[Guest]

Now, for my initial model I applied the Breusch and Pagan Lagrangian multiplier test, according to which the within-variance is relevant, pooled ols is not acceptable and a panel data estimation is preferable. After performing the Hausmann test, the coefficients of re and fe are not equal, i.e. within var explains most of the total variance and fe is finally the appropriate model. Is this interpretation correct? Can I build the baseline model on this and then introduce the moderation effects?

Please correct me if I have overlooked something, misinterpret or am on the wrong track! Thanks!

. reg esg_score curetr intan lev pb_ratio capint roa size salary_gap board ceo_duality gender ceo_tenure ceo_age i.yea
> r i.siccode

      Source |       SS           df       MS      Number of obs   =       856
-------------+----------------------------------   F(23, 832)      =     27.74
       Model |  114813.394        23  4991.88672   Prob > F        =    0.0000
    Residual |  149715.249       832  179.946213   R-squared       =    0.4340
-------------+----------------------------------   Adj R-squared   =    0.4184
       Total |  264528.643       855  309.390226   Root MSE        =    13.414

------------------------------------------------------------------------------
   esg_score |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      curetr |   2.042687   3.169883     0.64   0.519    -4.179221    8.264594
       intan |  -1.615983   5.408744    -0.30   0.765    -12.23237    9.000403
         lev |   7.755963   4.275132     1.81   0.070    -.6353493    16.14728
    pb_ratio |  -.0094807   .0713813    -0.13   0.894    -.1495894    .1306279
      capint |   10.70627   3.448553     3.10   0.002     3.937385    17.47516
         roa |   22.94966   9.100931     2.52   0.012     5.086176    40.81314
        size |   6.040562   .4092076    14.76   0.000     5.237361    6.843762
  salary_gap |   .0253781   .0062417     4.07   0.000     .0131267    .0376294
       board |  -.4597915   1.108344    -0.41   0.678     -2.63527    1.715687
 ceo_duality |   3.006441   1.132991     2.65   0.008     .7825841    5.230297
      gender |   4.920583   2.252003     2.18   0.029     .5003072    9.340858
  ceo_tenure |  -.4092416   .0833788    -4.91   0.000    -.5728991   -.2455841
     ceo_age |   .1471543    .093262     1.58   0.115    -.0359021    .3302107
             |
        year |
       2016  |   .4741067   1.565324     0.30   0.762    -2.598342    3.546555
       2017  |   1.058177    1.52088     0.70   0.487    -1.927036     4.04339
       2018  |   3.216315   1.495764     2.15   0.032     .2803999    6.152229
       2019  |   4.125925    1.49128     2.77   0.006     1.198811    7.053039
             |
     siccode |
          3  |   5.108371   3.625891     1.41   0.159    -2.008598    12.22534
          4  |   6.219285   2.549453     2.44   0.015      1.21517     11.2234
          5  |  -.2338521   2.822213    -0.08   0.934    -5.773347    5.305643
          6  |  -.5748507   3.553052    -0.16   0.872     -7.54885    6.399149
          7  |   2.136642     2.9022     0.74   0.462    -3.559852    7.833136
          8  |  -1.310868   2.822845    -0.46   0.642    -6.851602    4.229867
             |
       _cons |  -50.39228   8.387018    -6.01   0.000    -66.85449   -33.93008
------------------------------------------------------------------------------

. estimates store pooled

. hettest

Breusch-Pagan / Cook-Weisberg test for heteroskedasticity 
         Ho: Constant variance
         Variables: fitted values of esg_score

         chi2(1)      =    23.01
         Prob > chi2  =   0.0000

. xtreg esg_score curetr intan lev pb_ratio capint roa size salary_gap board ceo_duality gender ceo_tenure ceo_age i.y
> ear i.siccode, re

Random-effects GLS regression                   Number of obs     =        856
Group variable: id                              Number of groups  =        216

R-sq:                                           Obs per group:
     within  = 0.3258                                         min =          1
     between = 0.4106                                         avg =        4.0
     overall = 0.3675                                         max =          5

