Interaction effects and model selection (pooled OLS, FE, RE)

[Guest]

Hello to all! I am facing the following problems with my panel data analysis:

(1) I would like to create subgroups (currently two) in terms of age and check their interaction effects with another financial variable. For this purpose, I have created another age group variable via the recode command, which takes either the value 1 (first group) or 2 (second group), i.e. over and under 50 years. I would like to examine a similar interaction effect for years of service. However, when I run a simple regression, Stata does not show me a split for the subgroups. What can I do in this case to get usable results for both age categories?

(2) Regarding the choice of fixed effects, random effects, or pooled effects model: Am I right in assuming that because I do not have an identical sample in each year due to missing data, a pooled ols tends to be more appropriate here?

I have attached an excerpt from Stata and my data below. I appreciate any help!

recode ceo_age (min/50 = 1) (51/max = 2), gen(age_gp)
tab age_gp
recode ceo_tenure (min/3 = 1) (4/max = 2), gen(tenure_gp)
tab tenure_gp

reg esg_score c.curetr c.curetr#age_gp intan lev pb_ratio capint roa size salary_gap board ceo_duality gender ceo_ten
> ure i.year i.siccode, vce(r)

Linear regression                               Number of obs     =        851
                                                F(23, 827)        =      40.34
                                                Prob > F          =     0.0000
                                                R-squared         =     0.4384
                                                Root MSE          =     13.398

---------------------------------------------------------------------------------
                |               Robust
      esg_score |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
         curetr |  -4.400755   4.050604    -1.09   0.278    -12.35143    3.549919
                |
age_gp#c.curetr |
             2  |   8.772016   3.238446     2.71   0.007     2.415475    15.12856
                |
          intan |  -1.705206   5.018897    -0.34   0.734    -11.55648    8.146067
            lev |   6.247028   4.405853     1.42   0.157    -2.400942      14.895
       pb_ratio |  -.0245294   .0786188    -0.31   0.755    -.1788453    .1297865
         capint |    10.9656   4.537595     2.42   0.016     2.059042    19.87216
            roa |    24.8038    9.31881     2.66   0.008       6.5125     43.0951
           size |   6.171308   .3896329    15.84   0.000     5.406522    6.936094
     salary_gap |   .0251233   .0051702     4.86   0.000     .0149751    .0352715
          board |  -.2755872   1.125644    -0.24   0.807    -2.485042    1.933868
    ceo_duality |   3.043209   .9938728     3.06   0.002     1.092399    4.994019
         gender |   5.177933    1.81803     2.85   0.005     1.609437    8.746429
     ceo_tenure |  -.3893942   .0771052    -5.05   0.000    -.5407391   -.2380492
                |
           year |
          2016  |   .6911621   1.603866     0.43   0.667    -2.456966     3.83929
          2017  |   1.324798    1.60296     0.83   0.409    -1.821551    4.471147
          2018  |   3.527925   1.531031     2.30   0.021     .5227619    6.533089
          2019  |   4.524673   1.533702     2.95   0.003     1.514266    7.535079
                |
        siccode |
             3  |   5.422113   2.910965     1.86   0.063    -.2916361    11.13586
             4  |   6.625767    2.34169     2.83   0.005     2.029411    11.22212
             5  |   .3659336   2.602472     0.14   0.888    -4.742294    5.474161
             6  |   .1884965   3.168794     0.06   0.953    -6.031329    6.408322
             7  |   2.610705    2.43528     1.07   0.284    -2.169353    7.390762
             8  |  -.3438315   2.934011    -0.12   0.907    -6.102815    5.415152
                |
          _cons |   -45.3922   7.452458    -6.09   0.000    -60.02015   -30.76424
---------------------------------------------------------------------------------

