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  • #1

    Dropped year-dummies in panel regression

    Dear Statalisters,


    I have some issues understanding year-dummies being dropped in a fixed effects panel regression. I have about 280 entities with observations over 23 years, testing relation between firm stability and competition whereas z is the insolvency ratio, HHI the competition measure and the rest control variables. I get that the first year is omitted to avoid the dummy-trap. What I do not understand however, is why STATA instead drops the last four years. There are no missing variables, correlation between the regressors are low and a low VIF. Would greatly appreciate if you could help me on the way. Below are an example of the data set, regression commands and correlation diagnostic results.

    Code:
    * Example generated by -dataex-. To install: ssc install dataex
clear
input float z double(HHI INFLATION GDPG) byte BANKOWN float(TBT CTI lnta) byte(yr3 yr4)
 40.49671 963.8486627607208 .023 .026000000000000002 0 0 .17307693  6.569481 0 1
   50.642 963.8486627607208 .023 .026000000000000002 0 0 .16666667  6.651572 0 1
25.286806 963.8486627607208 .023 .026000000000000002 0 0 .20143884  7.620705 0 1
 58.28053 963.8486627607208 .023 .026000000000000002 0 0 .12676056  6.929517 0 1
        . 963.8486627607208 .023 .026000000000000002 0 0  .1847826  7.114769 0 1
 66.26539 963.8486627607208 .023 .026000000000000002 0 0 .12782194  8.328185 0 1
 32.80132 963.8486627607208 .023 .026000000000000002 0 0 .12658228  7.046647 0 1
  271.304 963.8486627607208 .023 .026000000000000002 0 0        .2 4.1108737 0 1
 26.37916 963.8486627607208 .023 .026000000000000002 0 0     .1875  5.342334 0 1
 72.42193 963.8486627607208 .023 .026000000000000002 0 0 .20754717  6.603944 0 1
 114.3582 963.8486627607208 .023 .026000000000000002 0 0   .171875   6.76273 0 1
230.14607 963.8486627607208 .023 .026000000000000002 0 0 .12795275 8.8454895 0 1
 63.12717 963.8486627607208 .023 .026000000000000002 0 0 .18333334  6.647688 0 1
  45.9433 963.8486627607208 .023 .026000000000000002 0 0       .24  6.001415 0 1
 44.64632 963.8486627607208 .023 .026000000000000002 0 0 .10756395   9.80593 0 1
 .9109095 963.8486627607208 .023 .026000000000000002 0 0  .3236181 8.7088375 0 1
 32.15652 963.8486627607208 .023 .026000000000000002 0 0 .17307693  6.507277 0 1
 21.87874 963.8486627607208 .023 .026000000000000002 0 0 .11764706  7.109879 0 1
12.687154 963.8486627607208 .023 .026000000000000002 0 1 .13198802 12.400545 0 1
 108.2294 963.8486627607208 .023 .026000000000000002 0 0 .13636364  5.888878 0 1
 49.57047 963.8486627607208 .023 .026000000000000002 0 0 .17857143  5.950643 0 1
 21.22993 963.8486627607208 .023 .026000000000000002 0 0  .2857143  5.365976 0 1
30.459864 963.8486627607208 .023 .026000000000000002 0 0  .2016129  7.431892 0 1
 43.08752 963.8486627607208 .023 .026000000000000002 0 0 .16949153  6.694562 0 1
 41.08426 963.8486627607208 .023 .026000000000000002 0 0 .22727273  5.583496 0 1
 54.58025 963.8486627607208 .023 .026000000000000002 0 0 .11438064 10.279215 0 1
24.860386 963.8486627607208 .023 .026000000000000002 0 0 .14285715  6.582025 0 1
 61.71256 963.8486627607208 .023 .026000000000000002 0 0 .15277778  6.884487 0 1
 46.07439 963.8486627607208 .023 .026000000000000002 0 0        .2  5.241747 0 1
 24.70525 963.8486627607208 .023 .026000000000000002 0 0 .14782609  7.357556 0 1
end


    Code:
    xtreg z HHI INFLATION GDPG BANKOWN TBT CTI lnta yr3 yr4 yr5 yr6 yr7 yr8 yr9 yr10 yr11 yr12 yr13 yr14 yr15 yr16 yr17 yr18 yr19 yr20 yr21 yr22 yr23, fe vce(robust)
    (Get the same results by using i.YEAR, but using dummies instead to run diagnostics).

    Code:
    note: yr20 omitted because of collinearity
note: yr21 omitted because of collinearity
note: yr22 omitted because of collinearity
note: yr23 omitted because of collinearity

Fixed-effects (within) regression               Number of obs     =      2,479
Group variable: banknumber                      Number of groups  =        183

R-sq:                                           Obs per group:
     within  = 0.2137                                         min =          1
     between = 0.0473                                         avg =       13.5
     overall = 0.1404                                         max =         21

                                                F(22,182)         =          .
corr(u_i, Xb)  = -0.2449                        Prob > F          =          .