                                                Wald chi2(23)     =     445.32
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
   esg_score |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      curetr |  -.8338998   1.600491    -0.52   0.602    -3.970805    2.303006
       intan |  -12.29118   5.118653    -2.40   0.016    -22.32356   -2.258807
         lev |   -3.60994   3.771824    -0.96   0.339    -11.00258    3.782699
    pb_ratio |   .0159199   .0371935     0.43   0.669     -.056978    .0888179
      capint |   7.148151   4.438289     1.61   0.107    -1.550735    15.84704
         roa |   14.28707   7.952804     1.80   0.072     -1.30014    29.87428
        size |   6.296488   .6116577    10.29   0.000     5.097661    7.495315
  salary_gap |  -.0092274   .0040254    -2.29   0.022    -.0171171   -.0013376
       board |  -.3348761   1.281028    -0.26   0.794    -2.845645    2.175893
 ceo_duality |  -2.230376   1.185582    -1.88   0.060    -4.554074     .093322
      gender |   2.763154   1.876106     1.47   0.141    -.9139464    6.440254
  ceo_tenure |  -.0513331   .0742079    -0.69   0.489     -.196778    .0941118
     ceo_age |   .0445396   .0684108     0.65   0.515    -.0895432    .1786224
             |
        year |
       2016  |   .9376148   .5897805     1.59   0.112    -.2183337    2.093563
       2017  |   2.460863   .5816949     4.23   0.000     1.320762    3.600964
       2018  |   4.726646   .5849545     8.08   0.000     3.580156    5.873136
       2019  |   5.986999   .6086724     9.84   0.000     4.794023    7.179975
             |
     siccode |
          3  |   2.007383    6.82585     0.29   0.769    -11.37104     15.3858
          4  |   2.774585   4.602779     0.60   0.547    -6.246696    11.79587
          5  |  -4.020915   5.254236    -0.77   0.444    -14.31903    6.277198
          6  |  -3.982444   6.786852    -0.59   0.557    -17.28443    9.319542
          7  |   2.134624   5.315651     0.40   0.688     -8.28386    12.55311
          8  |  -4.965262    4.95124    -1.00   0.316    -14.66951    4.738991
             |
       _cons |  -40.07806   11.31562    -3.54   0.000    -62.25627   -17.89984
-------------+----------------------------------------------------------------
     sigma_u |  12.978438
     sigma_e |  4.8091451
         rho |   .8792705   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. estimates store re

. xttest0

Breusch and Pagan Lagrangian multiplier test for random effects

        esg_score[id,t] = Xb + u[id] + e[id,t]

        Estimated results:
                         |       Var     sd = sqrt(Var)
                ---------+-----------------------------
               esg_score |   309.3902       17.58949
                       e |   23.12788       4.809145
                       u |   168.4399       12.97844

        Test:   Var(u) = 0
                             chibar2(01) =   911.86
                          Prob > chibar2 =   0.0000

. xtreg esg_score curetr intan lev pb_ratio capint roa size salary_gap board ceo_duality gender ceo_tenure ceo_age i.y
> ear, fe

Fixed-effects (within) regression               Number of obs     =        856
Group variable: id                              Number of groups  =        216

R-sq:                                           Obs per group:
     within  = 0.3400                                         min =          1
     between = 0.2139                                         avg =        4.0
     overall = 0.1883                                         max =          5

                                                F(17,623)         =      18.88
corr(u_i, Xb)  = 0.1080                         Prob > F          =     0.0000