. vif

    Variable |       VIF       1/VIF  
-------------+----------------------
      curetr |      1.98    0.503872
      age_gp#|
    c.curetr |
          2  |      2.04    0.490632
       intan |      1.54    0.650179
         lev |      1.47    0.679840
    pb_ratio |      1.62    0.618631
      capint |      1.82    0.549529
         roa |      2.09    0.478770
        size |      1.60    0.623381
  salary_gap |      1.28    0.779262
       board |      1.33    0.750410
 ceo_duality |      1.28    0.780442
      gender |      1.10    0.906361
  ceo_tenure |      1.17    0.858357
        year |
       2016  |      1.71    0.585061
       2017  |      1.81    0.553982
       2018  |      1.86    0.538775
       2019  |      1.88    0.533250
     siccode |
          3  |      2.12    0.471907
          4  |      7.74    0.129244
          5  |      3.66    0.273140
          6  |      2.11    0.474175
          7  |      3.30    0.302896
          8  |      6.44    0.155248
-------------+----------------------
    Mean VIF |      2.30

.

[Rich Goldstein]

you need to include 2 hash marks, not just the one you actually put in; i.e., where you "c.curetr#age_gp", you should have "c.curetr##age_gp"; note that the question is not completely clear so this is my best guess; see

h fvvarlist

[Guest]

Thank you! I have applied the change and hoped to get two different coefficients for the influence of age.

I would like to show that the generally negative influence of the continuous financial variable differs depending on the age group to which the executive belongs. Now I got the following output:

. reg esg_score c.curetr##age_gp intan lev pb_ratio capint roa size salary_gap board ceo_duality gender ceo_tenure i.ye
> ar i.siccode, vce(r)

Linear regression                               Number of obs     =        851
                                                F(24, 826)        =      38.77
                                                Prob > F          =     0.0000
                                                R-squared         =     0.4385
                                                Root MSE          =     13.405

---------------------------------------------------------------------------------
                |               Robust
      esg_score |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
         curetr |  -2.689088   5.821337    -0.46   0.644    -14.11544    8.737266
       2.age_gp |   .9006086   2.473469     0.36   0.716    -3.954416    5.755633
                |
age_gp#c.curetr |
             2  |   6.506266   6.767485     0.96   0.337    -6.777226    19.78976
                |
          intan |  -1.781469   5.016168    -0.36   0.723     -11.6274    8.064466
            lev |    6.33887   4.369675     1.45   0.147    -2.238102    14.91584
       pb_ratio |  -.0217364   .0792347    -0.27   0.784    -.1772614    .1337886
         capint |   10.91383   4.531687     2.41   0.016     2.018849     19.8088
            roa |   24.88531   9.295931     2.68   0.008     6.638882    43.13174
           size |   6.153849   .3860024    15.94   0.000     5.396188     6.91151
     salary_gap |   .0249771   .0052287     4.78   0.000      .014714    .0352401
          board |  -.2806724   1.127379    -0.25   0.803    -2.493538    1.932193
    ceo_duality |   3.063732   .9909795     3.09   0.002     1.118597    5.008866
         gender |   5.127804   1.823112     2.81   0.005     1.549327     8.70628
     ceo_tenure |  -.3930878   .0777844    -5.05   0.000    -.5457661   -.2404095
                |
           year |
          2016  |   .6562786   1.601332     0.41   0.682    -2.486879    3.799437
          2017  |   1.275072   1.599791     0.80   0.426    -1.865062    4.415206
          2018  |   3.503905   1.527639     2.29   0.022     .5053932    6.502416
          2019  |   4.486183   1.528451     2.94   0.003     1.486077    7.486289
                |
        siccode |
             3  |   5.452528   2.916654     1.87   0.062    -.2723979    11.17745
             4  |   6.570393   2.335822     2.81   0.005     1.985549    11.15524
             5  |   .3120088   2.613967     0.12   0.905    -4.818791    5.442808
             6  |   .1436769   3.168292     0.05   0.964    -6.075173    6.362527
             7  |   2.606018   2.429488     1.07   0.284    -2.162679    7.374716
             8  |  -.4137037   2.924082    -0.14   0.888    -6.153208    5.325801
                |
          _cons |  -45.69922   7.577271    -6.03   0.000    -60.57219   -30.82625
---------------------------------------------------------------------------------

