Interpretation of xtreg,fe

[Temirlan Talap]

Dear Community,

Could you please help with the interpretation of the -xtreg -fe results. Basically, I want to know why R-square in my regression is so small if Hausman test -xtoverid showed me to use random effect.

What is the Wald chi2 test show? How to interpret this number? And what is the sigma_u sigma_e and rho shows and how to interpret them?

Below is my code:

 xtreg ROE ENV SOC GOV Leverage NLTR GDP, re cluster (ID)

Random-effects GLS regression                   Number of obs     =        459
Group variable: ID                              Number of groups  =         51

R-squared:                                      Obs per group:
     Within  = 0.0302                                         min =          9
     Between = 0.1195                                         avg =        9.0
     Overall = 0.0928                                         max =          9

                                                Wald chi2(6)      =      17.67
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0071

                                    (Std. err. adjusted for 51 clusters in ID)
------------------------------------------------------------------------------
             |               Robust
         ROE | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         ENV |   .0002361   .0004906     0.48   0.630    -.0007255    .0011977
         SOC |   .0003609   .0008183     0.44   0.659     -.001243    .0019648
         GOV |   .0011957   .0005359     2.23   0.026     .0001453    .0022462
    Leverage |  -.0003589   .0003228    -1.11   0.266    -.0009916    .0002738
        NLTR |  -.0593318   .0243814    -2.43   0.015    -.1071184   -.0115452
         GDP |   .3779599   .5465431     0.69   0.489     -.693245    1.449165
       _cons |   .6365734   .2025927     3.14   0.002      .239499    1.033648
-------------+----------------------------------------------------------------
     sigma_u |  .19015154
     sigma_e |  .14583366
         rho |  .62964854   (fraction of variance due to u_i)
------------------------------------------------------------------------------

[Carlo Lazzaro]

Temirlan:
unsolicited advice: if you have so many doubts, you should study any decent textbook on panel data econometrics,
That said:
1) you reported code and outcome of -xtreg,re-
2) you should take a look at the between R-sq;
3) to investigate whether there's evidence of a panel-wise effect, run -xttest0- after -xtreg,re-;
4) wald chi2 gives back the the jointly significance of all the predictors, along with the related p-value;
5) as far as -sigma_e-, -sigma_u- and -rho- are concerned, see -xtreg- entry, Stata .pdf manual.

[Maxence Morlet]

Carlo provided an excellent answer, and as a complete aside if I may, I wouldn't recommend conducting a Hausman test if you're not certain all Gauss-Markov assumptions hold in your data. If they don't, which will most likely be the case, I would recommend performing a Mundlak test (1978). Subsequently, you will probably decide in favour of using fixed-effects.