Panel data random/fixed effects

[Claudia Nijhof]

Hi, I am wiritng my bachelor thesis about the effect of NAFTA on income inequality (using the GINI) in 17 industries from 1990-2010 in the US. I have panel data. I ran a Hausman test whcih showed me i should do random effect. I would like to control for year specific random effects and industry specific national effects. However when i run this in stata, one of my industry coefficients is omitted and 3 of the years are omitted, stata says that they both omitted are due to collinearity.

this is the code i have used :
xtset Industry_code year
xtreg GINI c.NAFTA_dummy##c.ed_cat GDP Inflation employmentrate union_membership_rate i.Industry_code i.year, re robust

Could someone help me figure out why or how i can fix this.
Thank you in advnace!!

[Carlo Lazzaro]

Claudia:
welcome to this forum.
You can't if you do not change your regression specification.
In addition:
1) you cannot include your fixed as a predictor;
2) why prefixing the categorical variable -NAFTA_dummy- with -c.-?
3) why not sharing what you typed and what Stata gave you back (as per FAQ)? Thanks.

[Jeff Wooldridge]

Claudia: Please do take Carlo’s helpful advice. The industry fixed effects are already accounted for when you use FE. And you can’t include them with RE. I’m guessing GDP, inflation, employmentrate only vary by time, not industry. They are perfectly collinear with the year dummies. Stata drops the last collinear variables listed. Instead, you should drop the aggregate economic variables unless you interact them with variables that change with industry.

[Claudia Nijhof]

Thank you for your response, I am not sure i understand what you mean by, I cannot include my fixed as a predictor. As for your second point, would it be better if i only prefixed the ed_cat variable with -c.- (This is also a categorical variable that shows average educational attainment for each industry ranging from 1-5). I was not sure if i could upload images, I have added an attachment to what STATA shows me. In addition, you are correct that GDP and inflation dont vary by industry but employment rate is the employment rate per industry. Jeff Woolridge, when using RE, would you recommend that i drop my aggregate economic variables (GDP, inflation) but still keep the industry economic controls (employment rate, union memebrship)?

Thank you,
Claudia

[Carlo Lazzaro]

Claudia:
1) you went -re- and the between_Rsq=1. You have overiftted your regression and should go for a more parsimonious (that is, less predictors) specification;
2) as per -help fvvarlist-, categorical and continous predctors should be prefixed with -i.- and -c.-, respectively;
3) as per FAQ, screenshots are deprectaed on this forum; please use CODE delimiters (see the FAQ agan) instead. Thanks.

[Claudia Nijhof]

Good evening,
I am not sure if i have used the code delimitters correct, but is this better? I dont understand what your first point is.

. xtreg GINI i.NAFTA_dummy##i.ed_cat GDP Inflation employmentrate union_membership_rate i.Industry_code i.year, re robust
note: 15.Industry_code omitted because of collinearity.
note: 17.Industry_code omitted because of collinearity.
note: 2008.year omitted because of collinearity.
note: 2009.year omitted because of collinearity.
note: 2010.year omitted because of collinearity.

Random-effects GLS regression                   Number of obs     =        357
Group variable: Industry_c~e                    Number of groups  =         17

R-squared:                                      Obs per group:
     Within  = 0.5730                                         min =         21
     Between = 1.0000                                         avg =       21.0
     Overall = 0.9454                                         max =         21

                                                Wald chi2(16)     =          .
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =          .