[Carlo Lazzaro]

Guest:
1) dicothomizing a continuous predictor, such age, is, in general, not the way to go (see https://pubmed.ncbi.nlm.nih.gov/16217841/). It is probably more informative to search for non-linear relationship between -age- and the regressand;
2) never heard about anything similat as far as you point #1, post #1 is concerned. Stata can handle both balanced and unbalanced panels;
3) your regression model neglect the panel data structure of your data (default instead of -vce(cluster panelid)- standarr error); under -regress- (but unlike -xtreg-, the -robust- option takes only heteroskedasticity into account).

[Guest]

Thanks for the feedback!

Regarding the first note: If dichotomizing a continuous predictor in the context of age is not suitable due to lack of linearity, can this be solved simply by introducing an age dummy? Or what would be the optimal way here? I am not really a statistician, so I am a bit confused about the general implementation of the modeling. Here, it is only important to distinguish between older and younger executives or a long and short period of service.

To 2 and 3: Is the Hausmann test to be carried out here, for example, or can a tendency regarding the modeling already be made at the structure and the variables (just to guarantee the consideration of the panel structure)?

[Carlo Lazzaro]

Guest:
1) if you want to test non-linearities between continuous predictors and the regressand, keeping the continuous predictors as they are but including their squared term too is the way to go:

c.age##c.age

This is what Rich already recommended.

Conversely, if one of your research goal is to check the difference between two levels of the same categorical variable (over vs. below a given age cut-off), a categorical variable is the way to go (despite the evidence that you lose part of its informative strenght upon dicotomizing).

2) despite its fragilities, -hausman- is the way to go if you want to compare -fe- vs. -re- and you adopt default standard errors. That said, the Mundlak approach (https://blog.stata.com/2015/10/29/fi...ndlak-approach) and the community-contributed module -xtoverid- are probably more flexible.

[Guest]

Thanks again! I have now splitted age into high and low and put them in interaction with my financial variable, but the cut-off for the older group was "omitted because of collinearity". In this case, would I better run two separate regressions for age_low and age_high? Before testing the models, I would like to manage to get the cut-offs for tenure and age to check that the general influence of the financial variable changes or is moderated by the group (age, tenure) to which the executive belongs.

. recode ceo_age min/50 = 1 51/max = 0, gen(age_low)
(1019 differences between ceo_age and age_low)

. recode ceo_age min/50 = 0 51/max = 1, gen(age_high)
(1019 differences between ceo_age and age_high)

. tab age_low age_high

 RECODE of |   RECODE of ceo_age
   ceo_age |       (ceo_age)
 (ceo_age) |         0          1 |     Total
-----------+----------------------+----------
         0 |         0        809 |       809 
         1 |       210          0 |       210 
-----------+----------------------+----------
     Total |       210        809 |     1,019

. regress esg_score c.curetr c.curetr#age_low c.curetr#age_high intan lev pb_ratio capint roa size salary_gap board ceo
> _duality gender ceo_tenure i.year i.siccode, vce(r)
note: 1.age_high#c.curetr omitted because of collinearity

Linear regression                               Number of obs     =        851
                                                F(23, 827)        =      40.34
                                                Prob > F          =     0.0000
                                                R-squared         =     0.4384
                                                Root MSE          =     13.398

