Panel dataset and omitted dummy variables for regression

[Can Deniz]

Dear experts,

I have a panel dataset of 77 variables and approximately 57.000 observations for the years 2014 - 2018. Therefore I use dummy variables for the independent variable company size (klein mittel groß) and industry sector (LuF BB, etc.). Using this, I ran regress to determine the effect on the tax burden (ETR_un) of companies.

I am using xtreg in Stata 15.1.

My problem is that as soon as I add the company size to my regression in addition to the industry dummies, 2 variables are immediately omitted. Therefore, the values of the independent variables are skewed.

I know that to avoid a dummy trap, I can remove one variable from the industry dummies and one from the company size, but the values still remain skewed.


How can I get around this problem?

 xtreg ETR_un LuF BB Verarbeitendes Energieversorg Wasserversorg Baugewerbe Handel Verkehr Gastgewerbe Inform_Kommun Finanz_Versich Grunds
> tücks_Wohnungswesen FreiWissTech_DL wirts_DL ÖV Erziehung_Unterr Gesundheit_Sozialwesen Kunst_Unterhaltung_Erholung sonst_DL klein mittel
>  groß i.year, re 
note: sonst_DL omitted because of collinearity
note: groß omitted because of collinearity

Random-effects GLS regression                   Number of obs     =     57,217
Group variable: ID                              Number of groups  =     18,389

R-sq:                                           Obs per group:
     within  = 0.0013                                         min =          1
     between = 0.0589                                         avg =        3.1
     overall = 0.0337                                         max =          5

                                                Wald chi2(24)     =    1163.20
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

---------------------------------------------------------------------------------------------
                     ETR_un |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
                        LuF |  -2.806153   1.724013    -1.63   0.104    -6.185157    .5728511
                         BB |   1.223227   1.931906     0.63   0.527    -2.563238    5.009692
             Verarbeitendes |   1.156536   .7854209     1.47   0.141    -.3828609    2.695932
             Energieversorg |  -1.362574   .8817548    -1.55   0.122    -3.090782    .3656336
              Wasserversorg |   1.335969   1.015181     1.32   0.188    -.6537506    3.325688
                 Baugewerbe |   .8637391   .8727683     0.99   0.322    -.8468553    2.574333
                     Handel |     2.5564    .789308     3.24   0.001     1.009385    4.103415
                    Verkehr |     1.4275   .8937224     1.60   0.110    -.3241637    3.179164
                Gastgewerbe |   2.483374   1.282375     1.94   0.053    -.0300348    4.996784
              Inform_Kommun |    2.36475   .8876878     2.66   0.008     .6249134    4.104586
             Finanz_Versich |   3.360829    .911962     3.69   0.000     1.573416    5.148241
  Grundstücks_Wohnungswesen |  -6.140547   .9226302    -6.66   0.000    -7.948869   -4.332225
            FreiWissTech_DL |   1.915703     .80875     2.37   0.018      .330582    3.500824
                   wirts_DL |    2.66731    .880347     3.03   0.002     .9418616    4.392758
                         ÖV |   6.128692   2.154682     2.84   0.004     1.905592    10.35179
           Erziehung_Unterr |  -7.485594   1.566971    -4.78   0.000     -10.5568   -4.414388
     Gesundheit_Sozialwesen |  -11.52747   .8984018   -12.83   0.000    -13.28831   -9.766636
Kunst_Unterhaltung_Erholung |   1.190228    1.34611     0.88   0.377      -1.4481    3.828556
                   sonst_DL |          0  (omitted)
                      klein |    .107322   .3644027     0.29   0.768    -.6068941    .8215381
                     mittel |  -.4489496   .2944976    -1.52   0.127    -1.026154    .1282552
                       groß |          0  (omitted)
                            |
                       year |
                        15  |   .3697264   .1749918     2.11   0.035     .0267489     .712704
                        16  |  -.2524269   .1744287    -1.45   0.148    -.5943008    .0894471
                        17  |   .3338847   .1742833     1.92   0.055    -.0077044    .6754738
                        18  |   .9312448   .2926599     3.18   0.001     .3576419    1.504848
                            |
                      _cons |   26.40237    .775345    34.05   0.000     24.88272    27.92202
----------------------------+----------------------------------------------------------------
                    sigma_u |    9.70098
                    sigma_e |   12.63551
                        rho |  .37085086   (fraction of variance due to u_i)