                                  (Std. err. adjusted for 17 clusters in Industry_code)
---------------------------------------------------------------------------------------
                      |               Robust
                 GINI | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
----------------------+----------------------------------------------------------------
        1.NAFTA_dummy |  -.3139705   .0751851    -4.18   0.000    -.4613306   -.1666104
                      |
               ed_cat |
                   3  |  -.1979845   .0161172   -12.28   0.000    -.2295736   -.1663954
                   4  |  -.0812386   .0044113   -18.42   0.000    -.0898845   -.0725927
                      |
   NAFTA_dummy#ed_cat |
                 1 3  |   .0155751   .0091585     1.70   0.089    -.0023753    .0335254
                 1 4  |   .0520322   .0055078     9.45   0.000     .0412371    .0628273
                      |
                  GDP |   .0000473   .0000114     4.15   0.000     .0000249    .0000696
            Inflation |   -.007009   .0013343    -5.25   0.000    -.0096242   -.0043938
       employmentrate |  -.1262629   .0913699    -1.38   0.167    -.3053447    .0528189
union_membership_rate |   .0262066   .0079493     3.30   0.001     .0106262     .041787
                      |
        Industry_code |
                   2  |  -.1702832   .0009962  -170.93   0.000    -.1722357   -.1683306
                   3  |   -.110989   .0034156   -32.49   0.000    -.1176834   -.1042945
                   4  |  -.1046701   .0031195   -33.55   0.000    -.1107842    -.098556
                   5  |  -.1327124   .0057879   -22.93   0.000    -.1440564   -.1213684
                   6  |  -.1650394   .0034425   -47.94   0.000    -.1717865   -.1582923
                   7  |   .0262884   .0138716     1.90   0.058    -.0008994    .0534762
                   8  |  -.0324865   .0166321    -1.95   0.051    -.0650848    .0001117
                   9  |   .0852957   .0118918     7.17   0.000     .0619882    .1086032
                  10  |  -.0018851   .0110897    -0.17   0.865    -.0236205    .0198502
                  11  |   .1056735     .01204     8.78   0.000     .0820755    .1292715
                  12  |   .1384792   .0147776     9.37   0.000     .1095156    .1674427
                  13  |    .183775   .0028767    63.89   0.000     .1781369    .1894131
                  14  |   .1264933    .006412    19.73   0.000     .1139259    .1390606
                  15  |          0  (omitted)
                  16  |   .0267203   .0189949     1.41   0.160    -.0105091    .0639497
                  17  |          0  (omitted)
                      |
                 year |
                1991  |  -.0152509   .0028752    -5.30   0.000    -.0208862   -.0096157
                1992  |  -.0415306   .0063162    -6.58   0.000      -.05391   -.0291512
                1993  |  -.0536018   .0101474    -5.28   0.000    -.0734902   -.0337133
                1994  |   .2327217   .0616373     3.78   0.000     .1119149    .3535286
                1995  |   .2185078   .0582936     3.75   0.000     .1042544    .3327611
                1996  |    .224553   .0544952     4.12   0.000     .1177444    .3313617
                1997  |   .2019201   .0489647     4.12   0.000     .1059511    .2978891
                1998  |   .1719832   .0406253     4.23   0.000      .092359    .2516074
                1999  |   .1445081   .0342935     4.21   0.000     .0772941    .2117221
                2000  |   .1178479   .0281513     4.19   0.000     .0626724    .1730235
                2001  |   .1202633   .0277467     4.33   0.000     .0658806    .1746459
                2002  |   .1020844   .0220827     4.62   0.000     .0588031    .1453657
                2003  |   .0896017   .0209128     4.28   0.000     .0486133      .13059
                2004  |   .0606832   .0143416     4.23   0.000     .0325743    .0887922
                2005  |    .046964   .0115106     4.08   0.000     .0244036    .0695243
                2006  |   .0246485   .0065286     3.78   0.000     .0118527    .0374443
                2007  |   .0031926   .0027936     1.14   0.253    -.0022828    .0086681
                2008  |          0  (omitted)
                2009  |          0  (omitted)
                2010  |          0  (omitted)
                      |
                _cons |   .0873464   .1111908     0.79   0.432    -.1305836    .3052764
----------------------+----------------------------------------------------------------
              sigma_u |          0
              sigma_e |  .01641237
                  rho |          0   (fraction of variance due to u_i)
---------------------------------------------------------------------------------------

Kind regards,
Claudia

[Carlo Lazzaro]

Claudia:
1) CODE delimiters are perfect: thanks;
2) my point is that a between R_sq=1 (you should consider it when gong -re-) is a clear warning chime that your regression raises issues;
3) this is also highlighted by the -sigma_u-=0 that means no panel-wise effect and points you to pooled OLS.