-----------------------------------------------------------------------------------
                  |               Robust
        esg_score |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
           curetr |   4.371261   3.555524     1.23   0.219    -2.607652    11.35017
                  |
 age_low#c.curetr |
               1  |  -8.772016   3.238446    -2.71   0.007    -15.12856   -2.415475
                  |
age_high#c.curetr |
               1  |          0  (omitted)
                  |
            intan |  -1.705206   5.018897    -0.34   0.734    -11.55648    8.146067
              lev |   6.247028   4.405853     1.42   0.157    -2.400942      14.895
         pb_ratio |  -.0245294   .0786188    -0.31   0.755    -.1788453    .1297865
           capint |    10.9656   4.537595     2.42   0.016     2.059042    19.87216
              roa |    24.8038    9.31881     2.66   0.008       6.5125     43.0951
             size |   6.171308   .3896329    15.84   0.000     5.406522    6.936094
       salary_gap |   .0251233   .0051702     4.86   0.000     .0149751    .0352715
            board |  -.2755872   1.125644    -0.24   0.807    -2.485042    1.933868
      ceo_duality |   3.043209   .9938728     3.06   0.002     1.092399    4.994019
           gender |   5.177933    1.81803     2.85   0.005     1.609437    8.746429
       ceo_tenure |  -.3893942   .0771052    -5.05   0.000    -.5407391   -.2380492
                  |
             year |
            2016  |   .6911621   1.603866     0.43   0.667    -2.456966     3.83929
            2017  |   1.324798    1.60296     0.83   0.409    -1.821551    4.471147
            2018  |   3.527925   1.531031     2.30   0.021     .5227619    6.533089
            2019  |   4.524673   1.533702     2.95   0.003     1.514266    7.535079
                  |
          siccode |
               3  |   5.422113   2.910965     1.86   0.063    -.2916361    11.13586
               4  |   6.625767    2.34169     2.83   0.005     2.029411    11.22212
               5  |   .3659336   2.602472     0.14   0.888    -4.742294    5.474161
               6  |   .1884965   3.168794     0.06   0.953    -6.031329    6.408322
               7  |   2.610705    2.43528     1.07   0.284    -2.169353    7.390762
               8  |  -.3438315   2.934011    -0.12   0.907    -6.102815    5.415152
                  |
            _cons |   -45.3922   7.452458    -6.09   0.000    -60.02015   -30.76424
-----------------------------------------------------------------------------------

[Guest]

I have now put the cut-off problematic aside and have taken care of the choice of the statistical model (see output below).

Based on "F test that all u_i=0: F(214, 622) = 28.65" and the Hausman test, can I assume that fixed effects is the right way to go here?

Thankful for every tip!

. xtsum esg_score curetr cashetr intan lev pb_ratio capint roa size salary_gap board ceo_duality gender ceo_age ceo_te
> nure

