Dummy variables - how to determine significance

Can Deniz

Join Date: Mar 2021
Posts: 16

Dummy variables - how to determine significance

26 Mar 2021, 19:42

Dear experts,

I have a panel data set with 77 variables and about 68,184 observations for the years 2014 - 2018. I use dummy variables for the independent variables firm size (kleine_KapG große_KapG) and industry sector (LuF BB, etc.). With these, I want to run a regression to find the effect on the tax burden (ETR) of the firms. For the dummy variables, I have set 3rd industry and medium firms as the base variable. I use xtreg in Stata 15.1.

My question is, how can I determine if industry or company size has a significant impact on ETR?

Can I only assess siginficance on dummy variables by looking at the p-values of the individual coefficients? When I do this, I can see that 9 of the 18 industry sectors are statistically significant at the 5% level. So does this mean that overall we cannot find a clear significant impact of industry sectors on ETR?

Regarding firm size, the dummy "kleine_KapG" seems to be insignificant. Does this mean that I cannot say with certainty here that the small size group exerts a significant influence on the tax ratio (ETR)?

And how can I interpret Prob > chi2 = 0.0000 in this context? As far as I know, the Wald test is not possible with dummy variables (if that is what I think it is)

Below is my regression output:

Code:

 xtreg ETR i.industry i.size, re

Random-effects GLS regression                   Number of obs     =     68,184
Group variable: ID                              Number of groups  =     17,613

R-sq:                                           Obs per group:
     within  = 0.0000                                         min =          1
     between = 0.0920                                         avg =        3.9
     overall = 0.0593                                         max =          5

                                                Wald chi2(20)     =    1698.32
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

----------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                           ETR |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------------------------------------------------------------------------------------+----------------------------------------------------------------
                                                                                      industry |
                                                      1. Land- und Forstwirtschaft, Fischerei  |  -2.256599   1.561742    -1.44   0.148    -5.317557    .8043591
                                               2. Bergbau und Gewinnung von Steinen und Erden  |  -.7683471   1.753351    -0.44   0.661    -4.204851    2.668157
                                                                         4. Energieversorgung  |  -3.122808   .4740867    -6.59   0.000    -4.052001   -2.193615
5. Wasserversorgung; Abwasser- und Abfallentsorgung und Beseitigung von Umweltverschmutzungen  |   .7762757   .6979841     1.11   0.266    -.5917479    2.144299
                                                                            6. Baugewerbe/Bau  |  -.8002177   .4634916    -1.73   0.084    -1.708644    .1082091
                                  7. Handel; Instandhaltung und Reparatur von Kraftfahrzeugen  |    1.42259   .2572426     5.53   0.000     .9184044    1.926777
                                                                       8. Verkehr und Lagerei  |  -.1100255   .4976104    -0.22   0.825    -1.085324     .865273
                                                  9. Gastgewerbe/Beherbergung und Gastronomie  |   1.345142   1.065188     1.26   0.207    -.7425888    3.432872
                                                            10. Information und Kommunikation  |    1.43946   .4952618     2.91   0.004     .4687649    2.410155
                                 11. Erbringung von Finanz- und Versicherungsdienstleistungen  |   1.752497   .5525703     3.17   0.002     .6694789    2.835515
                                                           12. Grundstücks- und Wohnungswesen  |  -8.606384   .5531698   -15.56   0.000    -9.690577   -7.522192
      13. Erbringung von freiberuflichen, wissenschaftlichen und technischen Dienstleistungen  |    .952567   .3197291     2.98   0.003     .3259095    1.579224
                               14. Erbringung von sonstigen wirtschaftlichen Dienstleistungen  |   1.294269    .479638     2.70   0.007     .3541957    2.234342
                                 15. Öffentliche Verwaltung, Verteidigung; Sozialversicherung  |   1.056461   2.118098     0.50   0.618    -3.094935    5.207857
                                                                 16. Erziehung und Unterricht  |  -12.56339   1.330064    -9.45   0.000    -15.17026   -9.956509
                                                             17. Gesundheits- und Sozialwesen  |  -15.35155   .4831442   -31.77   0.000    -16.29849    -14.4046
                                                         18. Kunst, Unterhaltung und Erholung  |    1.06332   1.146832     0.93   0.354    -1.184429     3.31107
                                                19. Erbringung von sonstigen Dienstleistungen  |  -.7305772   .8222466    -0.89   0.374    -2.342151    .8809965
                                                                                               |
                                                                                          size |
                                                                                1. große KapG  |  -.8383229   .2491426    -3.36   0.001    -1.326633   -.3500124
                                                                               2. kleine KapG  |   .1314099   .1553299     0.85   0.398    -.1730311    .4358509
                                                                                               |
                                                                                         _cons |   29.89383   .1793779   166.65   0.000     29.54225     30.2454
-----------------------------------------------------------------------------------------------+----------------------------------------------------------------
                                                                                       sigma_u |  10.978087
                                                                                       sigma_e |  9.8806548
                                                                                           rho |  .55246733   (fraction of variance due to u_i)
----------------------------------------------------------------------------------------------------------------------------------------------------------------

Many thanks.

Best wishes,
Can

Last edited by Can Deniz; 26 Mar 2021, 19:45.

