Panel Data Modelling - Methodological Issues

[Jan Brejzek]

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).

xtset Company YEAR, yearly

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

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

 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)

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?

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

[Phil Bromiley]

What is your panel? If you use firm as the panel, then you generally don't need industry. I would take the xtoverid results and go with random effects.

While this can be seen as a statistical issue, it is also a theoretical issue. Are the factors that you think influence etr stable features of the firms or not? Is the theory about within-panel changes or not? That is the fe estimate is based on the variation in the x's around their means, which may be a very different model than the levels of the variables. Indeed, the interpretation of variation around the mean may be totally different than the interpretation of the levels - it is changes in leverage over time, not the level of leverage for example. There is a massive difference between explaining differences across entities versus explaining differences in entity behavior over time.

[Jan Brejzek]

Thanks for the answer, Phil. I'm more concerned with the differences across the companies, rather than changes within them over time. As far as I understand, this is another argument against applying FE estimator (besides the actual test results), right?

[Carlo Lazzaro]

Jan:
if you're mainly interested in between-panel variation and -xtoverid- points you towards -re- specification, I would second Phil's wise advice to go -xtreg,re- (clustering your standard errors).

[Jan Brejzek]

Thank you both for the advice.