[Carlo Lazzaro]

Guest:
1) -curetr- refers to CEO aged <55: it is barely statistical significance and it has a negative effect on the regressand;
2) -age_split_>55-: it refers to the level 1 of your categorical variable when the -curetr-=0. Set aside the trivial consideration that this variable gives an unbelievable representation of the reality, it fails to reach statistical significance amd, as Jeff pointed out, you cannot rule out that ist coefficient=0;
3) the interaction between -CEO aged <55- and -curetr- is positive and reaches statistical significance.
4) as far as -lincom- is concerned, please find below a toy-example (I used -allbaselevels- estimatio options to have a clearer view of my code):

use "https://www.stata-press.com/data/r17/nlswork.dta"

. xtreg ln_wage i.msp##c.age, allbase fe vce(cluster idcode)

Fixed-effects (within) regression               Number of obs     =     28,494
Group variable: idcode                          Number of groups  =      4,710

R-squared:                                      Obs per group:
     Within  = 0.1081                                         min =          1
     Between = 0.0854                                         avg =        6.0
     Overall = 0.0776                                         max =         15

                                                F(3,4709)         =     332.16
corr(u_i, Xb) = 0.0194                          Prob > F          =     0.0000

                             (Std. err. adjusted for 4,710 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         msp |
          0  |          0  (base)
          1  |   .2385289   .0277337     8.60   0.000     .1841578       .2929
             |
         age |   .0231041   .0008404    27.49   0.000     .0214566    .0247517
             |
   msp#c.age |
          0  |          0  (base)
          1  |  -.0084631   .0010018    -8.45   0.000    -.0104271   -.0064991
             |
       _cons |   1.011791   .0231926    43.63   0.000     .9663223    1.057259
-------------+----------------------------------------------------------------
     sigma_u |  .40655792
     sigma_e |  .30250158
         rho |  .64365873   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. mat list e(b)

e(b)[1,6]
            0b.          1.                 0b.msp#      1.msp#            
           msp         msp         age      co.age       c.age       _cons
y1           0   .23852893   .02310413           0  -.00846311   1.0117906


. lincom [1.msp] + [1.msp#age]

 ( 1)  1.msp + 1.msp#c.age = 0

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         (1) |   .2300658   .0267675     8.59   0.000     .1775889    .2825427
------------------------------------------------------------------------------

.

[Guest]

Many thanks for the answer!

So in my own words (about the output with all baselevels): The output below basically says for curetr (a proxy for tax avoidance; high curetr equals low tax avoidance) and for the interaction age_split#c.curetr weak significance at p<0.05. Conversely, on the one hand, for the group under 56, the effect of the regressor curetr on esg as a regressand is negative (-4.01). age_split is insignificant (no effect), but if significant, in this case it would tell me that the older age group behaves "more negatively" to the regressand esg than the younger one (direct comparison for the cutoff). Regarding the interaction age_split#c.curetr, the age group over 55 has a less negative effect than group 1 (curetr of -4.01). Is it correct? Sorry if I'm making it complicated...

The other control variables could then again be interpreted independently of age for the entire sample, right?

. 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) allbase

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 |
              <56  |          0  (base)
              >55  |  -2.016321   1.113921    -1.81   0.072    -4.211926    .1792835
                   |
age_split#c.curetr |
              <56  |          0  (base)
              >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 |
             2015  |          0  (base)
             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) if the -age_split- is insignificant you should live with that. Any other interpretations sound to me like "If I were Roger Feder...";
2) -lincom- will give you the overall effect of -age_split- + the interaction term;
3) the effect on the regresand produced by each predictor is adjusted for the other predictors. In other words, different specification produce different coefficient.

[Guest]

Thanks for the explanation Carlo!

(1) I was concerned with the interpretation of the coefficients, especially with reference to base, regardless of significance and specific output, since I have never worked with fe and done such interactions. Assuming all coefficients above are significant. Could I then say that....