                           (Std. Err. adjusted for 183 clusters in banknumber)
------------------------------------------------------------------------------
             |               Robust
           z |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         HHI |  -.0303108   .0210892    -1.44   0.152    -.0719216       .0113
   INFLATION |  -76.55149   2956.977    -0.03   0.979    -5910.916    5757.813
        GDPG |   618.2998   6259.327     0.10   0.921    -11731.88    12968.48
     BANKOWN |   -51.5391   1.834326   -28.10   0.000    -55.15838   -47.91982
         TBT |   6.363655   7.903644     0.81   0.422    -9.230899    21.95821
         CTI |    .088925   .0078083    11.39   0.000     .0735187    .1043314
        lnta |  -2.797636   3.258536    -0.86   0.392    -9.227001    3.631729
         yr3 |  -3.499378   240.9092    -0.01   0.988    -478.8335    471.8348
         yr4 |  -12.13843   67.57561    -0.18   0.858    -145.4708    121.1939
         yr5 |  -9.316379   29.27241    -0.32   0.751     -67.0733    48.44054
         yr6 |   -25.4756   124.5805    -0.20   0.838    -271.2834    220.3322
         yr7 |  -26.15843   51.65594    -0.51   0.613      -128.08    75.76308
         yr8 |  -31.83699    42.2322    -0.75   0.452    -115.1647    51.49069
         yr9 |  -36.40373   38.43623    -0.95   0.345    -112.2416    39.43419
        yr10 |  -36.69725   83.37978    -0.44   0.660    -201.2126    127.8181
        yr11 |  -30.16158   35.28397    -0.85   0.394    -99.77982    39.45666
        yr12 |  -17.19835   39.88307    -0.43   0.667    -95.89101    61.49431
        yr13 |  -23.97309   31.51084    -0.76   0.448    -86.14663    38.20045
        yr14 |  -7.781279   36.09541    -0.22   0.830    -79.00055    63.43799
        yr15 |   18.64135   222.2024     0.08   0.933    -419.7826    457.0653
        yr16 |   5.363992   64.73919     0.08   0.934    -122.3719    133.0999
        yr17 |   6.543575   81.76287     0.08   0.936    -154.7814    167.8686
        yr18 |  -8.039695   3.074036    -2.62   0.010    -14.10503   -1.974364
        yr19 |   1.061594   62.29068     0.02   0.986    -121.8431    123.9663
        yr20 |          0  (omitted)
        yr21 |          0  (omitted)
        yr22 |          0  (omitted)
        yr23 |          0  (omitted)
       _cons |   108.1678   152.8147     0.71   0.480    -193.3485     409.684
-------------+----------------------------------------------------------------
     sigma_u |  32.204441
     sigma_e |  29.860322
         rho |  .53771512   (fraction of variance due to u_i)
------------------------------------------------------------------------------



    Code:
                 |        z      HHI INFLAT~N     GDPG  BANKOWN      TBT      CTI     lnta      yr3
-------------+---------------------------------------------------------------------------------
           z |   1.0000
         HHI |  -0.1890   1.0000
   INFLATION |   0.0934  -0.2442   1.0000
        GDPG |   0.1708  -0.3147  -0.2625   1.0000
     BANKOWN |  -0.1123   0.0414   0.0073  -0.0692   1.0000
         TBT |  -0.0454  -0.0204   0.0008   0.0119   0.1811   1.0000
         CTI |   0.0049   0.0210  -0.0013  -0.0067  -0.0022   0.1702   1.0000
        lnta |  -0.1420   0.3226  -0.0323  -0.1947   0.3210   0.4046   0.0824   1.0000
         yr3 |   0.2928  -0.3255   0.1032   0.5400  -0.0346   0.0207  -0.0006  -0.1550   1.0000
         yr4 |   0.1414  -0.3457   0.0521   0.1040  -0.0360   0.0189  -0.0021  -0.1240  -0.0540
         yr5 |   0.0911  -0.2151   0.0802   0.0041  -0.0178   0.0178  -0.0036  -0.1103  -0.0549
         yr6 |   0.0422  -0.2509   0.2711   0.2072  -0.0178   0.0025  -0.0036  -0.1015  -0.0549
         yr7 |   0.0104  -0.2862   0.2182   0.0212  -0.0183   0.0021  -0.0044  -0.0815  -0.0553
         yr8 |  -0.0448  -0.2938  -0.2223  -0.0986  -0.0092  -0.0133  -0.0041  -0.0518  -0.0555
         yr9 |  -0.0985  -0.2713   0.1075  -0.1820   0.0108  -0.0129  -0.0021  -0.0436  -0.0549
        yr10 |  -0.0831   0.0972  -0.4541   0.3344  -0.0161  -0.0118  -0.0001  -0.0378  -0.0535
        yr11 |  -0.0782  -0.0104  -0.1335   0.1023   0.0140   0.0043   0.0000  -0.0071  -0.0531
        yr12 |  -0.0475   0.0844   0.0512   0.0695   0.0042   0.0043  -0.0015   0.0163  -0.0531
        yr13 |  -0.0495   0.0542  -0.3601   0.1628   0.0169   0.0060  -0.0075   0.0263  -0.0515
        yr14 |  -0.0848   0.1080   0.4397  -0.2377   0.0655   0.0052  -0.0083   0.0626  -0.0522
        yr15 |  -0.0032   0.1443   0.0244  -0.5920   0.0356   0.0052  -0.0074   0.0621  -0.0522
        yr16 |   0.0144   0.0929   0.0709  -0.1909   0.0123   0.0094  -0.0067   0.0618  -0.0485
        yr17 |   0.0015   0.1906  -0.2009  -0.1509   0.0506   0.0075  -0.0070   0.0840  -0.0501
        yr18 |  -0.0555   0.3105  -0.3540   0.1057  -0.0073   0.0108  -0.0067   0.0488  -0.0473
        yr19 |  -0.0565   0.2909  -0.0014  -0.1401  -0.0172  -0.0061   0.0966   0.0632  -0.0466
        yr20 |  -0.0344   0.2984  -0.0014   0.0035  -0.0169  -0.0059  -0.0064   0.0729  -0.0463
        yr21 |   0.0103   0.2243  -0.0014   0.0035  -0.0073  -0.0243  -0.0060   0.0874  -0.0473
        yr22 |  -0.0117   0.1872   0.3512  -0.1132  -0.0073  -0.0243  -0.0059   0.0983  -0.0473
        yr23 |   0.0318   0.1459  -0.0677   0.0033  -0.0031  -0.0229  -0.0057   0.1096  -0.0445

