Moderating Variable - Panel Data

[Konstantin Wiesemann]

Hello friends and STATA experts,

after quick and great help with my last problem I've come to seek your wisdom again, hopefully.

I'm running a simple random effects regression: DV (ESG) and IV (Sh and Pa). So far, so good:

. xtreg $ylist $xlist, re

Random-effects GLS regression Number of obs = 4,801
Group variable: comp Number of groups = 683

R-sq: Obs per group:
within = 0.0312 min = 1
between = 0.0936 avg = 7.0
overall = 0.0531 max = 8

Wald chi2(2) = 204.63
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

------------------------------------------------------------------------------
ESG | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Sh | -.0717968 .0105774 -6.79 0.000 -.092528 -.0510655
Pa | -7.636461 .663959 -11.50 0.000 -8.937797 -6.335126
_cons | 56.73223 .7828353 72.47 0.000 55.1979 58.26656
-------------+----------------------------------------------------------------
sigma_u | 9.1761324
sigma_e | 19.153479
rho | .18667569 (fraction of variance due to u_i)
------------------------------------------------------------------------------

Now, I'm trying to include a moderating (dummy) variable to see if Industry effects affect the relationship of the DV and IV.
My moderaing variable is 1 for controversial industries and 0 for uncontroversial industries. I want to show that this variable moderates the realtionship between my DV(ESG) and one of my IV(Sh).
And at this point I'm not sure how to show that. I tried it this way:

. xtreg $ylist Sh Industry, re

Random-effects GLS regression Number of obs = 4,801
Group variable: comp Number of groups = 683

R-sq: Obs per group:
within = 0.0117 min = 1
between = 0.0283 avg = 7.0
overall = 0.0185 max = 8

Wald chi2(2) = 69.94
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

------------------------------------------------------------------------------
ESG | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Sh | -.0885863 .0106335 -8.33 0.000 -.1094275 -.0677451
Industry | -.692654 1.611324 -0.43 0.667 -3.85079 2.465483
_cons | 53.18053 .7455474 71.33 0.000 51.71928 54.64178
-------------+----------------------------------------------------------------
sigma_u | 9.6593325
sigma_e | 19.34267
rho | .19960292 (fraction of variance due to u_i)
------------------------------------------------------------------------------


Does this come close?
Can I forget all about the effect anyway because the p-value is lightyears from significance?

Thank you kindly for all help and comments in advance,
Konstantin

[Carlo Lazzaro]

Konstantin:
why not interacting the two predictors:

xtreg ESG i.industry##c.Sh, re///I assume that -Sh- is continuous

[Konstantin Wiesemann]

Oh yes, Carlo Lazzaro once again saving the day! I think this is exactly what I needed :D
You assumed right, Sh is continuous. So I assume what I coloured red is the reg result in absence of the second predictor and blue the reg result if Industry takes the value of 1 (uncontroversial industry). Can I see the result if it takes the value of 0 (controversial industry)?



. xtreg ESG i.Industry##c.Sh, re

Random-effects GLS regression Number of obs = 4,801
Group variable: comp Number of groups = 683

R-sq: Obs per group:
within = 0.0153 min = 1
between = 0.0268 avg = 7.0
overall = 0.0205 max = 8

Wald chi2(3) = 84.32
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

-------------------------------------------------------------------------------
ESG | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
1.Industry | 7.248824 2.650763 2.73 0.006 2.053425 12.44422
Sh | -.0756342 .0111586 -6.78 0.000 -.0975047 -.0537637
|
Industry#c.Sh |
1 | -.1371937 .0363524 -3.77 0.000 -.2084432 -.0659443
|
_cons | 52.49561 .7668998 68.45 0.000 50.99252 53.99871
--------------+----------------------------------------------------------------
sigma_u | 9.6771477
sigma_e | 19.309291
rho | .200746 (fraction of variance due to u_i)
-------------------------------------------------------------------------------

EDIT: I think I got it on my own:

. xtreg ESG i.Industry#c.Sh, re

Random-effects GLS regression Number of obs = 4,801
Group variable: comp Number of groups = 683

R-sq: Obs per group:
within = 0.0139 min = 1
between = 0.0234 avg = 7.0
overall = 0.0189 max = 8

Wald chi2(2) = 76.75
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

-------------------------------------------------------------------------------
ESG | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
Industry#c.Sh |
0 | -.0824393 .0108853 -7.57 0.000 -.1037742 -.0611044
1 | -.140694 .0224061 -6.28 0.000 -.1846091 -.0967788
|
_cons | 53.10258 .7344456 72.30 0.000 51.66309 54.54207
--------------+----------------------------------------------------------------
sigma_u | 9.6685904
sigma_e | 19.309291
rho | .20046227 (fraction of variance due to u_i)
-------------------------------------------------------------------------------

[Carlo Lazzaro]

Konstantin:
- the main issue with your model is that you have a very limited number of predictors (between = 0.0268 is pretty low); hence, your model may suffe from omitted variable bias. I would skim the literature in your research field and see what others did in the past when compared with the same research goal;
- for the future, please use CODE delimiters to share what you typed and what Stata gave you back. Thanks.