Relevance of Panel Data models

[Temirlan Talap]

Dear Community,

I have performed panel data regression using random and fixed model effects, with the following CODES:

reghdfe ROA ENV SOC GOV Leverage NL GDP, absorb(ID year) cluster(ID)
xtreg ROA ESG_total Leverage NL GDP, re cluster(ID)

However, I have doubts about the results that I obtained from the regressions. The Beta coefficient value is within the range of 0.0007-0.0001, which shows that the impact is no more than zero.

My variables are: ESG score, Environmental score, Social Score and Governance score (1-100 scale) and ratios of ROA ROE and Tobin's Q presented as a percentage.

What to do in such cases? These are not expected results. Can the data be omitted?

[Carlo Lazzaro]

Temirlan:
despite being symphatetic with your concern about "weird" coefficients (whatever this may mean), it's impossible to be more helpful without taking a look at what Stata gave you back under both codes. Thanks.

[Fei Wang]

A footnote to Carlo's comment: the estimation using -xtreg, re- falsely omitted year fixed effects which can be included by adding "i.year" to the list of regressors.

[Temirlan Talap]

Dear Carlo, the stata gave the following results in the attachment.

Please see.

[Temirlan Talap]

I also tried to use different panel data models such as GMM estimation. It gives me different results and at a significant level.

[Carlo Lazzaro]

Temirlan:
1) I would focus on -fe- and -re- estimators (-gmm- is a different, more demanding, beast);
2) you report the results of the community-contributed command -reghdfe- that, as far as I can see, do not raise concerns;
3) the -xtreg,re- outcome is missing. It would be interesting to see the -xttest0- outcome too.

As an aside, please use CODE delimiters instead of screenshots when you share codes/outcomes with interested listers (as per FAQ). Thanks.

[Temirlan Talap]

Dear Carlo, the panel data regression gives the following results which I believe are not satisfactory because of the small coefficient and p-value.

Can you review whether my regression makes sense in general?

 reghdfe ROA ESG_total Leverage NL GDP, absorb(ID year) cluster(ID)
(MWFE estimator converged in 2 iterations)

HDFE Linear regression                            Number of obs   =        459
Absorbing 2 HDFE groups                           F(   4,     50) =       5.68
Statistics robust to heteroskedasticity           Prob > F        =     0.0008
                                                  R-squared       =     0.8399
                                                  Adj R-squared   =     0.8143
                                                  Within R-sq.    =     0.1451
Number of clusters (ID)      =         51         Root MSE        =     0.0348

                                    (Std. err. adjusted for 51 clusters in ID)
------------------------------------------------------------------------------
             |               Robust
         ROA | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
   ESG_total |   .0004114   .0003377     1.22   0.229    -.0002668    .0010896
    Leverage |  -.0164481   .0050363    -3.27   0.002    -.0265639   -.0063323
          NL |  -.0254023   .0088393    -2.87   0.006    -.0431566    -.007648
         GDP |   .0725151   .1736336     0.42   0.678    -.2762382    .4212684
       _cons |   .2996926   .0704169     4.26   0.000      .158256    .4411291
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
          ID |        51          51           0    *|
        year |         9           0           9     |
-----------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

[Carlo Lazzaro]

Temirlan (sorry to repeat myself):
a) you report the results of the community-contributed command -reghdfe- that, as far as I can see, do not raise concerns;
b) the -xtreg,re- outcome is missing. It would be interesting to see the -xttest0- outcome too.

As an aside, please use CODE delimiters instead of screenshots when you share codes/outcomes with interested listers (as per FAQ). Thanks.

[Temirlan Talap]

Dear Carlo, please see results below:

For -reghdfe- :

reghdfe ROA ESG_total Leverage NL GDP, absorb(ID year) cluster(ID)
(MWFE estimator converged in 2 iterations)

HDFE Linear regression                            Number of obs   =        459
Absorbing 2 HDFE groups                           F(   4,     50) =       5.68
Statistics robust to heteroskedasticity           Prob > F        =     0.0008
                                                  R-squared       =     0.8399
                                                  Adj R-squared   =     0.8143
                                                  Within R-sq.    =     0.1451
Number of clusters (ID)      =         51         Root MSE        =     0.0348

                                    (Std. err. adjusted for 51 clusters in ID)
------------------------------------------------------------------------------
             |               Robust
         ROA | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
   ESG_total |   .0004114   .0003377     1.22   0.229    -.0002668    .0010896
    Leverage |  -.0164481   .0050363    -3.27   0.002    -.0265639   -.0063323
          NL |  -.0254023   .0088393    -2.87   0.006    -.0431566    -.007648
         GDP |   .0725151   .1736336     0.42   0.678    -.2762382    .4212684
       _cons |   .2996926   .0704169     4.26   0.000      .158256    .4411291
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
          ID |        51          51           0    *|
        year |         9           0           9     |
-----------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

For -xtreg- -fe:

xtreg ROA ESG_total Leverage NL GDP, fe cluster (ID)

Fixed-effects (within) regression               Number of obs     =        459
Group variable: ID                              Number of groups  =         51

R-squared:                                      Obs per group:
     Within  = 0.1808                                         min =          9
     Between = 0.2868                                         avg =        9.0
     Overall = 0.2645                                         max =          9

                                                F(4,50)           =       7.58
corr(u_i, Xb) = 0.0803                          Prob > F          =     0.0001