             |      yr4      yr5      yr6      yr7      yr8      yr9     yr10     yr11     yr12
-------------+---------------------------------------------------------------------------------
         yr4 |   1.0000
         yr5 |  -0.0562   1.0000
         yr6 |  -0.0562  -0.0571   1.0000
         yr7 |  -0.0567  -0.0576  -0.0576   1.0000
         yr8 |  -0.0569  -0.0578  -0.0578  -0.0583   1.0000
         yr9 |  -0.0562  -0.0571  -0.0571  -0.0576  -0.0578   1.0000
        yr10 |  -0.0549  -0.0558  -0.0558  -0.0562  -0.0564  -0.0558   1.0000
        yr11 |  -0.0544  -0.0553  -0.0553  -0.0558  -0.0560  -0.0553  -0.0540   1.0000
        yr12 |  -0.0544  -0.0553  -0.0553  -0.0558  -0.0560  -0.0553  -0.0540  -0.0535   1.0000
        yr13 |  -0.0528  -0.0537  -0.0537  -0.0541  -0.0543  -0.0537  -0.0524  -0.0520  -0.0520
        yr14 |  -0.0535  -0.0544  -0.0544  -0.0548  -0.0550  -0.0544  -0.0531  -0.0526  -0.0526
        yr15 |  -0.0535  -0.0544  -0.0544  -0.0548  -0.0550  -0.0544  -0.0531  -0.0526  -0.0526
        yr16 |  -0.0497  -0.0505  -0.0505  -0.0509  -0.0511  -0.0505  -0.0493  -0.0489  -0.0489
        yr17 |  -0.0514  -0.0522  -0.0522  -0.0527  -0.0529  -0.0522  -0.0510  -0.0506  -0.0506
        yr18 |  -0.0485  -0.0493  -0.0493  -0.0497  -0.0498  -0.0493  -0.0481  -0.0477  -0.0477
        yr19 |  -0.0477  -0.0485  -0.0485  -0.0489  -0.0491  -0.0485  -0.0473  -0.0469  -0.0469
        yr20 |  -0.0475  -0.0482  -0.0482  -0.0486  -0.0488  -0.0482  -0.0471  -0.0467  -0.0467
        yr21 |  -0.0485  -0.0493  -0.0493  -0.0497  -0.0498  -0.0493  -0.0481  -0.0477  -0.0477
        yr22 |  -0.0485  -0.0493  -0.0493  -0.0497  -0.0498  -0.0493  -0.0481  -0.0477  -0.0477
        yr23 |  -0.0457  -0.0464  -0.0464  -0.0468  -0.0469  -0.0464  -0.0453  -0.0449  -0.0449

             |     yr13     yr14     yr15     yr16     yr17     yr18     yr19     yr20     yr21
-------------+---------------------------------------------------------------------------------
        yr13 |   1.0000
        yr14 |  -0.0511   1.0000
        yr15 |  -0.0511  -0.0518   1.0000
        yr16 |  -0.0475  -0.0481  -0.0481   1.0000
        yr17 |  -0.0491  -0.0497  -0.0497  -0.0462   1.0000
        yr18 |  -0.0463  -0.0469  -0.0469  -0.0436  -0.0450   1.0000
        yr19 |  -0.0456  -0.0462  -0.0462  -0.0429  -0.0443  -0.0418   1.0000
        yr20 |  -0.0453  -0.0459  -0.0459  -0.0427  -0.0441  -0.0416  -0.0409   1.0000
        yr21 |  -0.0463  -0.0469  -0.0469  -0.0436  -0.0450  -0.0425  -0.0418  -0.0416   1.0000
        yr22 |  -0.0463  -0.0469  -0.0469  -0.0436  -0.0450  -0.0425  -0.0418  -0.0416  -0.0425
        yr23 |  -0.0436  -0.0442  -0.0442  -0.0410  -0.0424  -0.0400  -0.0394  -0.0392  -0.0400

             |     yr22     yr23
-------------+------------------
        yr22 |   1.0000
        yr23 |  -0.0400   1.0000

    Code:
    collin z HHI INFLATION GDPG BANKOWN TBT CTI lnta yr3 yr4 yr5 yr6 yr7 yr8 yr9 yr10 yr11 yr12 yr13 yr14 yr15 yr16 yr17 yr18 yr19 yr20 yr21 yr22 yr23
    Code:
    Collinearity Diagnostics