------------------------------------------------------------------------------
   esg_score |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      curetr |  -1.005083   1.623895    -0.62   0.536    -4.194054    2.183889
       intan |  -13.19336   5.940609    -2.22   0.027     -24.8594   -1.527314
         lev |  -7.618083   4.236213    -1.80   0.073    -15.93707    .7009037
    pb_ratio |   .0082271   .0377232     0.22   0.827     -.065853    .0823072
      capint |   6.477478   5.831057     1.11   0.267     -4.97343    17.92839
         roa |   7.678787   9.030856     0.85   0.395    -10.05582    25.41339
        size |   3.201307   1.259157     2.54   0.011     .7286021    5.674013
  salary_gap |  -.0129489   .0041528    -3.12   0.002    -.0211041   -.0047938
       board |  -1.823587   1.596923    -1.14   0.254    -4.959592    1.312418
 ceo_duality |  -4.019395    1.42484    -2.82   0.005    -6.817466   -1.221323
      gender |   2.089068   2.025743     1.03   0.303    -1.889043    6.067179
  ceo_tenure |   .0390599   .0813691     0.48   0.631    -.1207311    .1988508
     ceo_age |   .0029296   .0723492     0.04   0.968    -.1391483    .1450075
             |
        year |
       2016  |   1.250104   .5893418     2.12   0.034     .0927672    2.407441
       2017  |   2.999371   .5895928     5.09   0.000     1.841541    4.157201
       2018  |   5.538874     .62059     8.93   0.000     4.320173    6.757576
       2019  |   7.163519   .6930802    10.34   0.000     5.802463    8.524576
             |
       _cons |   14.91723   20.41296     0.73   0.465    -25.16931    55.00377
-------------+----------------------------------------------------------------
     sigma_u |  15.844433
     sigma_e |  4.8091451
         rho |  .91564524   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(215, 623) = 28.83                   Prob > F = 0.0000

. estimates store fe

. hausman fe re

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |       fe           re         Difference          S.E.
-------------+----------------------------------------------------------------
      curetr |   -1.005083    -.8338998        -.171183        .2747049
       intan |   -13.19336    -12.29118       -.9021744           3.015
         lev |   -7.618083     -3.60994       -4.008144        1.928432
    pb_ratio |    .0082271     .0159199       -.0076929        .0062996
      capint |    6.477478     7.148151       -.6706724        3.781907
         roa |    7.678787     14.28707       -6.608282        4.278935
        size |    3.201307     6.296488        -3.09518        1.100614
  salary_gap |   -.0129489    -.0092274       -.0037216        .0010205
       board |   -1.823587    -.3348761       -1.488711         .953484
 ceo_duality |   -4.019395    -2.230376       -1.789019        .7902944
      gender |    2.089068     2.763154        -.674086        .7641072
  ceo_tenure |    .0390599    -.0513331         .090393        .0333783
     ceo_age |    .0029296     .0445396         -.04161         .023545
        year |
       2016  |    1.250104     .9376148        .3124895               .
       2017  |    2.999371     2.460863        .5385079        .0961808
       2018  |    5.538874     4.726646        .8122283        .2072685
       2019  |    7.163519     5.986999        1.176521        .3314786
------------------------------------------------------------------------------
                           b = consistent under Ho and Ha; obtained from xtreg
            B = inconsistent under Ha, efficient under Ho; obtained from xtreg

    Test:  Ho:  difference in coefficients not systematic

                 chi2(17) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =       45.15
                Prob>chi2 =      0.0002
                (V_b-V_B is not positive definite)

[Carlo Lazzaro]

Guest:
1) your first PB test does not report what you probably expected it to, as it tests the presence of heteroskedasticity;
2) your second BP test is correct and it reports evidence of a panel-wise effect;
3) you also have a panel-wise effect under the -fe- specification;
4) I'm not clear with your sticking with default standard errors, though;
5) I'm also unclear with your introducing your moderataor in the right-hand side of your regression equation after the previous code. Your regression specification should be complete from the very start;
6) provided that -hausman- does not support non-default standard errors (and going default standard errors with -hausman- and replacing them with their non-default conterparts after the -hausman- outcome is not the way to go), its outcome is not decisive in your case;
7) therefeore, I woud test if the -re- specification is the way to go (or not) via the community-contributed module -xtoverid- (as recommended in one of my previous reply).

[Guest]

The first BP test was wrong, the second should distinguish between pooled as and panel models. my mistake.

I am unfortunately a statistics layman. What do you mean by sticking with default errors?

I did the test only on the baseline model. Hypotheses 2 and 3 are to split regressors (namely age and tenure) and test their factoreffect. Do I have to include all moderation effects directly for the test of the appropriate model? Unfortunately, the moderation effects have to be carried out, it would be suboptimal if this would not work with any model...

