How to include industry fixed effects rather than firm fixed effects

[Roy Steinvoort]

Hi all,

I have this panel dataset that spans over the period 2007-2013 with 1580 unique US firms that all fit to a particular industry (based on standard industrial classification (siccode)).

The panel data is set at xtset gvkey fyear (firms and fiscal year).

Now my question is how to include industry fixed effects rather than firm fixed effects in my model? I cannot set the panel data like xset siccode fyear (industries and fiscal years) because there are repeated time values within the panel since all firms are unique but the siccodes/industry classifications are obviously not unique since different firms can belong to the same industry over time (industries are like a group).

I would like to include these effects since CEO compensation or the use of compensation consultants may be industry specific and vary across industries.

My question is how to code this properly in stata with xtreg or areg commands.

Thanks in advance.

Best,

Roy

[Roy Steinvoort]

Hi all,

I have now tried the following:

 xtreg  compensationconsultantuse  CEO_PaySlice_win LnMarketcap BtM_win ROA_win ChangeInROA LagAnnualizedMonthl
> yReturn AgeCEO TenureCEO NewCEO Median_CompUse  CEOisChair Boardsize PercOutside_win PercBusy_win PercOld_win
> PercApptdAfterCEO_win i.fyear, fe cluster(gvkey)
note: Median_CompUse omitted because of collinearity

Fixed-effects (within) regression               Number of obs      =      9198
Group variable: gvkey                           Number of groups   =      1564

R-sq:  within  = 0.0369                         Obs per group: min =         1
       between = 0.0018                                        avg =       5.9
       overall = 0.0004                                        max =         7

                                                F(21,1563)         =      7.31
corr(u_i, Xb)  = -0.1995                        Prob > F           =    0.0000

                                             (Std. Err. adjusted for 1564 clusters in gvkey)
--------------------------------------------------------------------------------------------
                           |               Robust
 compensationconsultantuse |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------------------+----------------------------------------------------------------
          CEO_PaySlice_win |   .0261826   .0389252     0.67   0.501    -.0501685    .1025336
               LnMarketcap |   .0102649   .0032768     3.13   0.002     .0038375    .0166924
                   BtM_win |   .0062819   .0024811     2.53   0.011     .0014152    .0111487
                   ROA_win |   .0734868   .1026767     0.72   0.474    -.1279119    .2748854
               ChangeInROA |   .0530229   .0524244     1.01   0.312    -.0498066    .1558524
LagAnnualizedMonthlyReturn |   .0072145   .0065967     1.09   0.274    -.0057248    .0201537
                    AgeCEO |  -.0007173   .0009095    -0.79   0.430    -.0025013    .0010666
                 TenureCEO |   .0100984   .0065178     1.55   0.121    -.0026861    .0228829
                    NewCEO |   .0006515    .011672     0.06   0.955     -.022243    .0235461
            Median_CompUse |          0  (omitted)
                CEOisChair |   .0218589    .011212     1.95   0.051    -.0001332    .0438511
                 Boardsize |   .0010292   .0030932     0.33   0.739    -.0050382    .0070965
           PercOutside_win |  -.0057116   .0624545    -0.09   0.927    -.1282151    .1167919
              PercBusy_win |   .0355216   .0371651     0.96   0.339    -.0373771    .1084202
               PercOld_win |  -.0388758    .037629    -1.03   0.302    -.1126845    .0349328
     PercApptdAfterCEO_win |   -.049305   .0559676    -0.88   0.378    -.1590844    .0604744
                           |
                     fyear |
                     2008  |   .0277607    .010421     2.66   0.008       .00732    .0482013
                     2009  |   .0227927   .0135415     1.68   0.093    -.0037687     .049354
                     2010  |   .0509198   .0156706     3.25   0.001     .0201822    .0816574
                     2011  |   .0686212   .0195921     3.50   0.000     .0301917    .1070508
                     2012  |   .0848269   .0248539     3.41   0.001     .0360763    .1335774
                     2013  |   .0910781   .0297387     3.06   0.002     .0327462      .14941
                           |
                     _cons |   .5983235   .0837966     7.14   0.000     .4339578    .7626892
---------------------------+----------------------------------------------------------------
                   sigma_u |  .36562086
                   sigma_e |   .2361786
                       rho |  .70558091   (fraction of variance due to u_i)
--------------------------------------------------------------------------------------------

Above is my regular fixed effects model (based on firms) and below I have tried to convert this to the industry fixed effects model (based on siccodes).

 xtreg  compensationconsultantuse  CEO_PaySlice_win LnMarketcap BtM_win ROA_win ChangeInROA LagAnnualizedMonthl
> yReturn AgeCEO TenureCEO NewCEO Median_CompUse  CEOisChair Boardsize PercOutside_win PercBusy_win PercOld_win
> PercApptdAfterCEO_win i.fyear, i(SIC) fe cluster(SIC)
warning: existing panel variable is not SIC