                        SQRT                   R-
  Variable      VIF     VIF    Tolerance    Squared
----------------------------------------------------
         z      1.20    1.09    0.8355      0.1645
       HHI  2.77e+14 1.7e+07    0.0000      1.0000
 INFLATION  2.43e+13 4.9e+06    0.0000      1.0000
      GDPG  3.75e+13 6.1e+06    0.0000      1.0000
   BANKOWN      1.14    1.07    0.8763      0.1237
       TBT      1.29    1.13    0.7776      0.2224
       CTI      1.04    1.02    0.9596      0.0404
      lnta      1.55    1.25    0.6445      0.3555
       yr3 -5.37e+12       .   -0.0000      1.0000
       yr4  8.89e+12 3.0e+06    0.0000      1.0000
       yr5  2.19e+12 1.5e+06    0.0000      1.0000
       yr6  3.13e+12 1.8e+06    0.0000      1.0000
       yr7  5.94e+12 2.4e+06    0.0000      1.0000
       yr8  1.93e+13 4.4e+06    0.0000      1.0000
       yr9  1.34e+13 3.7e+06    0.0000      1.0000
      yr10 -2.64e+13       .   -0.0000      1.0000
      yr11 -9.59e+12       .   -0.0000      1.0000
      yr12  9.20e+12 3.0e+06    0.0000      1.0000
      yr13 -2.29e+13       .   -0.0000      1.0000
      yr14  3.14e+13 5.6e+06    0.0000      1.0000
      yr15 -1.15e+13       .   -0.0000      1.0000
      yr16  1.04e+12 1.0e+06    0.0000      1.0000
      yr17 -1.59e+13       .   -0.0000      1.0000
      yr18 -9.10e+12       .   -0.0000      1.0000
      yr19  1.58e+13 4.0e+06    0.0000      1.0000
      yr20  2.90e+13 5.4e+06    0.0000      1.0000
      yr21  1.70e+13 4.1e+06    0.0000      1.0000
      yr22  4.32e+13 6.6e+06    0.0000      1.0000
      yr23  1.21e+12 1.1e+06    0.0000      1.0000
----------------------------------------------------
  Mean VIF  1.51e+13

                           Cond
        Eigenval          Index
---------------------------------
    1     6.0418          1.0000
    2     1.4045          2.0741
    3     1.2390          2.2082
    4     1.1645          2.2778
    5     1.0941          2.3500
    6     1.0655          2.3813
    7     1.0148          2.4400
    8     1.0069          2.4496
    9     1.0001          2.4578
    10     1.0000          2.4580
    11     1.0000          2.4580
    12     1.0000          2.4580
    13     1.0000          2.4580
    14     1.0000          2.4580
    15     1.0000          2.4580
    16     1.0000          2.4580
    17     1.0000          2.4580
    18     1.0000          2.4580
    19     1.0000          2.4580
    20     1.0000          2.4580
    21     1.0000          2.4580
    22     0.9795          2.4835
    23     0.8795          2.6210
    24     0.7192          2.8985
    25     0.3726          4.0269
    26     0.0181         18.2487
    27     0.0000   29990992.1720
    28    -0.0000               .
    29    -0.0000               .
    30    -0.0000               .
---------------------------------
 Condition Number              . 
 Eigenvalues & Cond Index computed from scaled raw sscp (w/ intercept)
 Det(correlation matrix)    0.0000

    Thanks for any advice

    Best,
    Aaron
    Tags: None
  • #2
    Aaron:
    welcome to this forum.
    As reported by Stata outcome, omission is due to correlation with the fixed effect.
    Kind regards,
    Carlo
    (StataNow 18.5)

    Comment

    • #3
      Originally posted by Carlo Lazzaro View Post
      Aaron:
      welcome to this forum.
      As reported by Stata outcome, omission is due to correlation with the fixed effect.
      Thank you for your reply, Carlo. Do you mean the year fixed effects correlate with the entity-fixed effects? If that is so, where in the output do STATA report this?

      Comment

      • #4
        Aaron:
        yes, I meant so.
        Actually, Stata does not report any detail concerning (extreme) multicollinearity and subsequent variable(s) omission.
        Kind regards,
        Carlo
        (StataNow 18.5)

        Comment

        • #5
          Originally posted by Carlo Lazzaro View Post
          Aaron:
          yes, I meant so.
          Actually, Stata does not report any detail concerning (extreme) multicollinearity and subsequent variable(s) omission.
          Ok, thanks. So it essentially means the omitted variables have no explanatory power and the only chance to disprove that would be increasing the sample?

          Comment

          • #6
            Aaron:
            more trivially, it might be a model specification issue (by the way: does the omission remain under -re- specification?), as you can see from the following toy-example, in which the omission of - birth_yr- under -fe- is due to its time-invariant nature:
            Code:
            . use "http://www.stata-press.com/data/r15/nlswork.dta"
(National Longitudinal Survey.  Young Women 14-26 years of age in 1968)

. xtreg ln_wage age i.birth_yr i.year, fe
note: 42.birth_yr omitted because of collinearity
note: 43.birth_yr omitted because of collinearity
note: 44.birth_yr omitted because of collinearity
note: 45.birth_yr omitted because of collinearity
note: 46.birth_yr omitted because of collinearity
note: 47.birth_yr omitted because of collinearity
note: 48.birth_yr omitted because of collinearity
note: 49.birth_yr omitted because of collinearity
note: 50.birth_yr omitted because of collinearity
note: 51.birth_yr omitted because of collinearity
note: 52.birth_yr omitted because of collinearity
note: 53.birth_yr omitted because of collinearity
note: 54.birth_yr omitted because of collinearity

Fixed-effects (within) regression               Number of obs     =     28,510
Group variable: idcode                          Number of groups  =      4,710

R-sq:                                           Obs per group:
     within  = 0.1060                                         min =          1
     between = 0.0914                                         avg =        6.1
     overall = 0.0805                                         max =         15

                                                F(15,23785)       =     188.00
corr(u_i, Xb)  = 0.0467                         Prob > F          =     0.0000