UPDATE:

I have now run xtoverid for the baseline model without moderation and got the output below. And it remains with the fe model or how is the result to be understood?

. xi: xtreg esg_score curetr intan lev pb_ratio capint roa size salary_gap board ceo_duality gender ceo_age ceo_tenure
>  i.year i.siccode, re
i.year            _Iyear_2015-2019    (naturally coded; _Iyear_2015 omitted)
i.siccode         _Isiccode_2-8       (naturally coded; _Isiccode_2 omitted)

Random-effects GLS regression                   Number of obs     =        856
Group variable: id                              Number of groups  =        216

R-sq:                                           Obs per group:
     within  = 0.3258                                         min =          1
     between = 0.4106                                         avg =        4.0
     overall = 0.3675                                         max =          5

                                                Wald chi2(23)     =     445.32
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
   esg_score |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      curetr |  -.8338998   1.600491    -0.52   0.602    -3.970805    2.303006
       intan |  -12.29118   5.118653    -2.40   0.016    -22.32356   -2.258807
         lev |   -3.60994   3.771824    -0.96   0.339    -11.00258    3.782699
    pb_ratio |   .0159199   .0371935     0.43   0.669     -.056978    .0888179
      capint |   7.148151   4.438289     1.61   0.107    -1.550735    15.84704
         roa |   14.28707   7.952804     1.80   0.072     -1.30014    29.87428
        size |   6.296488   .6116577    10.29   0.000     5.097661    7.495315
  salary_gap |  -.0092274   .0040254    -2.29   0.022    -.0171171   -.0013376
       board |  -.3348761   1.281028    -0.26   0.794    -2.845645    2.175893
 ceo_duality |  -2.230376   1.185582    -1.88   0.060    -4.554074     .093322
      gender |   2.763154   1.876106     1.47   0.141    -.9139464    6.440254
     ceo_age |   .0445396   .0684108     0.65   0.515    -.0895432    .1786224
  ceo_tenure |  -.0513331   .0742079    -0.69   0.489     -.196778    .0941118
 _Iyear_2016 |   .9376148   .5897805     1.59   0.112    -.2183337    2.093563
 _Iyear_2017 |   2.460863   .5816949     4.23   0.000     1.320762    3.600964
 _Iyear_2018 |   4.726646   .5849545     8.08   0.000     3.580156    5.873136
 _Iyear_2019 |   5.986999   .6086724     9.84   0.000     4.794023    7.179975
 _Isiccode_3 |   2.007383    6.82585     0.29   0.769    -11.37104     15.3858
 _Isiccode_4 |   2.774585   4.602779     0.60   0.547    -6.246696    11.79587
 _Isiccode_5 |  -4.020915   5.254236    -0.77   0.444    -14.31903    6.277198
 _Isiccode_6 |  -3.982444   6.786852    -0.59   0.557    -17.28443    9.319542
 _Isiccode_7 |   2.134624   5.315651     0.40   0.688     -8.28386    12.55311
 _Isiccode_8 |  -4.965262    4.95124    -1.00   0.316    -14.66951    4.738991
       _cons |  -40.07806   11.31562    -3.54   0.000    -62.25627   -17.89984
-------------+----------------------------------------------------------------
     sigma_u |  12.978438
     sigma_e |  4.8091451
         rho |   .8792705   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. estimates store re

. xtoverid

Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re  
Sargan-Hansen statistic  45.704  Chi-sq(17)   P-value = 0.0002

[Guest]

Another thought on my part: It seems to me theoretically or based on the research question not plausible since age and tenure are the focus of the moderation and dummies for gender and board system are to be included in the control variables, whether the pooled regression should be performed instead of the fe approach?

[Carlo Lazzaro]

Guest:
1) go -xtreg,re- with moderator and -vce(cluster panelid)- standard errors;
2) repeat -xtoverid- and, if its outcome reaches statistical significance, then switch to -xtreg,fe- with moderator and -vce(cluster panelid)- standard errors.

[Guest]

Thanks for the reply Carlo!