Variable         |      Mean   Std. Dev.       Min        Max |    Observations
-----------------+--------------------------------------------+----------------
esg_sc~e overall |  65.15941   18.01747   3.248013    94.3814 |     N =    1019
         between |              18.1255   3.670674   92.48193 |     n =     239
         within  |             5.485627   39.56945   86.57859 | T-bar =  4.2636
                 |                                            |
curetr   overall |  .2963985   .1728918          0          1 |     N =    1077
         between |             .1415087          0          1 |     n =     240
         within  |             .1226713  -.1730071   .9636023 | T-bar =  4.4875
                 |                                            |
cashetr  overall |  .2807939   .1729476          0          1 |     N =    1018
         between |             .1306202          0          1 |     n =     225
         within  |             .1249657  -.1961174   .9162274 | T-bar = 4.52444
                 |                                            |
intan    overall |  .1103214   .1042906   .0007376   .4731707 |     N =    1110
         between |             .0985551   .0007376   .4731707 |     n =     242
         within  |             .0327775  -.1586331    .335545 | T-bar = 4.58678
                 |                                            |
lev      overall |  .1983574     .13546          0   .6064429 |     N =    1131
         between |             .1275905          0   .6064429 |     n =     246
         within  |             .0498542  -.1367616   .4665546 | T-bar = 4.59756
                 |                                            |
pb_ratio overall |  4.271298   7.399685  -3.739541   67.53844 |     N =    1097
         between |             6.859325  -3.495186   67.53844 |     n =     241
         within  |             4.311309  -24.23989   57.01255 | T-bar = 4.55187
                 |                                            |
capint   overall |  .2092085   .1795902   .0023625   .7968591 |     N =    1129
         between |             .1758292   .0023625   .7968591 |     n =     246
         within  |             .0366074   .0397671   .4665544 | T-bar = 4.58943
                 |                                            |
roa      overall |  .0851688    .071921   .0047447   .4876886 |     N =    1131
         between |             .0653814   .0058114   .4876886 |     n =     246
         within  |             .0269234  -.2643944   .3038462 | T-bar = 4.59756
                 |                                            |
size     overall |   15.9062    1.57227   12.02056   19.38892 |     N =    1133
         between |             1.601289   12.02056   19.38892 |     n =     246
         within  |             .2227371   14.01916   16.99831 | T-bar = 4.60569
                 |                                            |
salary~p overall |   79.5444   84.39617   2.153831   485.0087 |     N =     900
         between |             77.80715   2.153831   485.0087 |     n =     225
         within  |             40.81674  -167.0961   362.4479 | T-bar =       4
                 |                                            |
board    overall |  .6525173   .4764058          0          1 |     N =    1013
         between |             .4658496          0          1 |     n =     238
         within  |             .1066776  -.1474827   1.452517 | T-bar =  4.2563
                 |                                            |
ceo_du~y overall |  .3120707    .463566          0          1 |     N =    1019
         between |             .4478125          0          1 |     n =     239
         within  |             .1194837  -.4879293   .9787373 | T-bar =  4.2636
                 |                                            |
gender   overall |  .0431796    .203361          0          1 |     N =    1019
         between |             .2019322          0          1 |     n =     239
         within  |             .0838068  -.7568204   .8431796 | T-bar =  4.2636
                 |                                            |
ceo_age  overall |  55.80373   6.396581         32         75 |     N =    1019
         between |             5.693958         34         74 |     n =     239
         within  |             3.258413   31.40373   77.55373 | T-bar =  4.2636
                 |                                            |
ceo_te~e overall |  8.157998   7.015949          1         33 |     N =    1019
         between |             6.805384        1.5         32 |     n =     239
         within  |             2.798654    -13.042     27.658 | T-bar =  4.2636

. xtreg esg_score curetr intan lev pb_ratio capint roa size salary_gap board ceo_duality gender ceo_age ceo_tenure year
>  siccode, fe
note: siccode omitted because of collinearity

Fixed-effects (within) regression               Number of obs     =        851
Group variable: id                              Number of groups  =        215

R-sq:                                           Obs per group:
     within  = 0.3337                                         min =          1
     between = 0.2056                                         avg =        4.0
     overall = 0.1799                                         max =          5

                                                F(14,622)         =      22.25
corr(u_i, Xb)  = 0.0981                         Prob > F          =     0.0000

------------------------------------------------------------------------------
   esg_score |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      curetr |  -.8038043   1.620425    -0.50   0.620     -3.98597    2.378362
       intan |  -13.18428   5.928834    -2.22   0.027    -24.82724   -1.541324
         lev |  -7.614028    4.25824    -1.79   0.074     -15.9763    .7482415
    pb_ratio |   .0092747   .0376491     0.25   0.805    -.0646601    .0832094
      capint |    6.97544   5.739116     1.22   0.225    -4.294951    18.24583
         roa |   8.096053   8.917683     0.91   0.364    -9.416362    25.60847
        size |   3.145254    1.26049     2.50   0.013     .6699218    5.620586
  salary_gap |  -.0131164   .0041617    -3.15   0.002     -.021289   -.0049437
       board |   -1.85292   1.598393    -1.16   0.247    -4.991819     1.28598
 ceo_duality |  -4.260839    1.42028    -3.00   0.003    -7.049965   -1.471714
      gender |   2.067474   2.026263     1.02   0.308     -1.91167    6.046618
     ceo_age |  -.0110186   .0709685    -0.16   0.877    -.1503856    .1283483
  ceo_tenure |    .045644    .082457     0.55   0.580    -.1162839    .2075718
        year |   1.861248   .1599455    11.64   0.000     1.547149    2.175346
     siccode |          0  (omitted)
       _cons |  -3734.327   311.8842   -11.97   0.000    -4346.801   -3121.854
-------------+----------------------------------------------------------------
     sigma_u |  15.937382
     sigma_e |  4.8153758
         rho |  .91634615   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(214, 622) = 28.65                   Prob > F = 0.0000