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0125992   .0102163     1.23   0.217    -.0074253    .0326238
             |
    birth_yr |
         42  |          0  (omitted)
         43  |          0  (omitted)
         44  |          0  (omitted)
         45  |          0  (omitted)
         46  |          0  (omitted)
         47  |          0  (omitted)
         48  |          0  (omitted)
         49  |          0  (omitted)
         50  |          0  (omitted)
         51  |          0  (omitted)
         52  |          0  (omitted)
         53  |          0  (omitted)
         54  |          0  (omitted)
             |
        year |
         69  |   .0748621   .0159011     4.71   0.000      .043695    .1060292
         70  |   .0478697   .0235673     2.03   0.042     .0016763     .094063
         71  |   .0865577   .0327939     2.64   0.008     .0222795     .150836
         72  |   .0856757   .0424903     2.02   0.044     .0023919    .1689594
         73  |   .0880069    .052344     1.68   0.093    -.0145906    .1906044
         75  |   .0778607   .0720304     1.08   0.280    -.0633235    .2190449
         77  |    .108365   .0922272     1.17   0.240    -.0724063    .2891363
         78  |   .1309518   .1028143     1.27   0.203    -.0705707    .3324743
         80  |   .1142649    .122792     0.93   0.352    -.1264152     .354945
         82  |   .1090451   .1431112     0.76   0.446    -.1714619    .3895522
         83  |   .1211272   .1532018     0.79   0.429    -.1791581    .4214125
         85  |   .1465637   .1736146     0.84   0.399    -.1937321    .4868594
         87  |   .1382642   .1941163     0.71   0.476     -.242216    .5187445
         88  |   .1799741   .2079871     0.87   0.387    -.2276938     .587642
             |
       _cons |   1.203731   .1952306     6.17   0.000     .8210667    1.586396
-------------+----------------------------------------------------------------
     sigma_u |   .4058746
     sigma_e |  .30300411
         rho |  .64212421   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4709, 23785) = 8.80                 Prob > F = 0.0000

. xtreg ln_wage age i.birth_yr i.year, re

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

R-sq:                                           Obs per group:
     within  = 0.1059                                         min =          1
     between = 0.0958                                         avg =        6.1
     overall = 0.0836                                         max =         15

                                                Wald chi2(28)     =    3271.07
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |     .00638   .0088314     0.72   0.470    -.0109293    .0236893
             |
    birth_yr |
         42  |  -.3600023   .2295299    -1.57   0.117    -.8098726    .0898681
         43  |   -.411902   .2276901    -1.81   0.070    -.8581665    .0343624
         44  |  -.3669633   .2280949    -1.61   0.108    -.8140211    .0800945
         45  |  -.3465367    .229104    -1.51   0.130    -.7955722    .1024988
         46  |  -.3556043   .2304813    -1.54   0.123    -.8073393    .0961308
         47  |  -.3656108   .2321514    -1.57   0.115    -.8206191    .0893975
         48  |   -.363669   .2343196    -1.55   0.121     -.822927    .0955889
         49  |  -.3750348   .2366903    -1.58   0.113    -.8389392    .0888696
         50  |  -.3969479   .2394534    -1.66   0.097     -.866268    .0723721
         51  |  -.4187791   .2424796    -1.73   0.084    -.8940305    .0564722
         52  |  -.4461327   .2456146    -1.82   0.069    -.9275285    .0352631
         53  |  -.4237412   .2492429    -1.70   0.089    -.9122483    .0647658
         54  |  -.5753698   .4592161    -1.25   0.210    -1.475417    .3246773
             |
        year |
         69  |   .0814148    .014949     5.45   0.000     .0521152    .1107144
         70  |   .0604407   .0210803     2.87   0.004     .0191241    .1017573
         71  |   .1047769   .0288348     3.63   0.000     .0482617    .1612921
         72  |   .1129049   .0371072     3.04   0.002     .0401762    .1856336
         73  |   .1216363   .0455256     2.67   0.008     .0324077    .2108649
         75  |   .1229176    .062455     1.97   0.049      .000508    .2453273
         77  |   .1702024    .079867     2.13   0.033      .013666    .3267388
         78  |   .2025503   .0890169     2.28   0.023     .0280804    .3770201
         80  |   .1978706    .106257     1.86   0.063    -.0103892    .4061304
         82  |   .2025831    .123801     1.64   0.102    -.0400625    .4452286
         83  |   .2238365   .1325239     1.69   0.091    -.0359056    .4835786
         85  |   .2637994    .150153     1.76   0.079    -.0304951    .5580939
         87  |   .2669837   .1678642     1.59   0.112    -.0620241    .5959915
         88  |   .3145208   .1798453     1.75   0.080    -.0379696    .6670112
             |
       _cons |   1.688194   .3221243     5.24   0.000     1.056842    2.319546
-------------+----------------------------------------------------------------
     sigma_u |  .36615656
     sigma_e |  .30300411
         rho |  .59354246   (fraction of variance due to u_i)
------------------------------------------------------------------------------
            Kind regards,
            Carlo
            (StataNow 18.5)

            Comment

            • #7
              Originally posted by Carlo Lazzaro View Post
              Aaron:
              more trivially, it might be a model specification issue (by the way: does the omission remain under -re- specification?), as you can see from the following toy-example, in which the omission of - birth_yr- under -fe- is due to its time-invariant nature:
              Thank you for all the help. However, the omission remain under random effects and the Hausman-test strongly rejects the use of it. Furthermore, previous studies suggest the use of -fe-. May there be any other reason for the omission?

              Comment

              • #8
                It appears that you have variables that are invariant across firms (GDP, inflation, etc.). These will be collinear with the year dummies.