[Claudia Nijhof]

great! However I don't quite understand why some of my coefficients are missing (for industries 17 and 15 and years 2008-2010).
Thank you,
Claudia

[Jeff Wooldridge]

Claudia: if you put in industry dummies then you’re doing fixed effects. And you should be in this context. Once you include those dummies there’s no role for random effects. And the standard errors can’t be trusted. That’s why you’re getting a weird R-squared and why variables are being dropped. Your data dimensions are small and so clustering standard errors is questionable. You could compare with Driscoll-Kraay using xtscc. You’d still be doing FE but getting different stnd errors.

[Claudia Nijhof]

Jeff Wooldridge, I tried to run xtscc however stata tells me the command is unrecognised, I have STATA 17, I am not sure if this changed anything. So, you would suggest that I run fe instead of re ?
Thank you

[Jeff Wooldridge]

It's a user-written command so you have to install:

ssc install xtscc

Your problem calls for fixed effects. By putting in industry dummies, you are doing fixed effects. You either include the dummies in OLS or use xtreg, fe -- with the latter preferred because it won't report incorrect standard errors on the industry dummies. Both xtreg, fe and xtscc, fe use fixed effects. They compute standard errors differently. You have to specify a lag with xtscc. With T = 21, no more than two, I would think. You will get the same point estimates with xtreg, fe and xtscc, fe if you do it properly.

You should drop the GDP, inflation, and employmentrate variables because they change only across t, I think. You cannot identify the coefficients on these when you put in a full set of year dummies. So the coefficients are meaningless. You get estimates because Stata is dropping the last three collinear variables -- the year dummies. If you put GDP, inflation, and employmentrate at the end, I believe Stata will drop them rather than the time dummies.

The most flexible thing to do is to include industry and time fixed effects. Doing so makes variables that only change over time redundant. You don't need these control variables, just like you don't need to control for variables that change only across industry.

You should show your new output from xtreg, fe and xtscc, fe.

[Claudia Nijhof]

In my data i use an interaction term between NAFTA and educational category, which differs per industry but not through time. GDP and inflation only differ through time and not by industry. union membership rates and educational attainment differ both between industry and time.

This is what STATA gives me if i run xtscc, fe (while keeping GDP, inflation, employment rate and union membership)

. xtscc GINI i.NAFTA_dummy##i.ed_cat i.Industry_code i.year GDP Inflation employmentrate union_membership_rate, fe lag(20)

Regression with Driscoll-Kraay standard errors   Number of obs     =       357
Method: Fixed-effects regression                 Number of groups  =        17
Group variable (i): Industry_code                F( 24,    20)     =    215.41
maximum lag: 20                                  Prob > F          =    0.0000
                                                 within R-squared  =    0.5730