In the following you can see that the respective average tax rates of the industries and company sizes are not the same as in the output of the regression.

 tabstat ETR_un, statistics (count mean sd max min range) by(Branche)

Summary for variables: ETR_un
     by categories of: Branche (Branche)

         Branche |         N      mean        sd       max       min     range
-----------------+------------------------------------------------------------
1. Land- und For |       177  24.83884  12.81619  76.21348  1.072381   75.1411
2. Bergbau und G |       142  28.01898  17.38571  91.96083  1.116526   90.8443
3. Verarbeitende |     16119  28.02748  14.02538   99.6544  1.005321  98.64908
4. Energieversor |      2514  25.49997  15.52516  97.77159  1.019462  96.75213
5. Wasserversorg |      1067   27.8953  15.64467  99.73144  1.119681  98.61176
6. Baugewerbe/Ba |      2725  27.80223  12.44849  98.92137  1.014662  97.90671
7. Handel; Insta |     13455  29.22813  13.67265  99.76919  1.003844  98.76534
8. Verkehr und L |      2173  28.26321  14.86916  99.54535  1.024184  98.52117
9. Gastgewerbe/B |       417  29.41986  15.65624  99.04601  1.067991  97.97802
10. Information  |      2270  29.26193   15.2746  97.74427  1.017193  96.72708
11. Erbringung v |      1842  30.01445  18.04395  99.85857  1.026219  98.83235
12. Grundstücks- |      1679  20.97251  16.91162  99.36201  1.012189  98.34982
13. Erbringung v |      6944  28.79622  17.03924  99.88694  1.017734  98.86921
14. Erbringung v |      2441   29.4939    15.703  99.85537   1.02731  98.82806
15. Öffentliche  |       108  33.55072  27.06546  98.77544  1.449751  97.32569
16. Erziehung un |       206  20.88952  22.37715  99.39492  1.019612  98.37531
17. Gesundheits- |      1822  15.34987  16.67667    99.662  1.000133  98.66187
18. Kunst, Unter |       366  27.51446  19.84288  97.59387   1.18329  96.41058
19. Erbringung v |       750  27.34199  17.72626  98.51981  1.002463  97.51734
-----------------+------------------------------------------------------------
           Total |     57217  27.82532  15.28509  99.88694  1.000133  98.88681
------------------------------------------------------------------------------

tabstat ETR_un, statistics (count mean sd max min range) by(Größe_HP)  

Summary for variables: ETR_un
     by categories of: Größe_HP 

     Größe_HP |         N      mean        sd       max       min     range
--------------+------------------------------------------------------------
   große KapG |     45881  27.75923   15.2651  99.88694  1.001677  98.88526
  kleine KapG |      3250  28.64398   15.4276  99.27302  1.003844  98.26917
mittlere KapG |      8086  27.87132  15.33302  99.73144  1.000133   98.7313
--------------+------------------------------------------------------------
        Total |     57217  27.82532  15.28509  99.88694  1.000133  98.88681
---------------------------------------------------------------------------

Lastly, I wanted to ask whether I am correct with the REM regression? In the FEM, it showed me "omitted" for all industry dummies:

 xtreg ETR_un LuF BB Verarbeitendes Energieversorg Wasserversorg Baugewerbe Handel Verkehr Gastgewerbe Inform_Kommun Finanz_Versich Grunds
> tücks_Wohnungswesen FreiWissTech_DL wirts_DL ÖV Erziehung_Unterr Gesundheit_Sozialwesen Kunst_Unterhaltung_Erholung sonst_DL klein mittel
> , fe 
note: LuF omitted because of collinearity
note: BB omitted because of collinearity
note: Verarbeitendes omitted because of collinearity
note: Energieversorg omitted because of collinearity
note: Wasserversorg omitted because of collinearity
note: Baugewerbe omitted because of collinearity
note: Handel omitted because of collinearity
note: Verkehr omitted because of collinearity
note: Gastgewerbe omitted because of collinearity
note: Inform_Kommun omitted because of collinearity
note: Finanz_Versich omitted because of collinearity
note: Grundstücks_Wohnungswesen omitted because of collinearity
note: FreiWissTech_DL omitted because of collinearity
note: wirts_DL omitted because of collinearity
note: ÖV omitted because of collinearity
note: Erziehung_Unterr omitted because of collinearity
note: Gesundheit_Sozialwesen omitted because of collinearity
note: Kunst_Unterhaltung_Erholung omitted because of collinearity
note: sonst_DL omitted because of collinearity