                Comment

                • #9
                  Originally posted by Andrew Musau View Post
                  It appears that you have variables that are invariant across firms (GDP, inflation, etc.). These will be collinear with the year dummies.
                  Ok, but then shouldn't all the year dummies be omitted? Why only some of them? Are you saying the year dummies introduce heterogeneity covering the macro variables? Thanks
                  Last edited by Aaron Huckins; 03 May 2019, 11:01. Reason: typos

                  Comment

                  • #10
                    What I mean is that the coefficients of the variables that are invariant across firms in a given year are not identified in the regression with time effects as the variables are collinear with the time dummies. The problem with Stata's xtreg command is that is does not make this apparent, and I am not sure how many generations of Stata users have been reporting nonsensical coefficients in their papers. Try a different command like reghdfe from SSC and you will see that you cannot obtain an estimate for these variables. Here is a reproducible example that illustrates the point.

                    Code:
                    webuse grunfeld, clear
bys year: replace mvalue= mvalue[1]
bys year: replace kstock= kstock[1]
*WITH 2 VARIABLES, STATA BY DEFAULT DROPS THE LAST 2 TIME DUMMIES TO BREAK THE COLLINEARITY
xtreg invest mvalue kstock i.time, fe
*NOTICE THE COEFFICIENTS ON MVALUE AND KSTOCK CHANGE IF WE DROP DIFFERENT TIME DUMMIES
xtreg invest mvalue kstock o15.time o17.time i.time, fe
*ssc install reghdfe
*REGHDFE IS "SMART" AND CATCHES THE COLLINEARITY STRAIGHT AWAY
reghdfe invest mvalue kstock, a(company time)

                    Results:

                    Code:
                    . xtreg invest mvalue kstock i.time, fe
note: 19.time omitted because of collinearity
note: 20.time omitted because of collinearity

Fixed-effects (within) regression               Number of obs     =        200
Group variable: company                         Number of groups  =         10

R-sq:                                           Obs per group:
     within  = 0.2801                                         min =         20
     between =      .                                         avg =       20.0
     overall = 0.0672                                         max =         20

                                                F(19,171)         =       3.50
corr(u_i, Xb)  = -0.0000                        Prob > F          =     0.0000

------------------------------------------------------------------------------
      invest |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      mvalue |    .347759   .0766134     4.54   0.000     .1965291    .4989888
      kstock |  -1.200005   .2805274    -4.28   0.000    -1.753748   -.6462627
             |
        time |
          2  |   -190.312   49.25044    -3.86   0.000    -287.5291    -93.0949
          3  |  -1800.396   388.5255    -4.63   0.000    -2567.319   -1033.472
          4  |  -880.1618   177.2772    -4.96   0.000    -1230.095   -530.2283
          5  |   20.30903   44.90298     0.45   0.652    -68.32648    108.9445
          6  |   92.54097   50.25549     1.84   0.067    -6.660051     191.742
          7  |   166.0328   57.85686     2.87   0.005     51.82721    280.2384
          8  |   108.3439   51.32253     2.11   0.036     7.036656    209.6512
          9  |  -344.4432   72.46965    -4.75   0.000    -487.4935   -201.3929
         10  |  -120.5647   42.33838    -2.85   0.005    -204.1378   -36.99151
         11  |  -500.4488   106.6329    -4.69   0.000    -710.9351   -289.9626
         12  |   290.5617   77.57999     3.75   0.000     137.4239    443.6994
         13  |  -175.8023   52.19593    -3.37   0.001    -278.8336   -72.77099
         14  |   -100.989   45.02324    -2.24   0.026    -189.8619   -12.11606
         15  |   342.6629    92.9628     3.69   0.000     159.1605    526.1653
         16  |  -143.5402   47.56564    -3.02   0.003    -237.4316   -49.64873
         17  |   -75.2983   44.10573    -1.71   0.090    -162.3601     11.7635
         18  |  -17.83811   40.85529    -0.44   0.663    -98.48375    62.80754
         19  |          0  (omitted)
         20  |          0  (omitted)
             |
       _cons |   237.7454    30.6801     7.75   0.000     177.1849    298.3059
-------------+----------------------------------------------------------------
     sigma_u |  198.82421
     sigma_e |  97.202051
         rho |  .80709732   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(9, 171) = 83.68                     Prob > F = 0.0000

.
. *NOTICE THE COEFFICIENTS ON MVALUE AND KSTOCK CHANGE IF WE DROP DIFFERENT TIME
> DUMMIES

.
. xtreg invest mvalue kstock o15.time o17.time i.time, fe

Fixed-effects (within) regression               Number of obs     =        200
Group variable: company                         Number of groups  =         10

R-sq:                                           Obs per group:
     within  = 0.2801                                         min =         20
     between =      .                                         avg =       20.0
     overall = 0.0672                                         max =         20

                                                F(19,171)         =       3.50
corr(u_i, Xb)  = 0.0000                         Prob > F          =     0.0000

