Hello dear community,
I am currently analyzing a dataset to find out whether treatment effects differ between subgroups.
I have panel data (or at least i think i have) following individuals that gave answers to surveys at different points in time. The sample is unbalanced. I have answers from different individuals at different points in time. There are two treatments and a control group. Each individual is either in one of the treatments or the control group. The individuals can work in four different sectors (sec0_b sec1_b sec2_b sec3_b).
I want to find out if the two treatments have a significant impact on tprofits for each of the business sectors. I would also like to control for other factors such as secondaryedu, I_emp, tprofits_b and logage.

I did not find any evidence which regression to run in theory

I then ran these different regression but i was not able to interpret the differences

Pooled OLS: reg tprofits i.treat i.wave $controls if wave>=0 & wave<=7 & sec0_b==1
Fixed effects: xtreg tprofits i.treat i.wave if wave>=0 & wave<=7 & sec0_b==1, fe cluster(id)
Random effects: xtreg tprofits i.treat i.wave $controls if wave>=0 & wave<=7 & sec0_b==1, re cluster(id)

I am relatively new to STATA and statistics and have learned most of my knowledge "on the go" which is why I am sure that I have missed something and would therefore appreciate any hints that lead me towards the most unbiased results.
Thanks in advance