The xtoverid command could not be combined with the moderation effect (got the feedback 'operator invalid'). I have now inserted these separately and the result is the same, that fe is the appropriate way for the model. Am I right here?

And because of the content of the question: Since age and tenure change only slightly from year to year and time-invariant control variables (such as board, gender of executive) are included, isn't a model other than fe preferable, although the tests say otherwise?
Or, in other words, since tenure and age are colinear, the respective effects cannot be analyzed (?).

. xi: xtreg esg_score curetr age_split intan lev pb_ratio capint roa size salary_gap board ceo_duality gender ceo_tenu
> re i.year i.siccode, re vce(cluster id)
i.year            _Iyear_2015-2019    (naturally coded; _Iyear_2015 omitted)
i.siccode         _Isiccode_2-8       (naturally coded; _Isiccode_2 omitted)

Random-effects GLS regression                   Number of obs     =        856
Group variable: id                              Number of groups  =        216

R-sq:                                           Obs per group:
     within  = 0.3267                                         min =          1
     between = 0.4081                                         avg =        4.0
     overall = 0.3644                                         max =          5

                                                Wald chi2(23)     =     342.52
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

                                   (Std. Err. adjusted for 216 clusters in id)
------------------------------------------------------------------------------
             |               Robust
   esg_score |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      curetr |  -.9456175   1.727219    -0.55   0.584    -4.330905     2.43967
   age_split |  -.3601765   .8422017    -0.43   0.669    -2.010861    1.290508
       intan |  -12.35375   5.270684    -2.34   0.019     -22.6841   -2.023396
         lev |  -3.484036   4.023168    -0.87   0.386     -11.3693    4.401228
    pb_ratio |   .0151369   .0411374     0.37   0.713    -.0654908    .0957646
      capint |   7.085463   5.504035     1.29   0.198    -3.702248    17.87317
         roa |   14.59711    7.55538     1.93   0.053    -.2111648    29.40538
        size |   6.396595   .6773583     9.44   0.000     5.068997    7.724193
  salary_gap |  -.0091727   .0039623    -2.31   0.021    -.0169387   -.0014066
       board |  -.3268665   1.425361    -0.23   0.819    -3.120522    2.466789
 ceo_duality |  -2.257519   1.671938    -1.35   0.177    -5.534456    1.019419
      gender |   2.669488   1.862344     1.43   0.152    -.9806389    6.319614
  ceo_tenure |  -.0034066   .0743343    -0.05   0.963    -.1490992    .1422859
 _Iyear_2016 |   .9448057   .5228543     1.81   0.071    -.0799699    1.969581
 _Iyear_2017 |   2.492003   .6575149     3.79   0.000     1.203298    3.780709
 _Iyear_2018 |   4.738339   .7282981     6.51   0.000     3.310901    6.165777
 _Iyear_2019 |   6.012117   .7353967     8.18   0.000     4.570766    7.453468
 _Isiccode_3 |   1.656279   4.544878     0.36   0.716    -7.251519    10.56408
 _Isiccode_4 |   2.663538   3.607645     0.74   0.460    -4.407316    9.734392
 _Isiccode_5 |  -4.199982   4.833271    -0.87   0.385    -13.67302    5.273055
 _Isiccode_6 |  -3.916728   5.220533    -0.75   0.453    -14.14879    6.315329
 _Isiccode_7 |   1.839267   4.042896     0.45   0.649    -6.084663    9.763198
 _Isiccode_8 |   -5.15472   4.437906    -1.16   0.245    -13.85286    3.543416
       _cons |  -38.89791   11.94298    -3.26   0.001    -62.30572   -15.49009
-------------+----------------------------------------------------------------
     sigma_u |   12.97158
     sigma_e |  4.8058727
         rho |  .87930279   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. estimates store re

. xtoverid

Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re  robust cluster(id)
Sargan-Hansen statistic  49.592  Chi-sq(17)   P-value = 0.0000

[Carlo Lazzaro]

Guest:
go -fe-.
In addition, while nobody can stop you from going -re- even against any test outcomes, the substantive issue is that if you switch from -fe- to -re- when the former is the way to go, the latter will be inconsistent (and your coefficients unreliable).
You're obviously correct in stating that the -fe- estimator suffers when the within panel variation ot time-varying variables is not that impressive, but the flip side of the coin would recommend you to test whether the -re- main assumption (no correlation betweem the u term and the vector of regressors) actually holds under all the scenarios.

