I am carrying out a difference-in-difference analysis using 7 cycles of PISA data (2000-2018). I am comparing reading achievement outcomes between Portugal (treated country) and Hungary, Iceland, and Denamrk (control countries).
In my model I have included year (see variable labeled "pisa_cycle" in the linked output below) and country (cnt_fixedeffects) fixed effects, and clustered SEs at the country level. From the attached output (see below), you will notice that the fixed effects coefficients for 2018 and country 3 are omitted from the results, despite the fact that they are not the reference categories (year 2000 and country 4 (Portugal) are the reference groups, respectively).
The reason for this (I think!!) is because I am trying to include country and time-fixed effects when I only have four countries in the analysis and one in the treatment. So, if there's only one country in the treatment group, including a country-fixed effect for that country is redundant because it essentially captures the treatment effect.
I'm sort of at an impasse re how to proceed. I suspect I don't want to just drop country fixed effects entirely from the analysis. Do you have any suggestions?
Stata Code repest PISA,estimate(stata: reg pv@read i.treatment* i.pre_post did i.pisa_cycle b4.cnt_fixedeffect, robust cluster (cnt)) results(add(N)) svyparms([NBpv(5) final_weight_name(adjusted_w_fstuwt) rep_weight_name(w_fstr_adjusted) NREP(80)])
I've been reading up on the fixed effects literature, but I haven't come across anything that addresses the issue.