[Carlo Lazzaro]

Jihad:
yes, that's what I meant.
The main reason of your pooled OLS being no different from a mean estimate of the dependent variable is probably due to the small sample size.
Anyway, if you have no chance of collecting more data, I fear there's nothing to do but declaring it in your research report (if reporting inferential statistics is mandatory for you research project. If that were not the case, I would stop at descriptive statistics).

[Jihad El Yaagoubi]

yes reporting inferential statistics in mandatory, I must have an econometric model, not just descriptive statistics and I have no chance to get more data, this is the max of data I can have.
So what can I do? Report the pooled OLS model and say there is OVB so it may be unreliable?

[Jihad El Yaagoubi]

When I re run the analysis on 5 years not 6 as the precedent, I get these results. Is this reliable ?

. reg LOGROA i.CSR Size Risk ib2.Industry Age,vce(cluster Companyscode)

Linear regression                               Number of obs     =        135
                                                F(7, 27)          =       2.31
                                                Prob > F          =     0.0555
                                                R-squared         =     0.0326
                                                Root MSE          =     .57016

                          (Std. Err. adjusted for 28 clusters in Companyscode)
------------------------------------------------------------------------------
             |               Robust
      LOGROA |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       1.CSR |   .0820125   .1101638     0.74   0.463     -.144025    .3080499
        Size |  -.0855449   .0982912    -0.87   0.392    -.2872217    .1161319
        Risk |   .0302993   .0227689     1.33   0.194    -.0164186    .0770173
             |
    Industry |
          1  |  -.1187325   .1884803    -0.63   0.534    -.5054621    .2679971
          3  |  -.0112019   .2927613    -0.04   0.970    -.6118984    .5894947
          4  |   -.155525   .2092211    -0.74   0.464    -.5848113    .2737612
             |
         Age |   .0006165   .0026171     0.24   0.816    -.0047534    .0059864
       _cons |  -.5186358   .8567413    -0.61   0.550    -2.276524    1.239252
------------------------------------------------------------------------------

. linktest

      Source |       SS           df       MS      Number of obs   =       135
-------------+----------------------------------   F(2, 132)       =      2.93
       Model |  1.81242623         2  .906213114   Prob > F        =    0.0570
    Residual |  40.8639008       132  .309575006   R-squared       =    0.0425
-------------+----------------------------------   Adj R-squared   =    0.0280
       Total |   42.676327       134  .318480052   Root MSE        =    .55639

------------------------------------------------------------------------------
      LOGROA |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        _hat |   9.988904   7.718072     1.29   0.198    -5.278206    25.25601
      _hatsq |   3.465446   2.969945     1.17   0.245    -2.409399    9.340291
       _cons |   5.785171   4.998678     1.16   0.249    -4.102708    15.67305
------------------------------------------------------------------------------

. estat ovtest

Ramsey RESET test using powers of the fitted values of LOGROA
       Ho:  model has no omitted variables
                 F(3, 124) =      1.60
                  Prob > F =      0.1934

[Carlo Lazzaro]

Jihad:
I would be less tragic with saying that, due to the limited sample size, the regression model does not satisfy its methodological requirements (es OVB).
I would also stress that more resrach/more data are needed to perform reliable panel data analysis in this research field.
Last but not least I would have a comprehensive discussion with my teacher/professor/supervisor in order to share the best way to report my results..

[Jihad El Yaagoubi]

But R squared is very low 0.03. maybe it s not apporopriate

[Jihad El Yaagoubi]

what if I run a test of mean comparison, and see if there is a difference between the mean of the variance of each group (0 and 1) ?

[Carlo Lazzaro]

Jihad:
the low R-sq may be the offspring of a small sample size.
You probably mean a -ttest- comparing the mean of the same variable (which one?) by two groups (which ones?): this approach it's worth trying..

[Jihad El Yaagoubi]

yes this what i mean, I tried it , here the results

 ttest ROA, by(CSR)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |     110    .0762193    .0107109    .1123364    .0549907    .0974479
       1 |      58    .2276614    .1475595     1.12378   -.0678215    .5231442
---------+--------------------------------------------------------------------
combined |     168    .1285029    .0514374    .6667048    .0269515    .2300542
---------+--------------------------------------------------------------------
    diff |           -.1514421    .1078746               -.3644251    .0615409
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t =  -1.4039
Ho: diff = 0                                     degrees of freedom =      166

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0811         Pr(|T| > |t|) = 0.1622          Pr(T > t) = 0.9189

But which assumptions I should test to ensure reliability of results? I can't use the control variables

[Carlo Lazzaro]

Jihad:
the -ttest- outcome (by the way, I would have imposed unequal variances) mirrors what the pooled OLS already told you: there's no evidence of difference in ROA between the two groups.