[Guest]

I have now run two regressions and in no case is the age significant alone as well as in moderation. For the second regression where age is split into two groups (even if the coefficients are not significant), can it be shown that curetr (financial variable) has a negative effect on the esg score of the company, executives over 55 also, but that in contrast to the age group under 55 (base) the effect of the financial variable is less negative for a person over 55? Is this interpretation correct?

. xtreg esg_score curetr intan lev pb_ratio capint roa size salary_gap board ceo_duality gender ceo_age ceo_tenure i.y
> ear, fe vce(cluster id)

Fixed-effects (within) regression               Number of obs     =        856
Group variable: id                              Number of groups  =        216

R-sq:                                           Obs per group:
     within  = 0.3400                                         min =          1
     between = 0.2139                                         avg =        4.0
     overall = 0.1883                                         max =          5

                                                F(17,215)         =      10.28
corr(u_i, Xb)  = 0.1080                         Prob > F          =     0.0000

                                   (Std. Err. adjusted for 216 clusters in id)
------------------------------------------------------------------------------
             |               Robust
   esg_score |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      curetr |  -1.005083   1.634223    -0.62   0.539    -4.226234    2.216068
       intan |  -13.19336   6.538775    -2.02   0.045    -26.08167   -.3050454
         lev |  -7.618083   4.823215    -1.58   0.116    -17.12493    1.888759
    pb_ratio |   .0082271   .0380391     0.22   0.829    -.0667502    .0832044
      capint |   6.477478   6.111274     1.06   0.290    -5.568204    18.52316
         roa |   7.678787    8.57676     0.90   0.372    -9.226514    24.58409
        size |   3.201307   1.885977     1.70   0.091    -.5160648     6.91868
  salary_gap |  -.0129489   .0036729    -3.53   0.001    -.0201884   -.0057095
       board |  -1.823587   1.589186    -1.15   0.252    -4.955966    1.308792
 ceo_duality |  -4.019395   2.183479    -1.84   0.067    -8.323161    .2843718
      gender |   2.089068   2.132463     0.98   0.328    -2.114143    6.292279
     ceo_age |   .0029296   .0804214     0.04   0.971    -.1555858    .1614449
  ceo_tenure |   .0390599   .0909596     0.43   0.668     -.140227    .2183467
             |
        year |
       2016  |   1.250104   .5337512     2.34   0.020     .1980491     2.30216
       2017  |   2.999371   .6813952     4.40   0.000     1.656301    4.342441
       2018  |   5.538874   .7929871     6.98   0.000      3.97585    7.101899
       2019  |   7.163519   .8602485     8.33   0.000     5.467919     8.85912
             |
       _cons |   14.91723   30.28268     0.49   0.623    -44.77172    74.60618
-------------+----------------------------------------------------------------
     sigma_u |  15.844433
     sigma_e |  4.8091451
         rho |  .91564524   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. estat vce, corr