------------------------------------------------------------------------------
      invest |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      mvalue |   .1848804   .0637249     2.90   0.004     .0590916    .3106691
      kstock |   .3164732   .1973745     1.60   0.111    -.0731312    .7060775
             |
        time |
          2  |    72.1139    64.9162     1.11   0.268    -56.02639    200.2542
          3  |  -908.7553    312.851    -2.90   0.004    -1526.303    -291.208
          4  |  -490.4867   154.0424    -3.18   0.002    -794.5562   -186.4172
          5  |   3.369386   42.23465     0.08   0.937    -79.99903    86.73781
          6  |   30.28451    40.4074     0.75   0.455    -49.47703     110.046
          7  |   53.87586   39.61407     1.36   0.176     -24.3197    132.0714
          8  |   19.13219   37.35516     0.51   0.609    -54.60442     92.8688
          9  |   -292.492   100.0659    -2.92   0.004    -490.0154   -94.96859
         10  |   44.94112   49.88349     0.90   0.369     -53.5256    143.4078
         11  |  -271.1811   97.12343    -2.79   0.006    -462.8964    -79.4659
         12  |   35.63038   39.04112     0.91   0.363    -41.43421     112.695
         13  |   23.84217   46.16795     0.52   0.606     -67.2903    114.9747
         14  |    154.061    71.5787     2.15   0.033     12.76941    295.3527
         15  |          0  (omitted)
         16  |   4.750616   42.38285     0.11   0.911    -78.91032    88.41155
         17  |          0  (omitted)
         18  |   45.33986   40.37824     1.12   0.263    -34.36412    125.0438
         19  |  -1426.465   576.2514    -2.48   0.014    -2563.947    -288.983
         20  |   41.18679   48.93748     0.84   0.401    -55.41256    137.7861
             |
       _cons |  -14.38752   68.52885    -0.21   0.834    -149.6589    120.8839
-------------+----------------------------------------------------------------
     sigma_u |  198.82421
     sigma_e |  97.202051
         rho |  .80709732   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(9, 171) = 83.68                     Prob > F = 0.0000

.
. *ssc install reghdfe

.
. *REGHDFE IS "SMART" AND CATCHES THE COLLINEARITY STRAIGHT AWAY

.
. reghdfe invest mvalue kstock, a(company time)
note: mvalue is probably collinear with the fixed effects (all partialled-out val
> ues are close to zero; tol = 1.0e-09)
note: kstock is probably collinear with the fixed effects (all partialled-out val
> ues are close to zero; tol = 1.0e-09)
(MWFE estimator converged in 2 iterations)
note: mvalue omitted because of collinearity
note: kstock omitted because of collinearity

HDFE Linear regression                            Number of obs   =        200
Absorbing 2 HDFE groups                           F(   0,    171) =          .
                                                  Prob > F        =          .
                                                  R-squared       =     0.8274
                                                  Adj R-squared   =     0.7991
                                                  Within R-sq.    =     0.0000
                                                  Root MSE        =    97.2021

------------------------------------------------------------------------------
      invest |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      mvalue |          0  (omitted)
      kstock |          0  (omitted)
       _cons |   145.9583   6.873223    21.24   0.000      132.391    159.5255
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
     company |        10           0          10     |
        time |        20           1          19     |
-----------------------------------------------------+
                    Last edited by Andrew Musau; 03 May 2019, 13:47.

                    Comment

                    • #11
                      Originally posted by Carlo Lazzaro View Post
                      Aaron:
                      more trivially, it might be a model specification issue (by the way: does the omission remain under -re- specification?), as you can see from the following toy-example, in which the omission of - birth_yr- under -fe- is due to its time-invariant nature:
                      Code:
                      . use "http://www.stata-press.com/data/r15/nlswork.dta"
(National Longitudinal Survey. Young Women 14-26 years of age in 1968)

. xtreg ln_wage age i.birth_yr i.year, fe
note: 42.birth_yr omitted because of collinearity
note: 43.birth_yr omitted because of collinearity
note: 44.birth_yr omitted because of collinearity
note: 45.birth_yr omitted because of collinearity
note: 46.birth_yr omitted because of collinearity
note: 47.birth_yr omitted because of collinearity
note: 48.birth_yr omitted because of collinearity
note: 49.birth_yr omitted because of collinearity
note: 50.birth_yr omitted because of collinearity
note: 51.birth_yr omitted because of collinearity
note: 52.birth_yr omitted because of collinearity
note: 53.birth_yr omitted because of collinearity
note: 54.birth_yr omitted because of collinearity

Fixed-effects (within) regression Number of obs = 28,510
Group variable: idcode Number of groups = 4,710

R-sq: Obs per group:
within = 0.1060 min = 1
between = 0.0914 avg = 6.1
overall = 0.0805 max = 15

F(15,23785) = 188.00
corr(u_i, Xb) = 0.0467 Prob > F = 0.0000

------------------------------------------------------------------------------
ln_wage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .0125992 .0102163 1.23 0.217 -.0074253 .0326238
|
birth_yr |
42 | 0 (omitted)
43 | 0 (omitted)
44 | 0 (omitted)
45 | 0 (omitted)
46 | 0 (omitted)
47 | 0 (omitted)
48 | 0 (omitted)
49 | 0 (omitted)
50 | 0 (omitted)
51 | 0 (omitted)
52 | 0 (omitted)
53 | 0 (omitted)
54 | 0 (omitted)
|
year |
69 | .0748621 .0159011 4.71 0.000 .043695 .1060292
70 | .0478697 .0235673 2.03 0.042 .0016763 .094063
71 | .0865577 .0327939 2.64 0.008 .0222795 .150836
72 | .0856757 .0424903 2.02 0.044 .0023919 .1689594
73 | .0880069 .052344 1.68 0.093 -.0145906 .1906044
75 | .0778607 .0720304 1.08 0.280 -.0633235 .2190449
77 | .108365 .0922272 1.17 0.240 -.0724063 .2891363
78 | .1309518 .1028143 1.27 0.203 -.0705707 .3324743
80 | .1142649 .122792 0.93 0.352 -.1264152 .354945
82 | .1090451 .1431112 0.76 0.446 -.1714619 .3895522
83 | .1211272 .1532018 0.79 0.429 -.1791581 .4214125
85 | .1465637 .1736146 0.84 0.399 -.1937321 .4868594
87 | .1382642 .1941163 0.71 0.476 -.242216 .5187445
88 | .1799741 .2079871 0.87 0.387 -.2276938 .587642
|
_cons | 1.203731 .1952306 6.17 0.000 .8210667 1.586396
-------------+----------------------------------------------------------------
sigma_u | .4058746
sigma_e | .30300411
rho | .64212421 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4709, 23785) = 8.80 Prob > F = 0.0000

