My research question implies using several independent variables that describe country-years and countries in general (to keep question reasonably simple, let's suppose I don't have any '2nd level' variables, and all I have in the right-hand side differs on the country-year level).
The specific thing here is that the dependent variable I want to use is constant for some countries. E.g. in some countries, this indicator varied significantly, yet in others it could not to differ at all.
I want to draw conclusions about both (a) how to explain variance inside countries' histories and (b) how to explain variance between countries.
It seems like classic between/within trade-off, and multilevel modelling might be helpful, as well (given I actually have some 2nd level indicators).
Still, I am a little confused about what to do with those countries that experienced no fluctuations. Can I just model these dependencies in a straightforward way, like the dependent variable is OK?