Fixed-effects (within) regression               Number of obs     =     57,217
Group variable: ID                              Number of groups  =     18,389

R-sq:                                           Obs per group:
     within  = 0.0007                                         min =          1
     between = 0.0002                                         avg =        3.1
     overall = 0.0001                                         max =          5

                                                F(2,38826)        =      13.26
corr(u_i, Xb)  = -0.0121                        Prob > F          =     0.0000

---------------------------------------------------------------------------------------------
                     ETR_un |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
                        LuF |          0  (omitted)
                         BB |          0  (omitted)
             Verarbeitendes |          0  (omitted)
             Energieversorg |          0  (omitted)
              Wasserversorg |          0  (omitted)
                 Baugewerbe |          0  (omitted)
                     Handel |          0  (omitted)
                    Verkehr |          0  (omitted)
                Gastgewerbe |          0  (omitted)
              Inform_Kommun |          0  (omitted)
             Finanz_Versich |          0  (omitted)
  Grundstücks_Wohnungswesen |          0  (omitted)
            FreiWissTech_DL |          0  (omitted)
                   wirts_DL |          0  (omitted)
                         ÖV |          0  (omitted)
           Erziehung_Unterr |          0  (omitted)
     Gesundheit_Sozialwesen |          0  (omitted)
Kunst_Unterhaltung_Erholung |          0  (omitted)
                   sonst_DL |          0  (omitted)
                      klein |   1.206493   .2799578     4.31   0.000     .6577689    1.755217
                     mittel |   .5408651   .1822532     2.97   0.003     .1836443     .898086
                      _cons |   27.68036   .0611299   452.81   0.000     27.56054    27.80017
----------------------------+----------------------------------------------------------------
                    sigma_u |  13.079854
                    sigma_e |  12.638967
                        rho |  .51713756   (fraction of variance due to u_i)
---------------------------------------------------------------------------------------------
F test that all u_i=0: F(18388, 38826) = 2.44                Prob > F = 0.0000

Many thanks.

Kind regards
Can

[Clyde Schechter]

I'm going to rely here on rough English translations of your variable names, as I don't function in German.

You have three size levels, small, medium and large. But you put in three indicator ("dummy") variables, where you should only have three, with the missing one serving as the base or reference case. Whenever you have a categorical variables with n levels, the representation in a regression should be n-1 of them, with one left out. Stata noticed that and so omitted one of them, large, for you.

The same is true for sonst_DL which, I believe, is an "other" category for industry. You can't put in an indicator for every level of the category variable. So Stata picked one to omit for you.

The best way to improve this code is to use factor variable notation. (-help fvvarlist-). So first create the multi-level category variables: size, and industry. Size can be coded 1, 2, 3, for small, medium, large. Industry can start at 1 and count up to however many there are (I believe that's 19.) Then get rid of all those "dummy" variables you created. Then the code simplifies to

xtreg ETR_un i.industry i.size i.year, re

Stata will pick one level of each category variable to omit as the base category and then create "virtual" indicators for the rest (that do not clutter up your data set.) If you don't care for the choice Stata makes about wish, -help fvvarlist- explains how you can specify your preference.

When you go to fixed effects regression, then, unsurprisingly, the industry indicators all disappear because any given firm is in the same industry for all years in the study. In fixed-effects regression variables that do not change over time within panels are always omitted because they are colinear with the fixed effects themselves. Moreover, the effects of those omitted variables cannot be estimated in a fixed-effects model. If you try to juggle things to make Stata retain those variables, other variables will be lost instead. In the end, it is mathematically impossible to estimate the effects of time-invariant variables in a fixed-effects model.

