Issue of Model Validity and Resolving Heteroscedasticity

[Suren Perera]

Hello everyone,

I am conducting a panel regression analysis to evaluate the impact of dividend policy on the firm performance of the top 100 listed companies over a five-year period (2018 - 2022). In this study, I use Return on Equity (ROE) as the dependent variable to measure firm performance, while the dividend payout ratio (DPR) and dividend yield (DY) serve as the independent variables. Based on the results of the Hausman test, a fixed effects model was deemed appropriate for carrying out the panel regression analysis.

The results of the original panel data regression under random effects reported a Wald Chi-squared value of 24.65 with a probability value of 0.0006, indicating that the model is statistically significant. However, upon testing for heteroscedasticity, the results indicated that the model suffers from heteroscedasticity. To address this issue, I employed robust standard errors. However, under the robust regression model, the Wald Chi-squared value decreased to 7.64 with a probability value of 0.2564, rendering the model statistically insignificant.

My concern is

1. Why the model became invalid after applying robust standard errors? and;
2. What remedial measures can be taken to address this issue?

Thank you in advance for your prompt attention to this matter.

Suren

[George Ford]

you need to use clustered standard errors within the fixed effect model.

[Suren Perera]

Dear George,

Thank you very much for the solution you provided. However, despite using the clustered standard error option, the issue persists. In this scenario, what steps should I take to resolve the issue?

Thank you in advance for your prompt attention to this matter.

[George Ford]

What problem? A low F-stat? It's not a problem per se, it's just telling you that the model isn't very good at explaining Y. You need more regressors or maybe more time.

Have you looked at the literature to see how these models are typically specified?

[Suren Perera]

Dear George,

I understand your point and will consult additional literature to add variables or extend the time period considered. Your guidance has been invaluable and timely.
Thank you so much.

[Carlo Lazzaro]

Suren:
a drop in chi2 tells you only a part of the story. The main issue is whether your regression is correctly specified or not. In the following toy-example, the chi2 statistic drops to one third (from 3388.51 to 1258.33) after invoking cluster-robust standard errors (as I should, given 4710 panels), but in both cases the regerssion is (as expected) misspecified (as sq_fitted reach statistical significance):

. use "https://www.stata-press.com/data/r18/nlswork.dta"
(National Longitudinal Survey of Young Women, 14-24 years old in 1968)

. xtreg ln_wage c.age##c.age, re

Random-effects GLS regression                   Number of obs     =     28,510
Group variable: idcode                          Number of groups  =      4,710

R-squared:                                      Obs per group:
     Within  = 0.1087                                         min =          1
     Between = 0.1015                                         avg =        6.1
     Overall = 0.0870                                         max =         15

                                                Wald chi2(2)      =    3388.51
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   .0590339   .0027172    21.73   0.000     .0537083    .0643596
             |
 c.age#c.age |  -.0006758   .0000451   -15.00   0.000    -.0007641   -.0005876
             |
       _cons |   .5479714   .0397476    13.79   0.000     .4700675    .6258752
-------------+----------------------------------------------------------------
     sigma_u |   .3654049
     sigma_e |  .30245467
         rho |  .59342665   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. predict fitted, xb
(24 missing values generated)

. gen sq_fitted=fitted^2
(24 missing values generated)

. xtreg ln_wage fitted sq_fitted , re

Random-effects GLS regression                   Number of obs     =     28,510
Group variable: idcode                          Number of groups  =      4,710

R-squared:                                      Obs per group:
     Within  = 0.1088                                         min =          1
     Between = 0.1045                                         avg =        6.1
     Overall = 0.0887                                         max =         15

                                                Wald chi2(2)      =    3407.81
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
      fitted |   2.805959   .4327827     6.48   0.000      1.95772    3.654197
   sq_fitted |  -.5516341   .1320951    -4.18   0.000    -.8105358   -.2927324
       _cons |  -1.468083   .3527217    -4.16   0.000    -2.159405   -.7767613
-------------+----------------------------------------------------------------
     sigma_u |  .36481589
     sigma_e |  .30242516
         rho |  .59269507   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. xtreg ln_wage c.age##c.age, re r

Random-effects GLS regression                   Number of obs     =     28,510
Group variable: idcode                          Number of groups  =      4,710

R-squared:                                      Obs per group:
     Within  = 0.1087                                         min =          1
     Between = 0.1015                                         avg =        6.1
     Overall = 0.0870                                         max =         15

                                                Wald chi2(2)      =    1258.33
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

                             (Std. err. adjusted for 4,710 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   .0590339   .0041049    14.38   0.000     .0509884    .0670795
             |
 c.age#c.age |  -.0006758   .0000688    -9.83   0.000    -.0008107    -.000541
             |
       _cons |   .5479714   .0587198     9.33   0.000     .4328826    .6630601
-------------+----------------------------------------------------------------
     sigma_u |   .3654049
     sigma_e |  .30245467
         rho |  .59342665   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. predict fitted_2, xb
(24 missing values generated)

. gen sq_fitted_2=fitted_2^2
(24 missing values generated)

. xtreg ln_wage fitted_2 sq_fitted_2 , re r

Random-effects GLS regression                   Number of obs     =     28,510
Group variable: idcode                          Number of groups  =      4,710

R-squared:                                      Obs per group:
     Within  = 0.1088                                         min =          1
     Between = 0.1045                                         avg =        6.1
     Overall = 0.0887                                         max =         15

                                                Wald chi2(2)      =    1316.74
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

                             (Std. err. adjusted for 4,710 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    fitted_2 |   2.805959   .6246598     4.49   0.000     1.581648    4.030269
 sq_fitted_2 |  -.5516341   .1920793    -2.87   0.004    -.9281026   -.1751656
       _cons |  -1.468083   .5055433    -2.90   0.004     -2.45893   -.4772365
-------------+----------------------------------------------------------------
     sigma_u |  .36481589
     sigma_e |  .30242516
         rho |  .59269507   (fraction of variance due to u_i)
------------------------------------------------------------------------------

.

[Suren Perera]

Dear Carlo,

Your guidance has been invaluable and timely.
Thank you so much.