. estimates store fe

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

Random-effects GLS regression                   Number of obs     =        851
Group variable: id                              Number of groups  =        215

R-sq:                                           Obs per group:
     within  = 0.3183                                         min =          1
     between = 0.3940                                         avg =        4.0
     overall = 0.3529                                         max =          5

                                                Wald chi2(15)     =     428.02
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
   esg_score |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      curetr |  -.6947008   1.598843    -0.43   0.664    -3.828376    2.438974
       intan |  -12.63015   5.095914    -2.48   0.013    -22.61795   -2.642339
         lev |  -4.460946   3.768663    -1.18   0.237    -11.84739    2.925498
    pb_ratio |   .0189382   .0371655     0.51   0.610    -.0539048    .0917813
      capint |   7.052376   4.231222     1.67   0.096    -1.240667    15.34542
         roa |   14.28829   7.854178     1.82   0.069    -1.105619    29.68219
        size |   6.348736   .6115266    10.38   0.000     5.150165    7.547306
  salary_gap |  -.0085802   .0040289    -2.13   0.033    -.0164767   -.0006836
       board |  -.0631253   1.262641    -0.05   0.960    -2.537856    2.411606
 ceo_duality |  -2.425378   1.183155    -2.05   0.040     -4.74432    -.106437
      gender |   2.798001   1.871746     1.49   0.135    -.8705543    6.466556
     ceo_age |   .0296082   .0669177     0.44   0.658     -.101548    .1607644
  ceo_tenure |  -.0463446   .0748263    -0.62   0.536    -.1930015    .1003123
        year |   1.578911    .138727    11.38   0.000     1.307011    1.850811
     siccode |  -1.303797   .5272231    -2.47   0.013    -2.337135   -.2704587
       _cons |  -3215.284   277.2417   -11.60   0.000    -3758.667     -2671.9
-------------+----------------------------------------------------------------
     sigma_u |  12.927536
     sigma_e |  4.8153758
         rho |  .87815689   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. estimates store re

. hausman fe re

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |       fe           re         Difference          S.E.
-------------+----------------------------------------------------------------
      curetr |   -.8038043    -.6947008       -.1091035        .2635839
       intan |   -13.18428    -12.63015       -.5541346        3.030303
         lev |   -7.614028    -4.460946       -3.153082         1.98237
    pb_ratio |    .0092747     .0189382       -.0096636         .006015
      capint |     6.97544     7.052376       -.0769362        3.877397
         roa |    8.096053     14.28829       -6.192234        4.223383
        size |    3.145254     6.348736       -3.203482        1.102212
  salary_gap |   -.0131164    -.0085802       -.0045362        .0010428
       board |    -1.85292    -.0631253       -1.789794        .9801003
 ceo_duality |   -4.260839    -2.425378       -1.835461        .7857102
      gender |    2.067474     2.798001       -.7305268        .7760839
     ceo_age |   -.0110186     .0296082       -.0406268        .0236339
  ceo_tenure |     .045644    -.0463446        .0919885        .0346436
        year |    1.861248     1.578911        .2823366        .0796076
------------------------------------------------------------------------------
                           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(14) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =       59.35
                Prob>chi2 =      0.0000
                (V_b-V_B is not positive definite)

[Carlo Lazzaro]

Kaspar:
te way you plugged -year- in should have been:

i.year

What above holds for all the >2-level categorical predictor.

