Hello Statalist!

I have a large N, small T panel dataset on which I have run some fixed effects regressions. The model is predicting industry adjusted firm performance based on independent variables from one time period before. The choice of FE is supported by the Hausman test.

I am looking for some advice on which tests one would need to perform to demonstrate the valid model with BLUE estimators? I presume this would be all the Gauss Markov assumptions, but am unsure of how to test them.

I have the following conditions (and in some cases tests):
Normality of Residuals
Code:
predict rs
kdensity rs, normal
pnorm rs
swilk rs
Homoskedasticity
Code:
predict Fitted, xb
predict Epsilon, e
twoway (scatter Epsilon Fitted), ytitle(Epsilon residuals) xtitle(Fitted values)
Multicollinearity
Code:
pwcorr var1 var2 ... vark
Autocorrelation
Test unknown

Serial correlation
Test unknown

Exogeneity
Test unknown

Any advice on the assumptions which need to be tested and additional tests which would need to be performed would be most appreciated.

Thanks all!

Ayrton Da Silva