Dear Stata Users,

I experience some serious confusion while working on my model due to the fact, that I'm not sure whether the 'things' I do are right and in proper order. That being said, I'd like to ask for Your help, hoping it will clarify my doubts and prevent from methodological mistakes.

My model aims to explain the variability of effective tax rates (ETR) with firm characteristics (company-specific financial-statement-based data), controlling for year and industry as it is commonly practiced in literature. There are 450 companies, 2975 observations of ETR (alternative formulation of ETR: 1608 obs) in the time range of 2004-2016; each company has min. 3 observations and my panel is strongly unbalanced.

First I want to decide, whether it is FE or RE model, that should be used. I compute both, test the significance of dummies and then (after dropping industry) test with Hausman, in favour of FE, (at least assuming 10% level of significance, but so I did when keeping time dummies in).
Code:
xtset Company YEAR, yearly
Code:
xtreg  TotalETR SIZE LEVERAGE ROA INTNG CAPINT INVINT i.YEAR, fe
testparm i(2005/2016).YEAR

 F( 12,  2572) =    1.56
            Prob > F =    0.0959

estimates store fixed
Code:
xtreg  TotalETR SIZE LEVERAGE ROA INTNG CAPINT INVINT i.YEAR i.INDUSTRY, re
testparm i(2/8).INDUSTRY

           chi2(  7) =    4.85
         Prob > chi2 =    0.6779

xtreg  TotalETR SIZE LEVERAGE ROA INTNG CAPINT INVINT i.YEAR, re
testparm i(2005/2016).YEAR


           chi2( 12) =   18.90
         Prob > chi2 =    0.0909
Code:
 hausman fixed ., sigmamore

    Test:  Ho:  difference in coefficients not systematic

                 chi2(18) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =       26.63
                Prob>chi2 =      0.0862
Now I think the model should be tested for heteroskedasticity and autocorrelation. Therefore I do the following and conclude, that both are present (at least in FE, since I couldn't apply xttest3 to RE)
Code:
xttest3

Modified Wald test for groupwise heteroskedasticity
in fixed effect regression model

H0: sigma(i)^2 = sigma^2 for all i

chi2 (385)  =   2.2e+06
Prob>chi2 =      0.0000

xtserial TotalETR SIZE ROA LEVERAGE CAPINT INVINT INTNG

Wooldridge test for autocorrelation in panel data
H0: no first-order autocorrelation
    F(  1,     340) =     13.334
           Prob > F =      0.0003
I've read that in such a case one should estimate the models using vce(cluster id) variance estimator and repeat all the previous steps, that is the significance tests of dummies (time dummies jointly significant) and the Hausman test (xtoverid, so I had to recode time dummy to Y1,..). The results indicate, that the RE model is preferred. Am I right or is everything wrong?
Code:
xtreg  TotalETR SIZE LEVERAGE ROA INTNG CAPINT INVINT  Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10 Y11 Y12 Y13, vce (cluster Company) re

xtoverid

Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re  robust cluster(Company)
Sargan-Hansen statistic  22.983  Chi-sq(18)   P-value = 0.1912