. xtreg ln_wage age i.birth_yr i.year, re

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

R-sq: Obs per group:
within = 0.1059 min = 1
between = 0.0958 avg = 6.1
overall = 0.0836 max = 15

Wald chi2(28) = 3271.07
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

------------------------------------------------------------------------------
ln_wage | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .00638 .0088314 0.72 0.470 -.0109293 .0236893
|
birth_yr |
42 | -.3600023 .2295299 -1.57 0.117 -.8098726 .0898681
43 | -.411902 .2276901 -1.81 0.070 -.8581665 .0343624
44 | -.3669633 .2280949 -1.61 0.108 -.8140211 .0800945
45 | -.3465367 .229104 -1.51 0.130 -.7955722 .1024988
46 | -.3556043 .2304813 -1.54 0.123 -.8073393 .0961308
47 | -.3656108 .2321514 -1.57 0.115 -.8206191 .0893975
48 | -.363669 .2343196 -1.55 0.121 -.822927 .0955889
49 | -.3750348 .2366903 -1.58 0.113 -.8389392 .0888696
50 | -.3969479 .2394534 -1.66 0.097 -.866268 .0723721
51 | -.4187791 .2424796 -1.73 0.084 -.8940305 .0564722
52 | -.4461327 .2456146 -1.82 0.069 -.9275285 .0352631
53 | -.4237412 .2492429 -1.70 0.089 -.9122483 .0647658
54 | -.5753698 .4592161 -1.25 0.210 -1.475417 .3246773
|
year |
69 | .0814148 .014949 5.45 0.000 .0521152 .1107144
70 | .0604407 .0210803 2.87 0.004 .0191241 .1017573
71 | .1047769 .0288348 3.63 0.000 .0482617 .1612921
72 | .1129049 .0371072 3.04 0.002 .0401762 .1856336
73 | .1216363 .0455256 2.67 0.008 .0324077 .2108649
75 | .1229176 .062455 1.97 0.049 .000508 .2453273
77 | .1702024 .079867 2.13 0.033 .013666 .3267388
78 | .2025503 .0890169 2.28 0.023 .0280804 .3770201
80 | .1978706 .106257 1.86 0.063 -.0103892 .4061304
82 | .2025831 .123801 1.64 0.102 -.0400625 .4452286
83 | .2238365 .1325239 1.69 0.091 -.0359056 .4835786
85 | .2637994 .150153 1.76 0.079 -.0304951 .5580939
87 | .2669837 .1678642 1.59 0.112 -.0620241 .5959915
88 | .3145208 .1798453 1.75 0.080 -.0379696 .6670112
|
_cons | 1.688194 .3221243 5.24 0.000 1.056842 2.319546
-------------+----------------------------------------------------------------
sigma_u | .36615656
sigma_e | .30300411
rho | .59354246 (fraction of variance due to u_i)
------------------------------------------------------------------------------
                      Hi Sir, I met similar time-dummy problem like Aaron. Thanks for your explanation here.
                      But in my case, the macro variable is kind of important, because i need to discuss the impact of X on Y, depending on the decrease of the macro variable, and interaction term of macro variable and X is also included in the regression. So i think i cannot delete the macro variable to avoid collinearity.
                      Are there any other ways to fix time effect without deleting macro variables?
                      My post is here if you need more detailed information: https://www.statalist.org/forums/for...-and-unit-root

                      Thanks!!

                      Comment

                      • #12
                        Originally posted by Andrew Musau View Post
                        What I mean is that the coefficients of the variables that are invariant across firms in a given year are not identified in the regression with time effects as the variables are collinear with the time dummies. The problem with Stata's xtreg command is that is does not make this apparent, and I am not sure how many generations of Stata users have been reporting nonsensical coefficients in their papers. Try a different command like reghdfe from SSC and you will see that you cannot obtain an estimate for these variables. Here is a reproducible example that illustrates the point.
                        Thank you for the clarification, Andrew. These control variables is considered by literature to have great effects on the dep.var. What would you suggest to deal with this? Is there any other regression methods implemented in STATA that would deal with it?

                        Comment

                        • #13
                          There is no trick to escape the collinearity except that in your case you could:

                          1. Sample firms from more than one country so that your variables, e.g., inflation and GDP, vary between firms.
                          2. Either drop the time dummies or drop the variables that are invariant across firms in a given year.

                          Usually, if these are just control variables (i.e., not of immediate interest to your study), then it does not matter that they are omitted. However, if they are part of your study, the only options are either 1 or 2.

                          Comment

                          • #14
                            Originally posted by Andrew Musau View Post
                            There is no trick to escape the collinearity except that in your case you could:

                            1. Sample firms from more than one country so that your variables, e.g., inflation and GDP, vary between firms.
                            2. Either drop the time dummies or drop the variables that are invariant across firms in a given year.

                            Usually, if these are just control variables (i.e., not of immediate interest to your study), then it does not matter that they are omitted. However, if they are part of your study, the only options are either 1 or 2.
                            Thanks for the help Andrew, it clarified a lot of my questions.

                            Comment

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