Fixed-effects (within) regression               Number of obs      =      9198
Group variable: SIC                             Number of groups   =        59

R-sq:  within  = 0.1634                         Obs per group: min =        18
       between = 0.2328                                        avg =     155.9
       overall = 0.1611                                        max =       845

                                                F(22,58)           =    101.74
corr(u_i, Xb)  = -0.0961                        Prob > F           =    0.0000

                                                 (Std. Err. adjusted for 59 clusters in SIC)
--------------------------------------------------------------------------------------------
                           |               Robust
 compensationconsultantuse |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------------------+----------------------------------------------------------------
          CEO_PaySlice_win |   .2602651   .0639909     4.07   0.000     .1321734    .3883569
               LnMarketcap |   .0150352   .0034832     4.32   0.000     .0080628    .0220076
                   BtM_win |   .0100159   .0033712     2.97   0.004     .0032677    .0167642
                   ROA_win |  -.1906018   .1080907    -1.76   0.083    -.4069689    .0257653
               ChangeInROA |   .0273446   .0631149     0.43   0.666    -.0989936    .1536828
LagAnnualizedMonthlyReturn |   .0078107   .0099189     0.79   0.434    -.0120442    .0276656
                    AgeCEO |  -.0008634   .0010573    -0.82   0.417    -.0029799     .001253
                 TenureCEO |  -.0045949   .0020292    -2.26   0.027    -.0086569    -.000533
                    NewCEO |  -.0138393   .0104336    -1.33   0.190    -.0347244    .0070458
            Median_CompUse |   .4226366   .0470164     8.99   0.000     .3285231    .5167502
                CEOisChair |   -.007633   .0133136    -0.57   0.569    -.0342829     .019017
                 Boardsize |   .0208741   .0039643     5.27   0.000     .0129388    .0288095
           PercOutside_win |   .5011666   .0891698     5.62   0.000     .3226738    .6796594
              PercBusy_win |   .1615346   .0437149     3.70   0.000     .0740298    .2490394
               PercOld_win |  -.2391962   .0486825    -4.91   0.000    -.3366448   -.1417476
     PercApptdAfterCEO_win |    .031224   .0450014     0.69   0.491    -.0588562    .1213041
                           |
                     fyear |
                     2008  |   .0259233    .010687     2.43   0.018      .004531    .0473156
                     2009  |   .0318246   .0111705     2.85   0.006     .0094645    .0541848
                     2010  |   .0554147   .0161617     3.43   0.001     .0230635     .087766
                     2011  |   .0753052   .0165004     4.56   0.000     .0422762    .1083343
                     2012  |   .1067023   .0161906     6.59   0.000     .0742934    .1391112
                     2013  |   .1166929   .0151909     7.68   0.000     .0862851    .1471008
                           |
                     _cons |  -.3965265   .0831389    -4.77   0.000    -.5629471    -.230106
---------------------------+----------------------------------------------------------------
                   sigma_u |  .08783366
                   sigma_e |  .36995323
                       rho |  .05335969   (fraction of variance due to u_i)
--------------------------------------------------------------------------------------------

Could anyone tell me whether I did it correct or not?

And could anyone also indicate how I run a non-linear "pooled" regression with group fixed effects?

Thanks in advance.

Best,

Roy

[Clyde Schechter]

Well, you "did it correctly" in the sense that this is what you would get using industry rather than firm-level fixed-effects. By the way, you could also have done this by just -xtset SIC-. You don't have to specify a time variable when you run -xtset-. If you do specify a time variable, then panel and time must uniquely identify observations. But you can omit the time variable from -xtset- and still run most of the -xt- commands--you only lose the ability to run those that rely on lags and leads, or do autoregressive estimation. -xtreg- works fine without a time variable declared.

That said, you should reflect seriously on whether this is a sensible way to model your data. When you had firm as the fixed effect, you were automatically adjusting your results for any unobserved effects of industry, because industry did not vary over time within firm. So the omitted variable bias that usually motivates the use of fixed-effects estimation was taken care of. But in your current model, there may be unobserved attributes of firms that influence your results here--but they will not be captured by the SIC fixed effects unless those attributes are constant throughout the industry. So you have gone from a model that is pretty robust to one that is a bit wobbly.

If you are specifically interested in capturing both firm and industry-level effects in the same model, you need to go to the multi-level models, such as -mixed-. Be aware, however, that these use random effects estimators, which are often frowned upon in economics and finance because these estimators may not be consistent when their assumptions are not fully met.