                                    (Std. err. adjusted for 51 clusters in ID)
------------------------------------------------------------------------------
             |               Robust
         ROA | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
   ESG_total |   .0001402   .0002842     0.49   0.624    -.0004306    .0007111
    Leverage |  -.0169754   .0053667    -3.16   0.003    -.0277548    -.006196
          NL |   -.029669   .0095643    -3.10   0.003    -.0488795   -.0104584
         GDP |   .2015548   .1741644     1.16   0.253    -.1482648    .5513743
       _cons |   .3461188    .077446     4.47   0.000     .1905639    .5016736
-------------+----------------------------------------------------------------
     sigma_u |  .06163664
     sigma_e |  .03500805
         rho |   .7560892   (fraction of variance due to u_i)
------------------------------------------------------------------------------

For -xtreg- -re with -xttest0-

 xtreg ROA ESG_total Leverage NL GDP, re cluster (ID)

Random-effects GLS regression                   Number of obs     =        459
Group variable: ID                              Number of groups  =         51

R-squared:                                      Obs per group:
     Within  = 0.1748                                         min =          9
     Between = 0.3660                                         avg =        9.0
     Overall = 0.3264                                         max =          9

                                                Wald chi2(4)      =      51.14
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

                                    (Std. err. adjusted for 51 clusters in ID)
------------------------------------------------------------------------------
             |               Robust
         ROA | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
   ESG_total |   .0004268   .0002703     1.58   0.114     -.000103    .0009566
    Leverage |  -.0157366   .0053987    -2.91   0.004    -.0263179   -.0051552
          NL |   -.037081   .0071035    -5.22   0.000    -.0510036   -.0231584
         GDP |   .2475518   .1726037     1.43   0.152    -.0907453    .5858489
       _cons |   .3912335   .0595587     6.57   0.000     .2745005    .5079664
-------------+----------------------------------------------------------------
     sigma_u |  .05179423
     sigma_e |  .03500805
         rho |  .68641267   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. xttest0

Breusch and Pagan Lagrangian multiplier test for random effects

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

        Estimated results:
                         |       Var     SD = sqrt(Var)
                ---------+-----------------------------
                     ROA |   .0065126       .0807006
                       e |   .0012256       .0350081
                       u |   .0026826       .0517942

        Test: Var(u) = 0
                             chibar2(01) =   735.62
                          Prob > chibar2 =   0.0000

[Carlo Lazzaro]

Temirlan:
as per -rho- and -xttest0- outcomes, you seem to have evidence of panle-wise effect.
Before checking via the community-contributed module -xtoverid- whether -re- is the way to go, I would re-run the regressions with -i.year- in both your codes and test the joint significance of -i.year- via -testparm-.

[Temirlan Talap]

Dear Carlo, I have tested joint significance of i.year and I cannot reject the null hypothesis. What does it mean for my regression analysis?

xtreg ROA ESG_total Leverage NLTR GDP i.year, fe cluster (ID)

Fixed-effects (within) regression               Number of obs     =        459
Group variable: ID                              Number of groups  =         51

R-squared:                                      Obs per group:
     Within  = 0.1538                                         min =          9
     Between = 0.3052                                         avg =        9.0
     Overall = 0.2390                                         max =          9

                                                F(12,50)          =       3.74
corr(u_i, Xb) = 0.1924                          Prob > F          =     0.0005

                                    (Std. err. adjusted for 51 clusters in ID)
------------------------------------------------------------------------------
             |               Robust
         ROA | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
   ESG_total |   .0007522    .000554     1.36   0.181    -.0003606     .001865
    Leverage |  -.0002658   .0000785    -3.39   0.001    -.0004234   -.0001082
        NLTR |  -.0154839   .0137294    -1.13   0.265    -.0430601    .0120923
         GDP |  -.1282887   .2029065    -0.63   0.530    -.5358385    .2792611
             |
        year |
       2012  |  -.0280475   .0197379    -1.42   0.162    -.0676922    .0115973
       2013  |  -.0336754   .0201762    -1.67   0.101    -.0742005    .0068496
       2014  |  -.0458879   .0213809    -2.15   0.037    -.0888327   -.0029431
       2015  |  -.0491021   .0218699    -2.25   0.029    -.0930291   -.0051751
       2016  |  -.0524412   .0228225    -2.30   0.026    -.0982816   -.0066008
       2017  |  -.0499533   .0238037    -2.10   0.041    -.0977644   -.0021423
       2018  |  -.0566059    .024248    -2.33   0.024    -.1053094   -.0079023
       2019  |  -.0564179   .0243467    -2.32   0.025    -.1053197   -.0075161
             |
       _cons |   .2508932   .1120491     2.24   0.030      .025836    .4759504
-------------+----------------------------------------------------------------
     sigma_u |  .06527875
     sigma_e |   .0544429
         rho |  .58977327   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. testparm i.year

 ( 1)  2012.year = 0
 ( 2)  2013.year = 0
 ( 3)  2014.year = 0
 ( 4)  2015.year = 0
 ( 5)  2016.year = 0
 ( 6)  2017.year = 0
 ( 7)  2018.year = 0
 ( 8)  2019.year = 0

       F(  8,    50) =    1.75
            Prob > F =    0.1096

[Carlo Lazzaro]

Temirlan:
that there's no evidence of a joint statistically signifcant contribution to within panel variation of the regressand made by -i.year- when adjusted for the remaning predictors.
You can keep -i.year- in or leaving it out (I would do the latter) also in the light of the literature in your research field.