I am referring to this paper on school quality and returns to schooling. The econometric specification has been described by eqn (1) on page 4.
The authors have taken "cohort specific fixed effect for each state of birth" and "cohort specific fixed effect for each state of residence". Am I correct in understanding this is is a form of interaction between cohort and state, which I can obtain by creating group identifiers based on cohort and state such that different combinations of values of cohort-state are generated?
If so, what situations would justify using such fixed effects instead of just using cohort fixed effects and state fixed effects separately?
Moreover, there is an interaction between years of education and returns to education, where returns to education consists of two components: cohort and state of birth effects, and cohort and region of residence effect. While I have gone through their rationale in that section, I'm still having a hard time understanding what exact purpose this form of specification serves.
Would appreciate it if someone takes some time to help resolve these doubts. Thanks!