[Roy Steinvoort]

Thanks for your reply Clyde.

I will think about whether I use firm or industry fixed effects. I tend towards firm fixed effects but in two other key papers I use they implemented industry fixed effects.

Could you help me with how I run a non-linear "pooled" regression with group fixed effects? The models above are Linear probability models since "compensationconsultantuse" is a 0,1 dummy variable. Now I also want to run a pooled regression with group fixed effects on this dependent variable "compensationconsultantuse".

Thanks in advance.

Best,

Roy

[Clyde Schechter]

It is not clear to me what you mean by a pooled regression with group fixed effects. Can you be more explicit?

[Roy Steinvoort]

Clyde,

I am sorry if I was not clear.

I want to run a regression with industry fixed effects rather than firm fixed effects (hence group fixed effects). It should have the form of a non-linear 'pooled' regression and rather than a linear probability model (as is presented below). But I don't know whether there is a difference between both if my dependent variable is binary (0,1).

How can I perform a pooled regression that is non linear?

Thanks in advance,

Roy

. xtreg  compensationconsultantuse  CEO_PaySlice_win LnMarketcap BtM_win ROA_win ChangeInROA LagAnnualizedMonthl
> yReturn AgeCEO TenureCEO NewCEO Median_CompUse  CEOisChair Boardsize PercOutside_win PercBusy_win PercOld_win
> PercApptdAfterCEO_win i.fyear, fe cluster(gvkey)
note: Median_CompUse omitted because of collinearity

Fixed-effects (within) regression               Number of obs      =      9198
Group variable: gvkey                           Number of groups   =      1564

R-sq:  within  = 0.0369                         Obs per group: min =         1
       between = 0.0018                                        avg =       5.9
       overall = 0.0004                                        max =         7

                                                F(21,1563)         =      7.31
corr(u_i, Xb)  = -0.1995                        Prob > F           =    0.0000

                                             (Std. Err. adjusted for 1564 clusters in gvkey)
--------------------------------------------------------------------------------------------
                           |               Robust
 compensationconsultantuse |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------------------+----------------------------------------------------------------
          CEO_PaySlice_win |   .0261826   .0389252     0.67   0.501    -.0501685    .1025336
               LnMarketcap |   .0102649   .0032768     3.13   0.002     .0038375    .0166924
                   BtM_win |   .0062819   .0024811     2.53   0.011     .0014152    .0111487
                   ROA_win |   .0734868   .1026767     0.72   0.474    -.1279119    .2748854
               ChangeInROA |   .0530229   .0524244     1.01   0.312    -.0498066    .1558524
LagAnnualizedMonthlyReturn |   .0072145   .0065967     1.09   0.274    -.0057248    .0201537
                    AgeCEO |  -.0007173   .0009095    -0.79   0.430    -.0025013    .0010666
                 TenureCEO |   .0100984   .0065178     1.55   0.121    -.0026861    .0228829
                    NewCEO |   .0006515    .011672     0.06   0.955     -.022243    .0235461
            Median_CompUse |          0  (omitted)
                CEOisChair |   .0218589    .011212     1.95   0.051    -.0001332    .0438511
                 Boardsize |   .0010292   .0030932     0.33   0.739    -.0050382    .0070965
           PercOutside_win |  -.0057116   .0624545    -0.09   0.927    -.1282151    .1167919
              PercBusy_win |   .0355216   .0371651     0.96   0.339    -.0373771    .1084202
               PercOld_win |  -.0388758    .037629    -1.03   0.302    -.1126845    .0349328
     PercApptdAfterCEO_win |   -.049305   .0559676    -0.88   0.378    -.1590844    .0604744
                           |
                     fyear |
                     2008  |   .0277607    .010421     2.66   0.008       .00732    .0482013
                     2009  |   .0227927   .0135415     1.68   0.093    -.0037687     .049354
                     2010  |   .0509198   .0156706     3.25   0.001     .0201822    .0816574
                     2011  |   .0686212   .0195921     3.50   0.000     .0301917    .1070508
                     2012  |   .0848269   .0248539     3.41   0.001     .0360763    .1335774
                     2013  |   .0910781   .0297387     3.06   0.002     .0327462      .14941
                           |
                     _cons |   .5983235   .0837966     7.14   0.000     .4339578    .7626892
---------------------------+----------------------------------------------------------------
                   sigma_u |  .36562086
                   sigma_e |   .2361786
                       rho |  .70558091   (fraction of variance due to u_i)
--------------------------------------------------------------------------------------------

[Ariel Karlinsky]

have a look at XT in general (not just xtreg). to be more specific, estimating probability on panel data is mostly done with logit or probit - so have a look at:
xtprobit
xtlogit