As for whether to use fixed effects or random effects, in economics and finance there is a tendency to rely on the Hausman test (-help xtoverid-). I am not a fan of that approach, and I think that in general with observational data and when we are trying to estimate within-panel effects, we should just use -fe-, even if Hausman says -re- is OK. If your research goals require you to estimate the effects of time-invariant variables like industry (that is, you need to actually estimate their effects, not just try to deal with omitted variable bias), then you can't use -fe-, no matter what Hausman says. In that case, -xthybrid- offers an alternative that is something like the best of both worlds. I reserve -re- primarily for analysis of randomized experiments.

[Can Deniz]

First of all, I would like to thank you for the explanations.

As you suggested, I have now run my regression using the variable factor notation.

Nevertheless, a problem remains. If you look at the mean values from the first tabstat, you can see that for example the mean value for the industry "Bergbau und Gewinnung.." is not the same as when you take the value of the factor variable and add it to the constants.


I used the following code as the factor variable and used the most frequent value as the base variable:

fvset base frequent industry size

This is the tabstat for all industries with their mean respectively effective tax rates (ETR_un):

tabstat ETR_un, statistics (count mean sd max min range) by(industry)

Summary for variables: ETR_un
     by categories of: industry (Branche)

        industry |         N      mean        sd       max       min     range
-----------------+------------------------------------------------------------
1. Land- und For |       177  24.83884  12.81619  76.21348  1.072381   75.1411
2. Bergbau und G |       142  28.01898  17.38571  91.96083  1.116526   90.8443
3. Verarbeitende |     16119  28.02748  14.02538   99.6544  1.005321  98.64908
4. Energieversor |      2514  25.49997  15.52516  97.77159  1.019462  96.75213
5. Wasserversorg |      1067   27.8953  15.64467  99.73144  1.119681  98.61176
6. Baugewerbe/Ba |      2725  27.80223  12.44849  98.92137  1.014662  97.90671
7. Handel; Insta |     13455  29.22813  13.67265  99.76919  1.003844  98.76534
8. Verkehr und L |      2173  28.26321  14.86916  99.54535  1.024184  98.52117
9. Gastgewerbe/B |       417  29.41986  15.65624  99.04601  1.067991  97.97802
10. Information  |      2270  29.26193   15.2746  97.74427  1.017193  96.72708
11. Erbringung v |      1842  30.01445  18.04395  99.85857  1.026219  98.83235
12. Grundstücks- |      1679  20.97251  16.91162  99.36201  1.012189  98.34982
13. Erbringung v |      6944  28.79622  17.03924  99.88694  1.017734  98.86921
14. Erbringung v |      2441   29.4939    15.703  99.85537   1.02731  98.82806
15. Öffentliche  |       108  33.55072  27.06546  98.77544  1.449751  97.32569
16. Erziehung un |       206  20.88952  22.37715  99.39492  1.019612  98.37531
17. Gesundheits- |      1822  15.34987  16.67667    99.662  1.000133  98.66187
18. Kunst, Unter |       366  27.51446  19.84288  97.59387   1.18329  96.41058
19. Erbringung v |       750  27.34199  17.72626  98.51981  1.002463  97.51734
-----------------+------------------------------------------------------------
           Total |     57217  27.82532  15.28509  99.88694  1.000133  98.88681
------------------------------------------------------------------------------

This is the new regression output:

 xtreg ETR_un i.industry i.size i.year, re

Random-effects GLS regression                   Number of obs     =     57,217
Group variable: ID                              Number of groups  =     18,389

R-sq:                                           Obs per group:
     within  = 0.0013                                         min =          1
     between = 0.0589                                         avg =        3.1
     overall = 0.0337                                         max =          5