---------------------------------------------------------------------------------------
                      |             Drisc/Kraay
                 GINI | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
----------------------+----------------------------------------------------------------
          NAFTA_dummy |
                   0  |          0  (empty)
                   1  |   .0259817   .0014118    18.40   0.000     .0230368    .0289267
                      |
               ed_cat |
                   2  |          0  (empty)
                   3  |          0  (omitted)
                   4  |          0  (omitted)
                      |
   NAFTA_dummy#ed_cat |
                 0 2  |          0  (empty)
                 0 3  |          0  (empty)
                 0 4  |          0  (empty)
                 1 2  |          0  (empty)
                 1 3  |   .0155751   .0028394     5.49   0.000     .0096522     .021498
                 1 4  |   .0520322    .008337     6.24   0.000     .0346415    .0694229
                      |
        Industry_code |
                   1  |          0  (empty)
                   2  |          0  (omitted)
                   3  |          0  (omitted)
                   4  |          0  (omitted)
                   5  |          0  (omitted)
                   6  |          0  (omitted)
                   7  |          0  (omitted)
                   8  |          0  (omitted)
                   9  |          0  (omitted)
                  10  |          0  (omitted)
                  11  |          0  (omitted)
                  12  |          0  (omitted)
                  13  |          0  (omitted)
                  14  |          0  (omitted)
                  15  |          0  (omitted)
                  16  |          0  (omitted)
                  17  |          0  (omitted)
                      |
                 year |
                1990  |          0  (empty)
                1991  |   .0259155   .0005052    51.30   0.000     .0248617    .0269692
                1992  |   .0501688   .0008813    56.92   0.000     .0483304    .0520073
                1993  |   .0469881    .000893    52.62   0.000     .0451253    .0488509
                1994  |   .0148554   .0002133    69.65   0.000     .0144105    .0153003
                1995  |          0  (omitted)
                1996  |   .0108128   .0001881    57.47   0.000     .0104204    .0112052
                1997  |   .0206166   .0000924   223.19   0.000     .0204239    .0208093
                1998  |   .0305462    .000299   102.17   0.000     .0299226    .0311698
                1999  |  -.0062718   .0001055   -59.47   0.000    -.0064918   -.0060518
                2000  |  -.0633944   .0007884   -80.41   0.000    -.0650389   -.0617499
                2001  |  -.0384837   .0005796   -66.39   0.000    -.0396928   -.0372746
                2002  |  -.0073203   .0001881   -38.92   0.000    -.0077127    -.006928
                2003  |  -.0354672   .0012382   -28.64   0.000      -.03805   -.0328843
                2004  |   -.066588   .0015509   -42.93   0.000    -.0698232   -.0633528
                2005  |  -.0942223   .0013594   -69.31   0.000     -.097058   -.0913866
                2006  |  -.1010411   .0014248   -70.92   0.000    -.1040132    -.098069
                2007  |  -.1021389   .0013374   -76.37   0.000    -.1049287   -.0993491
                2008  |  -.1400376   .0017151   -81.65   0.000    -.1436152   -.1364601
                2009  |          0  (omitted)
                2010  |   -.061578   .0009086   -67.77   0.000    -.0634733   -.0596827
                      |
                  GDP |   .0000258   1.96e-07   131.29   0.000     .0000254    .0000262
            Inflation |    .028589   .0004009    71.32   0.000     .0277529    .0294252
       employmentrate |  -.1262629   .0289652    -4.36   0.000    -.1866832   -.0658425
union_membership_rate |   .0262066   .0116508     2.25   0.036     .0019034    .0505097
                _cons |          0  (omitted)
---------------------------------------------------------------------------------------

This is what STATA shows me when i do xtscc and drop the control variables:

. xtscc GINI i.NAFTA_dummy##i.ed_cat i.Industry_code i.year, fe lag(20)

Regression with Driscoll-Kraay standard errors   Number of obs     =       357
Method: Fixed-effects regression                 Number of groups  =        17
Group variable (i): Industry_code                F( 22,    20)     =     25.17
maximum lag: 20                                  Prob > F          =    0.0000
                                                 within R-squared  =    0.5558