That said, as

(V_b-V_B is not positive definite)

possibly because of singletons, I would give the community-contributed module -xtoverid- a shot, being aware of:
1) you shoud run the -xtreg.re- regression only and then invoke xtoverid- (its null is: -re- is the way to go);
2) being a bit old-fashioned, -xtoverid- does not support -fvvarlist- notation.
The usual work-around is to prefix your -xtreg,re- code with -xi:- (see related helpfile).

As an aside, with 215 panels, -vce(cluster panelid)- standard errors are almost mandatory (and, unlike -hausman-, -xtoverid- allows them).

[Guest]

Thanks for the help and as feedback! I have run a pooled ols below with a split/cut-off for the age. Can this be interpreted so that if in a previously run baseline model the financial variable has a positive effect on y as a regressand, this effect reverses in the case of a person under 50 and remains positive for a person over 50?

. regress esg_score c.curetr#age_split intan lev pb_ratio capint roa size salary_gap board ceo_duality gender ceo_tenu
> re i.year i.siccode, vce(cluster id)

Linear regression                               Number of obs     =        856
                                                F(23, 215)        =      16.71
                                                Prob > F          =     0.0000
                                                R-squared         =     0.4364
                                                Root MSE          =     13.386

                                         (Std. Err. adjusted for 216 clusters in id)
------------------------------------------------------------------------------------
                   |               Robust
         esg_score |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------------+----------------------------------------------------------------
age_split#c.curetr |
              <51  |  -4.455077   6.006009    -0.74   0.459    -16.29328    7.383121
              >50  |   4.401703   4.950248     0.89   0.375    -5.355528    14.15893
                   |
             intan |  -1.608273   8.633886    -0.19   0.852    -18.62617    15.40963
               lev |   7.054297   7.406431     0.95   0.342    -7.544217    21.65281
          pb_ratio |  -.0182793   .1000134    -0.18   0.855    -.2154115     .178853
            capint |   11.03918   8.593623     1.28   0.200    -5.899354    27.97772
               roa |   24.37592   15.91685     1.53   0.127     -6.99714    55.74898
              size |     6.0983   .6999447     8.71   0.000     4.718667    7.477932
        salary_gap |   .0251173   .0080556     3.12   0.002     .0092392    .0409953
             board |  -.4904315   2.056146    -0.24   0.812    -4.543217    3.562353
       ceo_duality |   3.039087    1.72797     1.76   0.080    -.3668436    6.445018
            gender |   5.154833   3.241542     1.59   0.113    -1.234438     11.5441
        ceo_tenure |  -.3837145   .1316186    -2.92   0.004    -.6431425   -.1242865
                   |
              year |
             2016  |   .7183898   .8026196     0.90   0.372    -.8636208      2.3004
             2017  |   1.370076   1.013297     1.35   0.178    -.6271935    3.367345
             2018  |   3.546741   1.049974     3.38   0.001      1.47718    5.616302
             2019  |   4.519355   1.138251     3.97   0.000     2.275795    6.762916
                   |
           siccode |
                3  |   5.510268   5.060263     1.09   0.277     -4.46381    15.48435
                4  |   6.702689   4.354213     1.54   0.125    -1.879721     15.2851
                5  |   .2033887   4.914786     0.04   0.967    -9.483946    9.890723
                6  |    .115709   6.154554     0.02   0.985    -12.01528     12.2467
                7  |   2.600354   4.415066     0.59   0.556    -6.102001    11.30271
                8  |  -.5217566   5.449333    -0.10   0.924    -11.26271     10.2192
                   |
             _cons |  -44.23435     13.549    -3.26   0.001    -70.94023   -17.52846
------------------------------------------------------------------------------------

[Carlo Lazzaro]

Guest:
not quite.
You should code your interaction as follows:

 c.curetr##age_split

[Guest]

Thanks Carlo! I have applied this, but then I only get the data for one split (the older age group) in the regression output, but I would like to be able to see both moderation effects in order to compare them, even if the interpretation is difficult? or is it not possible to implement such a control of the moderation for both age groups or age in general as factor?

