Dear community,

after having found heteroscedasticity and autocorrelation in my panel data, I account for it with -xtreg ..., fe/re vce (cluster Company_ID)-. Because of this, I am unable to execute the conventional -hausman- command.

My regression is as follows: ROA = c.Var1_c##i.Industry Var2 Var3 Var4 Var5 i.Year, with Var1 being compensation to the CEO, Var2-5 control variables and Industry being a dummy variable (1 to 10 for different industries). I winsorized at (5 95). Var1_c is the mean-centered version of Var1, which itself is the squareroot of compensation to the CEO. This was done to account for multicollinearity arising from the interaction term.

I have come across two ways to determine whether to use RE or FE: 1) the -xtoverid- command and 2) Variable Addition Test (VAT) as discussed by J. Wooldridge.

1) -xtoverid-

Code:
. gen Interaction = Var1_c*Industry

. xi: xtreg ROA c.Var1_c i.Industry Interaction Var2 Var3 Var4 Var5 i.Year, re vce(cluster Company_ID)

. xtoverid

Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re  robust cluster(Company_ID)
Sargan-Hansen statistic  26.143  Chi-sq(11)   P-value = 0.0062
This result indicates, that I should use FE.

2) Variable Addition Test

Code:
. egen Var1bar = mean(Var1_c), by(Company_ID)

. xtreg ROA c.Var1_c Var1bar i.Industry c.Var1_c#i.Industry Var2 Var3 Var4 Var5 i.Year, re vce(cluster Company_ID)

Random-effects GLS regression                   Number of obs     =        466
Group variable: Company_ID                      Number of groups  =         99

R-sq:                                           Obs per group:
     within  = 0.2107                                         min =          1
     between = 0.3837                                         avg =        4.7
     overall = 0.4470                                         max =          6

                                                Wald chi2(29)     =     312.45
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

                                       (Std. Err. adjusted for 99 clusters in Company_ID)
-----------------------------------------------------------------------------------------
                        |               Robust
                ROA_new |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------------+----------------------------------------------------------------
                Var1_c  |   .0004388   .0002735     1.60   0.109    -.0000973    .0009749
               Var1bar  |   .0001705    .000198     0.86   0.389    -.0002176    .0005585
                        |
             ...
                        |
                   Year |
                  2015  |   .0009689   .0020876     0.46   0.643    -.0031227    .0050605
                  2016  |   .0001361   .0021731     0.06   0.950     -.004123    .0043952
                  2017  |   .0041183   .0030348     1.36   0.175    -.0018297    .0100663
                  2018  |  -.0000602   .0035568    -0.02   0.986    -.0070314     .006911
                  2019  |  -.0037212   .0041598    -0.89   0.371    -.0118744    .0044319
                        |
                  _cons |   .1900278   .0648387     2.93   0.003     .0629462    .3171093
------------------------+----------------------------------------------------------------
                sigma_u |  .03361633
                sigma_e |  .01488897
                    rho |  .83600278   (fraction of variance due to u_i)
-----------------------------------------------------------------------------------------
As Var1bar > 0.05, this result indicates, that I should use RE.

What method should I use? Did I execute both commands/methods correctly?

Thank you,
Pietro