I have panel data for individuals in an economy that experienced fluctuations in employment levels. I also have some health information for these individuals, BMI, self-rated health etc.,
My question is this, my dataset is quite small, (1500 people wave one, 1000 wave two, 700 people wave three), I am aware that fixed effects regressions can really cut down the number of individuals I can examine observations in comparison to random effects. Hausman tests aside, are there any theoretical good arguments for using a random effects model in the case where fixed effects decreases the number of individuals analysed to just a handful of people?
Similarly, in a fixed effects regression is it necessary to include control variables? After all, surely this kind of regression is only examining within individual variation, such that control variables are not necessary?
Basically, as fixed-effects models are looking at the determinants of within-subject variability. If there is no variability within a subject, there is nothing to examine. If I am analyzing something that rarely changes across time, or if very few individuals are in a binary group that I would like to examine, there wouldn’t be many cases left for a fixed effects analysis. Thus some of the sample will be dropped from the analysis. Which is what I mean by "reduce the number of individuals (in my sample)". I am aware that other techniques, like random effects or xtreg, fe, won’t cost so many cases and would like a sound theoretical argument to support the use of these techniques.
Any and all insight is greatly appreciated,