- curetr: in age group one, the effect is negative on esg
- age_split: compared to age group one (base), the effect of the older age group on esg is slightly "more negative"
- age_split#c.curetr: the effect of the upper age group on the base is more "positive", i.e. curetr is higher if the person comes from this group in comparison to the younger aged ceos (base)

. 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) allbase

Fixed-effects (within) regression               Number of obs     =        789
Group variable: id                              Number of groups  =        200

R-sq:                                           Obs per group:
     within  = 0.3354                                         min =          1
     between = 0.2261                                         avg =        3.9
     overall = 0.2031                                         max =          5

                                                F(17,199)         =      10.16
corr(u_i, Xb)  = 0.1601                         Prob > F          =     0.0000

                                         (Std. Err. adjusted for 200 clusters in id)
------------------------------------------------------------------------------------
                   |               Robust
         esg_score |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------------+----------------------------------------------------------------
            curetr |  -4.668148   2.129563    -2.19   0.030    -8.867553   -.4687435
                   |
         age_split |
              <56  |          0  (base)
              >55  |  -2.085222   1.157187    -1.80   0.073    -4.367144    .1966996
                   |
age_split#c.curetr |
              <56  |          0  (base)
              >55  |   5.702373   2.895064     1.97   0.050    -.0065681    11.41131

(2) Regarding lincom, is the formulation for the second age group below correct and how should it be interpreted?

. lincom 2.age_split + 2.age_split#c.curetr

 ( 1)  2.age_split + 2.age_split#c.curetr = 0

------------------------------------------------------------------------------
   esg_score |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         (1) |   3.617151   2.132552     1.70   0.091    -.5881498    7.822452
------------------------------------------------------------------------------

(3) Other question: furthermore, does winsorizing make sense based on individual outliers or is clustering the standard errors for the individual ids sufficient?

[Carlo Lazzaro]

Guest:
1) you can only say that "curetr: in age group one, the effect is negative on esg";
The other coefficients may well be zero.
2) the -lincom- is coded correct and confirms the lack of a statistical significant effect on the regressand when the conditional mean and the interaction effect for the second age group were summedup together;
3) I would shy away from winsorizing. I'm under the impression that you're trying to test different tricks to make the data fulfilling your expectations. Please note that this approach is not only highly questionable from a methodological viewpoint, but it is also very eay to detect by those who are familiar with this kind of stuff. Just to wrap-up: please do not do it.
4) That said: what's your supervisor's role in all this methidological turmoil?

[Guest]

So the other coefficients cannot be interpreted? This is my main point here. At best, the coefficients should be interpretable and the subgroups comparable.

I am not trying to get optimal results, but to find a way and the appropriate static model, how I can compare two groups of one sample with the introduction of interaction terms that should contain both age and tenure. That it turns out so difficult goes then probably on my limited static skills! Sorry for that!

[Carlo Lazzaro]

Guest:
1) all the coefficients are interpretable, provided that you consider that their effect is adjusted for the other predictors;
2) the interaction that you've in mind is somethng like:

i.age_group##c.tenure

[Guest]

@Carlo:
I'm sorry, but I didn't quite understand what the term base for the categories was all about (except that it describes the group 1) and how to interpret the model and its coefficients - regardless of significance - now. So I tried an interpretation above that I'm not sure is feasible.

Age and tenure should not coincide, but represent two different hypotheses.

H1: Effect of x (financial variable, continuous variable) on y decreases/increases if the person belongs to one or the other age group. -> cut-off age

H2: Effect of x (financial variable, continuous variable) on y decreases/increases if the person is below or above a certain tenure. -> cut-off tenure

[Carlo Lazzaro]

Guest:
I fear you're experiencing a bit of overload, that does not help.
If you refer to my interaction code, -tenure- was assumed to be continuos (see -c.- prefix).
Therefore your interpretation (forgetting significance for a while) is correct for H1 only.
Again, couldn't your supervisor/more experienced colleague lend you a hand?