Hello everybody,

I am running a fixed effects model panel analysis for my masters thesis. My supervisor told me to also discuss Gauß Markov theorem and general OLS assumptions in my thesis, run OLS first, discuss tests and the switch to panel data model. So what I'm looking at are especially the following assumptions:

(1) E(ut) = 0

(2) var(ut) = σ2 < ∞

(3) cov(ui, u j) = 0

(4) cov(ut, xt) = 0

(5) ut ∼ N(0, σ2)

1. Question: For me that means as much as: no autocorrelation, no heterogeneity, normality of residuals. Did I miss anything? Also I guess you always have to test for omitted variables and multicollinearity, right?

So I start with running some tests after using regress at first:

estat imtest
estat ovtest
xtserial
estat vif
sktest

2. Question: Which other tests should I use on the initial OLS regression?

Also, after I switch to panel data I use the command:

xtreg depvar indepvars, fe vce(cluster ID)

3. Question: As far as I understand using the fe command with vce (cluster ID) already corrects for heteroscedasticity and autocorrelation, but what about the other assumptions? Do they still have to be met?
Also I understood that as long as I have a constant in my regression, assumption 1 is always met, but the fixed effects transformation drops my constant, no?
And what about normality of residuals, is there a test I can use after xtreg?

4. Question: I have a lot of different models I have to test and chose from and interaction terms to add after initially testing without etc. etc. Do I actually have to perform all those tests on aaaall my models separately?

5. Question: What can I actually do if in the end I still have non normality of residuals and omitted variables? I guess not much?

Thank you so much for your help!! I've been on this for days and googled so much but most tutorials I see are only on normal OLS, and often only on one independent variable so you can use plots etc...

Best,

Sabrina