------------------------------------------------------------------------------------
                   |             Drisc/Kraay
              GINI | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------------+----------------------------------------------------------------
       NAFTA_dummy |
                0  |          0  (empty)
                1  |   .0307346   .0014173    21.69   0.000     .0277782     .033691
                   |
            ed_cat |
                2  |          0  (empty)
                3  |          0  (omitted)
                4  |          0  (omitted)
                   |
NAFTA_dummy#ed_cat |
              0 2  |          0  (empty)
              0 3  |          0  (empty)
              0 4  |          0  (empty)
              1 2  |          0  (empty)
              1 3  |   .0131869   .0018586     7.10   0.000     .0093099    .0170638
              1 4  |   .0516688   .0075091     6.88   0.000     .0360051    .0673324
                   |
     Industry_code |
                1  |          0  (empty)
                2  |          0  (omitted)
                3  |          0  (omitted)
                4  |          0  (omitted)
                5  |          0  (omitted)
                6  |          0  (omitted)
                7  |          0  (omitted)
                8  |          0  (omitted)
                9  |          0  (omitted)
               10  |          0  (omitted)
               11  |          0  (omitted)
               12  |          0  (omitted)
               13  |          0  (omitted)
               14  |          0  (omitted)
               15  |          0  (omitted)
               16  |          0  (omitted)
               17  |          0  (omitted)
                   |
              year |
             1990  |          0  (empty)
             1991  |  -.0075282   4.71e-16 -1.6e+13   0.000    -.0075282   -.0075282
             1992  |  -.0087243   1.67e-16 -5.2e+13   0.000    -.0087243   -.0087243
             1993  |  -.0066486   1.89e-15 -3.5e+12   0.000    -.0066486   -.0066486
             1994  |  -.0412917   2.09e-15 -2.0e+13   0.000    -.0412917   -.0412917
             1995  |    -.04297   2.33e-15 -1.8e+13   0.000      -.04297     -.04297
             1996  |  -.0175846   1.95e-15 -9.0e+12   0.000    -.0175846   -.0175846
             1997  |  -.0112601   2.92e-15 -3.8e+12   0.000    -.0112601   -.0112601
             1998  |  -.0090653   2.18e-15 -4.2e+12   0.000    -.0090653   -.0090653
             1999  |  -.0117613   3.58e-15 -3.3e+12   0.000    -.0117613   -.0117613
             2000  |  -.0209324   1.91e-15 -1.1e+13   0.000    -.0209324   -.0209324
             2001  |  -.0082572   1.44e-15 -5.7e+12   0.000    -.0082572   -.0082572
             2002  |  -.0064432   1.83e-15 -3.5e+12   0.000    -.0064432   -.0064432
             2003  |   -.006215   1.82e-15 -3.4e+12   0.000     -.006215    -.006215
             2004  |  -.0110298   1.94e-15 -5.7e+12   0.000    -.0110298   -.0110298
             2005  |  -.0029857   1.78e-15 -1.7e+12   0.000    -.0029857   -.0029857
             2006  |  -.0032011   1.67e-15 -1.9e+12   0.000    -.0032011   -.0032011
             2007  |  -.0064752   1.64e-15 -3.9e+12   0.000    -.0064752   -.0064752
             2008  |  -.0156316   1.54e-15 -1.0e+13   0.000    -.0156316   -.0156316
             2009  |  -.0067819   1.50e-15 -4.5e+12   0.000    -.0067819   -.0067819
             2010  |          0  (omitted)
                   |
             _cons |   .4125109   1.90e-16  2.2e+15   0.000     .4125109    .4125109
------------------------------------------------------------------------------------

Finally, this is the output when using xtreg,fe without the controls:

. xtreg GINI i.NAFTA_dummy##i.ed_cat i.Industry_code i.year, fe 
note: 3.ed_cat omitted because of collinearity.
note: 4.ed_cat omitted because of collinearity.
note: 2.Industry_code omitted because of collinearity.
note: 3.Industry_code omitted because of collinearity.
note: 4.Industry_code omitted because of collinearity.
note: 5.Industry_code omitted because of collinearity.
note: 6.Industry_code omitted because of collinearity.
note: 7.Industry_code omitted because of collinearity.
note: 8.Industry_code omitted because of collinearity.
note: 9.Industry_code omitted because of collinearity.
note: 10.Industry_code omitted because of collinearity.
note: 11.Industry_code omitted because of collinearity.
note: 12.Industry_code omitted because of collinearity.
note: 13.Industry_code omitted because of collinearity.
note: 14.Industry_code omitted because of collinearity.
note: 15.Industry_code omitted because of collinearity.
note: 16.Industry_code omitted because of collinearity.
note: 17.Industry_code omitted because of collinearity.
note: 2010.year omitted because of collinearity.

Fixed-effects (within) regression               Number of obs     =        357
Group variable: Industry_c~e                    Number of groups  =         17

R-squared:                                      Obs per group:
     Within  = 0.5558                                         min =         21
     Between = 0.0277                                         avg =       21.0
     Overall = 0.0952                                         max =         21

                                                F(22,318)         =      18.09
corr(u_i, Xb) = 0.0032                          Prob > F          =     0.0000

