether (2) is a good specification because it is using population-averages? (if it wasn't for the fractional DV, I would go with a fixed effect model because of the unobserved heterogeneity. Is PA more like a RE or FE model or entirely different?)
3. Are there alternatives to those? What would be a good specification?

Thanks in advance,
Katharina

[Andrew Musau]

On the issue of whether it is appropriate to use the (linear) fixed effects (FE) estimator when you have a fractional dependent variable, Papke and Wooldridge (2008) in the paper that you reference note:

It seems evident that, for estimating the marginal effect of a given percentage change in [the independent variable], the difference between linear and nonlinear models is not important

In most empirical cases, the marginal effects are what we are interested in. Therefore, I don't see any reason for disregarding the FE estimator (with clustered standard errors for robust inference). Also note that the vast majority of empirical studies where the dependent variable is a fraction do use a linear estimator..



Reference.
Papke E.L. and Wooldridge J.M. (2008). Panel data methods for fractional response variables with an application to test pass rates. Journal of Econometrics

[Katharina Koe]

Hi Andrew,
many thanks for your reply!

It surprises me that the significance of the explanatory variables changes a lot (from regular xtreg, fe to xtgee). How do I make sense of that? Which significance is more "relevant"?

And regarding the marginal effects, after the -xtgee command, should I use the -margin command or interpret the values given in the output? The -margin commands yields much smaller effects.

Thanks a lot!

[Andrew Musau]

For comparison, the process is a little bit more involved. Leslie has the do files from the 2008 paper in her website, so you should download these and follow the procedure

http://econ.msu.edu/faculty/papke/index.php