Tags: None

Joseph Coveney

Join Date: Apr 2014

Posts: 4377
#2

26 Mar 2021, 21:16

Originally posted by Can Deniz View Post

how can I determine if industry or company size has a significant impact on ETR?

Can I only assess siginficance on dummy variables by looking at the p-values of the individual coefficients?

You can use -testparm- after fitting the model:

Code:

testparm i.industry testparm i.size
Comment
Joro Kolev

Join Date: Aug 2018

Posts: 3047
#3

26 Mar 2021, 22:13

The short answer is that you evaluate significance of dummies just like you evaluate significance of any other variable.

Joseph showed how you can test the dummies as a group.

These are two different questions. Say you have three sizes: small, medium and large, and you have chosen medium as your base category. 1) Testing whether only the Small dummy is significant, tests whether there is small firms effect. 2) Testing Small and Large dummies jointly, tests whether there is size effect overall, be it big, or small.
Comment

Can Deniz

Join Date: Mar 2021
Posts: 16

27 Mar 2021, 08:30

Thank you very much for the previous comments so far. However, I have some unclear points:

1) Is testparm not only applicable for time-fixed models? However, I have a REM.

2) And how can I measure the significance of the size or industry group in a normal main regression ?

3) The result from testparm on REM shows me that the size seems to be overall significant:

Code:

. testparm i.industry

 ( 1)  1.industry = 0
 ( 2)  2.industry = 0
 ( 3)  4.industry = 0
 ( 4)  5.industry = 0
 ( 5)  6.industry = 0
 ( 6)  7.industry = 0
 ( 7)  8.industry = 0
 ( 8)  9.industry = 0
 ( 9)  10.industry = 0
 (10)  11.industry = 0
 (11)  12.industry = 0
 (12)  13.industry = 0
 (13)  14.industry = 0
 (14)  15.industry = 0
 (15)  16.industry = 0
 (16)  17.industry = 0
 (17)  18.industry = 0
 (18)  19.industry = 0

           chi2( 18) = 1636.63
         Prob > chi2 =    0.0000

. 
. testparm i.size

 ( 1)  1.size = 0
 ( 2)  2.size = 0

           chi2(  2) =   13.30
         Prob > chi2 =    0.0013

However, the p-value from the regression output below shows me that there is no statistical significance for small firms.

Code:

 
     size 
 1. large firms  |  -.8383229   .2491426    -3.36   0.001    -1.326633   -.3500124
 2. small firms  |   .1314099   .1553299     0.85   0.398    -.1730311    .4358509                   
   _cons         |   29.89383   .1793779   166.65   0.000     29.54225     30.2454

... Does this mean there is actually an overall significance but none for that of small enterprises?

And is the correct interpretation in this case that if a company is in the 3rd industry and a medium-sized one, it cannot be assumed that small companies have an effect on y?

Many thanks.

Comment

Joro Kolev

Join Date: Aug 2018

Posts: 3047
#5

28 Mar 2021, 02:23

I did not understand anything of what you said. What are "time-fixed models," what is a "REM" and what is a "normal main regression"?

-testparm - does what the name says, it tests whether parameters are 0.

As for 3), yes, it is what you are saying. You cannot find the small firms effect significant, but when you test small and big firms jointly, they are jointly significant, so you do have overall size effect.

Originally posted by Can Deniz View Post

Thank you very much for the previous comments so far. However, I have some unclear points:

1) Is testparm not only applicable for time-fixed models? However, I have a REM.

2) And how can I measure the significance of the size or industry group in a normal main regression ?

3) The result from testparm on REM shows me that the size seems to be overall significant:

Code:

. testparm i.industry ( 1) 1.industry = 0 ( 2) 2.industry = 0 ( 3) 4.industry = 0 ( 4) 5.industry = 0 ( 5) 6.industry = 0 ( 6) 7.industry = 0 ( 7) 8.industry = 0 ( 8) 9.industry = 0 ( 9) 10.industry = 0 (10) 11.industry = 0 (11) 12.industry = 0 (12) 13.industry = 0 (13) 14.industry = 0 (14) 15.industry = 0 (15) 16.industry = 0 (16) 17.industry = 0 (17) 18.industry = 0 (18) 19.industry = 0 chi2( 18) = 1636.63 Prob > chi2 = 0.0000 . . testparm i.size ( 1) 1.size = 0 ( 2) 2.size = 0 chi2( 2) = 13.30 Prob > chi2 = 0.0013

However, the p-value from the regression output below shows me that there is no statistical significance for small firms.

Code:

size 1. large firms | -.8383229 .2491426 -3.36 0.001 -1.326633 -.3500124 2. small firms | .1314099 .1553299 0.85 0.398 -.1730311 .4358509 _cons | 29.89383 .1793779 166.65 0.000 29.54225 30.2454

... Does this mean there is actually an overall significance but none for that of small enterprises?

And is the correct interpretation in this case that if a company is in the 3rd industry and a medium-sized one, it cannot be assumed that small companies have an effect on y?

Many thanks.
Comment
Can Deniz

Join Date: Mar 2021

Posts: 16
#6

28 Mar 2021, 07:09

I mean by REM - Random Effect Models
FEM - fixed effect models (or time -fixed models)

and main regression means: regress i.size i.industry.

But I understood your point. Thanks a lot
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