[Jihad El Yaagoubi]

But we said in the pooled ols that it's significant at 0.1 level so it's indicate a relationship

[Carlo Lazzaro]

Jihad:
claiming that pooled OLS F-test (p=0.0555) reject the null of no difference between regression and -mean ROA- would sound as a bit weak statement (however it may be perfectly acceptable in your research field; discuss with your supervisor about this topic).
The main issue is that you have a small sample size.

[Jihad El Yaagoubi]

when I reduce the sample size to 24 firms, I get this results

xtreg ROA i.CSR Size Risk ib2.Industry Age,re

Random-effects GLS regression                   Number of obs     =        143
Group variable: Companyscode                    Number of groups  =         24

R-sq:                                           Obs per group:
     within  = 0.9577                                         min =          5
     between = 0.9184                                         avg =        6.0
     overall = 0.9504                                         max =          6

                                                Wald chi2(7)      =    2828.41
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
         ROA |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       1.CSR |   .0014123   .0328655     0.04   0.966    -.0630028    .0658274
        Size |  -.0025944   .0352183    -0.07   0.941     -.071621    .0664322
        Risk |   .9676044   .0184278    52.51   0.000     .9314865    1.003722
             |
    Industry |
          1  |  -.1654682    .062308    -2.66   0.008    -.2875897   -.0433467
          3  |  -.1392238   .0839058    -1.66   0.097    -.3036761    .0252286
          4  |   -.130692   .0732616    -1.78   0.074    -.2742822    .0128982
             |
         Age |   .0016721   .0011349     1.47   0.141    -.0005523    .0038965
       _cons |   .0923157   .3037684     0.30   0.761    -.5030593    .6876908
-------------+----------------------------------------------------------------
     sigma_u |  .07611041
     sigma_e |  .14965201
         rho |  .20550193   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. xttest0

Breusch and Pagan Lagrangian multiplier test for random effects

        ROA[Companyscode,t] = Xb + u[Companyscode] + e[Companyscode,t]

        Estimated results:
                         |       Var     sd = sqrt(Var)
                ---------+-----------------------------
                     ROA |   .5189751       .7203993
                       e |   .0223957        .149652
                       u |   .0057928       .0761104

        Test:   Var(u) = 0
                             chibar2(01) =     6.34
                          Prob > chibar2 =   0.0059

. reg ROS i.CSR Size Risk ib2.Industry Age,vce(cluster Companyscode)

Linear regression                               Number of obs     =        142
                                                F(7, 23)          =     298.62
                                                Prob > F          =     0.0000
                                                R-squared         =     0.2838
                                                Root MSE          =     1.2404

                          (Std. Err. adjusted for 24 clusters in Companyscode)
------------------------------------------------------------------------------
             |               Robust
         ROS |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       1.CSR |  -.3327764   .1063773    -3.13   0.005    -.5528345   -.1127183
        Size |   -.234059   .1658956    -1.41   0.172    -.5772401    .1091221
        Risk |    .911794   .0438524    20.79   0.000     .8210784     1.00251
             |
    Industry |
          1  |  -.4359061   .2685911    -1.62   0.118    -.9915291    .1197169
          3  |   -.296361   .3961831    -0.75   0.462    -1.115928    .5232061
          4  |  -.3317121   .4137356    -0.80   0.431    -1.187589    .5241652
             |
         Age |  -.0018197   .0044994    -0.40   0.690    -.0111274    .0074881
       _cons |   2.957767    1.47031     2.01   0.056    -.0838001    5.999334
------------------------------------------------------------------------------

. estat ovtest

Ramsey RESET test using powers of the fitted values of ROS
       Ho:  model has no omitted variables
                 F(3, 131) =      1.32
                  Prob > F =      0.2695

What do you think ?

[Jihad El Yaagoubi]

Which value should take the standard error ?

[Carlo Lazzaro]

Jihad:
the R-sqs of your first model look suspiciously high: it would seem as a make-up to existing data has been applied (obviously, I could be wrong).
Besides, after -xtest0- you should perform -hausman- to check whether -re- specification outperforms the -fe- one.
Your second model considers a different dependent variable (return on sales vs return on assets): I cannot comment on the reason of your decision. However, I fail to get why you used -xtreg- in your first model and pooled OLS in the second one, though.
Set aside technicalities, I'm under the impression that you're hunting for "the best" model (whatever "best" means in this context): I would recommend you to be very cautious about that: bad specifications and overfitting hit experts' eyes immediately.

[Jihad El Yaagoubi]

Yes Carlo, you're right im looking for the best model and the best model for me as a beginner is significant pvalue, best R-sq, No OVB...
i am really confused for this I try several models to choose one. For ROS and ROA I must use theme both because they important depvar in literature.
if the sample size is 24 firms, is that a problem ?