                                                Wald chi2(24)     =    1163.20
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------------------
                  ETR_un |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------------------+----------------------------------------------------------------
                industry |
1. Land- und Forstwir..  |  -3.962689   1.553406    -2.55   0.011    -7.007309   -.9180681
2. Bergbau und Gewinn..  |   .0666913   1.781272     0.04   0.970    -3.424538    3.557921
   4. Energieversorgung  |   -2.51911   .4672614    -5.39   0.000    -3.434925   -1.603294
5. Wasserversorgung; ..  |   .1794327   .6868463     0.26   0.794    -1.166761    1.525627
      6. Baugewerbe/Bau  |  -.2927967   .4503032    -0.65   0.516    -1.175375    .5897814
7. Handel; Instandhal..  |   1.399864   .2529276     5.53   0.000     .9041353    1.895593
 8. Verkehr und Lagerei  |   .2709643   .4897853     0.55   0.580    -.6889973    1.230926
9. Gastgewerbe/Beherb..  |   1.326839   1.042053     1.27   0.203    -.7155468    3.369224
10. Information und K..  |   1.208214   .4785792     2.52   0.012     .2702159    2.146212
11. Erbringung von Fi..  |   2.204293    .521939     4.22   0.000     1.181311    3.227275
12. Grundstücks- und ..  |  -7.297083   .5403712   -13.50   0.000    -8.356191   -6.237975
13. Erbringung von fr..  |   .7591671   .3081107     2.46   0.014     .1552813    1.363053
14. Erbringung von so..  |   1.510774   .4651008     3.25   0.001     .5991934    2.422355
15. Öffentliche Verwa..  |   4.972156   2.020833     2.46   0.014     1.011395    8.932917
16. Erziehung und Unt..  |   -8.64213   1.377064    -6.28   0.000    -11.34113   -5.943135
17. Gesundheits- und ..  |  -12.68401   .4978721   -25.48   0.000    -13.65982    -11.7082
18. Kunst, Unterhaltu..  |   .0336924   1.119337     0.03   0.976    -2.160169    2.227554
19. Erbringung von so..  |  -1.156536   .7854209    -1.47   0.141    -2.695932    .3828609
                         |
                    size |
         2. kleine KapG  |    .107322   .3644027     0.29   0.768    -.6068941    .8215381
       3. mittlere KapG  |  -.4489496   .2944976    -1.52   0.127    -1.026154    .1282552
                         |
                    year |
                     15  |   .3697264   .1749918     2.11   0.035     .0267489     .712704
                     16  |  -.2524269   .1744287    -1.45   0.148    -.5943008    .0894471
                     17  |   .3338847   .1742833     1.92   0.055    -.0077044    .6754738
                     18  |   .9312448   .2926599     3.18   0.001     .3576419    1.504848
                         |
                   _cons |   27.55891   .2044604   134.79   0.000     27.15817    27.95964
-------------------------+----------------------------------------------------------------
                 sigma_u |    9.70098
                 sigma_e |   12.63551
                     rho |  .37085086   (fraction of variance due to u_i)
------------------------------------------------------------------------------------------

Here is the way I calculate the coefficient value of the industry "Bergbau und Gewinnung":

"Bergbau und Gewinnung.." true mean from the tabstat = 28.01
"_cons" from the regression output = 27.55891
"Bergbau und Gewinnung.." Coefficient from the regression output = 0.0666913

Thus, the coefficient value of "Bergbau und Gewinnung" (27.55891 + 0.0666913) would be 27.625 , although in reality it is 28.01.

Question: How can I set up the regression so that the coefficients are not biased ?

And as you can see from my R-squared value, it is very low. .. Is this typical for regressions with factor variables?


Many thanks.

[David Mangen]

I suspect that your interpretation of the coefficients is slightly flawed. The value that you present (27.625) is the predicted value for that industry when the size is equal to the omitted value and year equals the omitted value. But even if you were to drill down in the tabstats and get the averages for those subgroups I would not expect it to be exactly equal, simply because there is error in the equation and the predicted values are those that minimize the residuals.

Therefore, your assertion that the coefficients are biased is flawed.

The R-squared is not terribly large, but is about what I would expect given the limited explanatory variables.

[Can Deniz]

Hi David, thank you very much for your last advice.

I have futher question regarding the interpretation of the coefficients. I have tested my industry and size dummies for overall significance.

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)
----------------------------------------------------------------------------------------------------------------------------------------------------------------

. 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

I can see that the overall significance of a group is statistically signifikant. However the p-value (0.398) from the regression output shows me that there is no statistical significance for kleine_KapG (engl. = small firms), right?

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.