------------------------------------------------------------------------------------
              GINI | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------------+----------------------------------------------------------------
     1.NAFTA_dummy |   .0307346   .0063228     4.86   0.000     .0182947    .0431745
                   |
            ed_cat |
                3  |          0  (omitted)
                4  |          0  (omitted)
                   |
NAFTA_dummy#ed_cat |
              1 3  |   .0131869   .0046729     2.82   0.005     .0039932    .0223805
              1 4  |   .0516688   .0099126     5.21   0.000     .0321662    .0711714
                   |
     Industry_code |
                2  |          0  (omitted)
                3  |          0  (omitted)
                4  |          0  (omitted)
                5  |          0  (omitted)
                6  |          0  (omitted)
                7  |          0  (omitted)
                8  |          0  (omitted)
                9  |          0  (omitted)
               10  |          0  (omitted)
               11  |          0  (omitted)
               12  |          0  (omitted)
               13  |          0  (omitted)
               14  |          0  (omitted)
               15  |          0  (omitted)
               16  |          0  (omitted)
               17  |          0  (omitted)
                   |
              year |
             1991  |  -.0075282   .0057231    -1.32   0.189     -.018788    .0037317
             1992  |  -.0087243   .0057231    -1.52   0.128    -.0199842    .0025355
             1993  |  -.0066486   .0057231    -1.16   0.246    -.0179084    .0046113
             1994  |  -.0412917   .0057231    -7.21   0.000    -.0525516   -.0300319
             1995  |    -.04297   .0057231    -7.51   0.000    -.0542299   -.0317102
             1996  |  -.0175846   .0057231    -3.07   0.002    -.0288444   -.0063247
             1997  |  -.0112601   .0057231    -1.97   0.050    -.0225199   -2.36e-07
             1998  |  -.0090653   .0057231    -1.58   0.114    -.0203251    .0021945
             1999  |  -.0117613   .0057231    -2.06   0.041    -.0230211   -.0005014
             2000  |  -.0209324   .0057231    -3.66   0.000    -.0321922   -.0096725
             2001  |  -.0082572   .0057231    -1.44   0.150    -.0195171    .0030026
             2002  |  -.0064432   .0057231    -1.13   0.261     -.017703    .0048167
             2003  |   -.006215   .0057231    -1.09   0.278    -.0174749    .0050448
             2004  |  -.0110298   .0057231    -1.93   0.055    -.0222896    .0002301
             2005  |  -.0029857   .0057231    -0.52   0.602    -.0142455    .0082741
             2006  |  -.0032011   .0057231    -0.56   0.576     -.014461    .0080587
             2007  |  -.0064752   .0057231    -1.13   0.259    -.0177351    .0047846
             2008  |  -.0156316   .0057231    -2.73   0.007    -.0268914   -.0043718
             2009  |  -.0067819   .0057231    -1.19   0.237    -.0180418    .0044779
             2010  |          0  (omitted)
                   |
             _cons |   .4125109   .0040468   101.93   0.000      .404549    .4204728
-------------------+----------------------------------------------------------------
           sigma_u |   .0627177
           sigma_e |  .01668543
               rho |  .93390094   (fraction of variance due to u_i)
------------------------------------------------------------------------------------
F test that all u_i=0: F(16, 318) = 284.21                   Prob > F = 0.0000

.

Thank you

[Jeff Wooldridge]

Several problems here. When you do FE, you don't also include the dummy variables for industry. Including them IS fixed effects. Those should be dropped. Second, you cannot use a lag of 20 in xtscc when T = 21. I said at most two. Now it appears that ed_cat does not change over time, so those also drop out of FE. But you can interact NAFTA with ed_cat still to see if there are differential effects.

xtreg GINI c.NAFTA_dummy c.NAFTA_dummy#i.ed_cat i.year, fe vce(robust)
xtscc GINI c.NAFTA_dummy c.NAFTA_dummy#i.ed_ca i.year, fe lag(2)

[Jeff Wooldridge]

And potentially an even bigger problem. I wonder if your NAFTA_dummy changes only across time. I was assuming you had selecting some control industries that would not be affected by NAFTA and treated industries that would be affected. But the fact that the 2010 dummy is dropping out makes me think NAFTA_dummy goes from zero to one for all industries. Is that true?

[Claudia Nijhof]

Indeed, this is true that NAFTA goes from 0 to 1 for all industries (as all industries experienced NAFTA at the same time). My only concern now is that I cannot see how NAFTA affected income inequality within different industries. I cannot see the fixed effect of each industry, like I can for the years. Would it be possible to also incorporate this ? Just to make sure i have the correct understanding of my interaction term coefficients, they are both relative to when educational level is equal to 2 (so 2 is the reference category). In addition, just to confirm, ed_cat is the same over time.
Thank you very much for your help!