Pseudo Panel Estimation

[kirill.serykh]

Hello! I'm trying to estimate the pseudo panel data regression, where I have 4 levels of data: year. country, school and student (I'm estimating students results of test from their own and their school's characteristics). As far as I understood, in this model an error consists of 4 parts - error that is associated with year, country, school and student. I have 5 years and 33 countries, so I made a dummy variables for them in order to avoid bias and inconsistency in coefficients. But the data has the following specific feature: each country every year changes the number of schools and the number of students (in this test every year participate different students due to the restrictions in age and different schools are chosen, but sometimes they interact, database does not provide this information). Making dummies for schools is impossible, thus the total number of schools is >20000 (totally I have over 600000 observations in my regression). What should I do?
As far as I understood, I should use FE or RE models, but how to do it with pseudo panel data?
Also I read that it could be done using ML model, where I will recieve consistent estimators in order to estimate the dispersion based on remainders from ML. After that using this estimator of dispersion I could get effective estimators based on GLS but I also don't know how to do it.
Finally, I really need your advice!
Thanks in advance.
I use Eviews 7.2.