Correlation matrix of coefficients of xtreg model

             |                                                                                                    
        e(V) |   curetr     intan       lev  pb_ratio    capint       roa      size  salary~p     board  ceo_du~y 
-------------+----------------------------------------------------------------------------------------------------
      curetr |   1.0000                                                                                           
       intan |  -0.0008    1.0000                                                                                 
         lev |   0.0405   -0.0471    1.0000                                                                       
    pb_ratio |   0.0689    0.0013    0.0136    1.0000                                                             
      capint |   0.0009    0.3114   -0.3835   -0.1307    1.0000                                                   
         roa |   0.2281    0.0611    0.1660    0.0590   -0.0438    1.0000                                         
        size |  -0.0336   -0.4632   -0.0906    0.1176   -0.1319    0.2398    1.0000                               
  salary_gap |   0.0833    0.0100    0.1176   -0.0357   -0.0796   -0.1567   -0.0763    1.0000                     
       board |   0.0969   -0.1399    0.0262    0.0330    0.0166    0.1089    0.2623   -0.0868    1.0000           
 ceo_duality |   0.0430    0.2076   -0.1295   -0.0373    0.0760   -0.1433   -0.2334    0.0297    0.0491    1.0000 
      gender |   0.0578    0.1150   -0.0410   -0.0429    0.0602    0.1395   -0.0426    0.0188   -0.0127    0.0298 
     ceo_age |  -0.0560    0.2125   -0.0676    0.0038    0.1568   -0.0950    0.0114    0.0181    0.0133    0.0219 
  ceo_tenure |   0.0750   -0.0669   -0.0473   -0.0223   -0.0092   -0.0636   -0.0817   -0.2189   -0.0175    0.0550 
   2016.year |   0.0365   -0.0049    0.0561   -0.0264    0.1383    0.1765   -0.1415   -0.0321   -0.0795   -0.1649 
   2017.year |   0.0338    0.0044   -0.1163   -0.0184    0.2011    0.0009   -0.2250    0.0162   -0.1581   -0.0025 
   2018.year |   0.0629    0.0362   -0.0854   -0.0722    0.2243   -0.0481   -0.3966    0.0152   -0.1156    0.0518 
   2019.year |   0.0692    0.1135   -0.0814   -0.0663    0.0894    0.0294   -0.5346   -0.0081   -0.1231    0.1095 
       _cons |   0.0112    0.3970    0.0845   -0.1201    0.0692   -0.2588   -0.9871    0.0738   -0.2996    0.2046 

             |                                   2016.     2017.     2018.     2019.          
        e(V) |   gender   ceo_age  ceo_te~e      year      year      year      year     _cons 
-------------+--------------------------------------------------------------------------------
      gender |   1.0000                                                                       
     ceo_age |   0.2588    1.0000                                                             
  ceo_tenure |  -0.1716   -0.6818    1.0000                                                   
   2016.year |  -0.0844   -0.1829    0.1657    1.0000                                         
   2017.year |  -0.1761   -0.1911    0.2143    0.6643    1.0000                               
   2018.year |  -0.0640   -0.1116    0.1832    0.6168    0.8396    1.0000                     
   2019.year |  -0.0433   -0.1526    0.1725    0.5003    0.6982    0.8703    1.0000           
       _cons |  -0.0016   -0.1490    0.1621    0.1471    0.2341    0.3897    0.5365    1.0000 

. xtreg esg_score c.curetr##age_split intan lev pb_ratio capint roa size salary_gap board ceo_duality gender i.year, f
> e vce(cluster id)

Fixed-effects (within) regression               Number of obs     =        856
Group variable: id                              Number of groups  =        216

R-sq:                                           Obs per group:
     within  = 0.3447                                         min =          1
     between = 0.2355                                         avg =        4.0
     overall = 0.2067                                         max =          5

                                                F(17,215)         =      10.68
corr(u_i, Xb)  = 0.1218                         Prob > F          =     0.0000

