Panel regression - subgroup analysis

[Max Duerkop]

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

[George Ford]

This looks like pooled cross section to me, unless all individuals are observed in each t. Are the treatments given at the same time?

[Max Duerkop]

Hello, all individuals are not observed in each t but the treatments are given at the same time.
Is a pooled cross section the same as a pooled OLS?
Kind regards
Max

[Carlo Lazzaro]

Max:
my gut-feeling is that you're dealing with survey waves (hence -the -svy- suite should be something to take a look at).
If you do not have all the information concerning the survey setup (say, PSU) and you cannot retrieve them, you should probably switch to an OLS. I would not label it as a pooled OLS, as you do not have the same sample measured at different points in time (or, put differently, you do niot have a panel dataset).

[George Ford]

You can use fixed effects in this case if you think there's omitted variables at some relevant level they can absorb (e.g., industry, country, etc).