Generally speaking, I am not sure if pooled ols, re or fe is the right way? My panel data are not very equally balanced, i.e. per id some observations are missing. Can fixed effects estimator be correct here at all?

. reg esg_score c.cashetr##age_split intan lev pb_ratio capint roa size salary_gap board ceo_duality gender ceo_tenure
>  i.year i.siccode, vce(r)

Linear regression                               Number of obs     =        809
                                                F(24, 784)        =      39.28
                                                Prob > F          =     0.0000
                                                R-squared         =     0.4488
                                                Root MSE          =     13.251

-------------------------------------------------------------------------------------
                    |               Robust
          esg_score |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------------+----------------------------------------------------------------
            cashetr |   .0234409   5.638519     0.00   0.997    -11.04494    11.09182
                    |
          age_split |
               >55  |  -1.074025   2.319986    -0.46   0.644    -5.628145    3.480096
                    |
age_split#c.cashetr |
               >55  |   8.441995   6.729818     1.25   0.210    -4.768601    21.65259

[Carlo Lazzaro]

Guest:
it makes sense, as you have a two-level categorical variable (age cut-off):

. use "C:\Program Files\Stata17\ado\base\a\auto.dta"
(1978 automobile data)

. regress price i.foreign##i.rep78, allbase
note: 1.foreign#1b.rep78 identifies no observations in the sample.
note: 1.foreign#2.rep78 identifies no observations in the sample.
note: 1.foreign#5.rep78 omitted because of collinearity.

      Source |       SS           df       MS      Number of obs   =        69
-------------+----------------------------------   F(7, 61)        =      0.39
       Model |    24684607         7  3526372.43   Prob > F        =    0.9049
    Residual |   552112352        61  9051022.16   R-squared       =    0.0428
-------------+----------------------------------   Adj R-squared   =   -0.0670
       Total |   576796959        68  8482308.22   Root MSE        =    3008.5

-------------------------------------------------------------------------------
        price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
--------------+----------------------------------------------------------------
      foreign |
    Domestic  |          0  (base)
     Foreign  |   2088.167   2351.846     0.89   0.378     -2614.64    6790.974
              |
        rep78 |
           1  |          0  (base)
           2  |   1403.125   2378.422     0.59   0.557    -3352.823    6159.073
           3  |   2042.574   2204.707     0.93   0.358    -2366.011    6451.159
           4  |   1317.056   2351.846     0.56   0.578    -3385.751    6019.863
           5  |       -360   3008.492    -0.12   0.905    -6375.851    5655.851
              |
foreign#rep78 |
  Domestic#1  |          0  (base)
  Domestic#2  |          0  (base)
  Domestic#3  |          0  (base)
  Domestic#4  |          0  (base)
  Domestic#5  |          0  (base)
   Foreign#1  |          0  (empty)
   Foreign#2  |          0  (empty)
   Foreign#3  |  -3866.574   2980.505    -1.30   0.199    -9826.462    2093.314
   Foreign#4  |  -1708.278   2746.365    -0.62   0.536    -7199.973    3783.418
   Foreign#5  |          0  (omitted)
              |
        _cons |     4564.5   2127.325     2.15   0.036      310.651    8818.349
-------------------------------------------------------------------------------

.

The -allbaselevels- option, described in -help estimation options- can be useful.
That said, if there's evidence of a panel-wise effect, pooled OLS in not your first choice; I would start from -xtreg,fe-.

[Guest]

Thanks Carlo for the quick answer! I will try the fe model again but the r-squared there was very low.

How are the base levels to be interpreted? If I am given a value for one group and the other represents the base?

[Carlo Lazzaro]

Guest:
1) for -xtreg,fe- the within R_sq is the one to look at;
2) correct. Provided that you do not code things different via -fvvarlist- option, the level 0 (or recoded so by Stata) is the reference category.