                                         (Std. Err. adjusted for 216 clusters in id)
------------------------------------------------------------------------------------
                   |               Robust
         esg_score |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------------+----------------------------------------------------------------
            curetr |  -4.012713   2.022165    -1.98   0.048     -7.99852   -.0269058
                   |
         age_split |
              >55  |  -2.016321   1.113921    -1.81   0.072    -4.211926    .1792835
                   |
age_split#c.curetr |
              >55  |   5.692798   2.657991     2.14   0.033     .4537408    10.93185
                   |
             intan |  -12.98363   6.465436    -2.01   0.046    -25.72738   -.2398697
               lev |  -7.542046   4.848706    -1.56   0.121    -17.09913    2.015041
          pb_ratio |   .0125283   .0403672     0.31   0.757    -.0670379    .0920944
            capint |    6.57072   6.165645     1.07   0.288    -5.582131    18.72357
               roa |   8.054123   8.716485     0.92   0.357    -9.126585    25.23483
              size |   3.366338   1.887686     1.78   0.076    -.3544025    7.087078
        salary_gap |  -.0122074   .0034951    -3.49   0.001    -.0190964   -.0053185
             board |  -1.852525   1.629314    -1.14   0.257       -5.064     1.35895
       ceo_duality |  -4.111687   2.171824    -1.89   0.060    -8.392481    .1691069
            gender |   2.261247   2.385406     0.95   0.344     -2.44053    6.963024
                   |
              year |
             2016  |   1.323084   .5269023     2.51   0.013      .284528    2.361639
             2017  |   3.065592   .6738027     4.55   0.000     1.737487    4.393698
             2018  |   5.544902   .7867214     7.05   0.000     3.994228    7.095576
             2019  |   7.144722   .8518624     8.39   0.000      5.46565    8.823793
                   |
             _cons |   13.65209   30.01424     0.45   0.650    -45.50776    72.81193
-------------------+----------------------------------------------------------------
           sigma_u |  15.667821
           sigma_e |  4.7920893
               rho |  .91445495   (fraction of variance due to u_i)
------------------------------------------------------------------------------------

[Carlo Lazzaro]

Guest:
1) due to its border-line statistical significance, -curetr- should be handled with care;
2) the only coefficient that seems to be interesting (in addition to -salary_gap-) is -age_split#c.curetr- for managers aged >55 years (and it may kake sense);
3) as a general rule, when a coefficient does not reach statistical significance, stating that is "less negative than..." sounds to skilled readers/reviewers like clutching at straws.

[Guest]

Thanks Carlo! Based on the expression, would you agree that collinearity is not a problem?

Is the interpretation correct (apart from the significance) that in contrast to the age group under 55 (base) the effect of the financial variable is 'less negative' for a person over 55?

[Carlo Lazzaro]

Guest:
from the -estat vce,corr- matrix, collinearity does not seem to be an issue.
As far as your last statement is concerned, if I were a reviewer I would have hard times in making you get away with it.

[Jeff Wooldridge]

The effect is essentially zero for those above 55 and negative for those under. Add the the coefficients using lincom to get a test.

[Guest]

@Carlo Thank you for the honest feedback!

Is it better to use another model like pooled ols or how can the problem of moderation be solved most elegantly by dividing the sample into two age groups?

I still don't quite understand, because independent variables such as board system, gender etc. (which vary in part depending on the id due to e.g. change of manager in the company) are also time-invariant. Why can fixed effects still useful here?

@Jeff: Thanks! What exactly do I use to make the interpretation of the age limit? unfortunately I can not intuitively understand this

And to which coefficients is lincom to be referred?

[Carlo Lazzaro]

Guest:
1) the issue is exactly the one Jeff spotted, and playing around with different estimators just to torture your data until they confess what you want to hear is not the right approach, unless you plan to present your reserach to an audience with a very poor smattering of panel data econometrics (but I do not think that is the case here). I think you should change the way you look at your results: non-significant results are as informative as their significant counterparts (as data and results are what they are and we have to live with them, provided that we did not make severe mistakes upward when planning the analysis and collecting the data);
2) I fail to get your statement: if there's a within-panel change in a given variable, how can it be time-invariant? If in a given panel the CEO was a man in 2021 and is a woman in 2022, there's obviously a change. I suspect that you're reasoning in a different way (which is not quite correct): if a given thing is red, is red, if it is green, is green, This is correct in -fe- estimator jargon as long as your variable is always red (or green) during all the timespan your panel data regression stretches over, but if it turns from red to green, you have a change, and your variable is no more time-invariant.
3) what above is really easy to check via the -fe- estimator: if no within-panel change occurs during the years, you get no coefficient at all for the time-invariant variable.

[Guest]

Thank you very much! I will stick with the fixed effects for the baseline model and the interactions.

I would appreciate if you could explain again how you arrive at the interpretation of the output ('zero for those above 55 and negative for those under' as Jeff said). Can't quite understand it yet and furthermore I wonder how to implement the lincom command?

If you could give me another tip here, then I won't take up any more of your time!