Year dummy omitted in FE but not in RE. Why?

[Budu Gulo]

When I fit an FE model, the year dummy 2001 is omitted. However, the RE model does not omit it. Why?

. table YEAR

--------------------
        |  Frequency
--------+-----------
Year    |           
  1995  |        279
  1996  |        267
  1997  |        271
  1998  |        277
  1999  |        271
  2000  |        283
  2001  |        274
  Total |      1,922
--------------------

. xtreg LEV COLLAT SIZE PROF GROWTH AGE i.YEAR, fe vce (cluster id)
note: 2001.YEAR omitted because of collinearity.

Fixed-effects (within) regression               Number of obs     =      1,922
Group variable: id                              Number of groups  =        355

R-squared:                                      Obs per group:
     Within  = 0.0779                                         min =          1
     Between = 0.0080                                         avg =        5.4
     Overall = 0.0082                                         max =          7

                                                F(10, 354)        =      11.37
corr(u_i, Xb) = -0.6147                         Prob > F          =     0.0000

                                   (Std. err. adjusted for 355 clusters in id)
------------------------------------------------------------------------------
             |               Robust
         LEV | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      COLLAT |   .1016437   .0773286     1.31   0.190    -.0504374    .2537249
        SIZE |   .1114536    .028439     3.92   0.000     .0555229    .1673842
        PROF |  -.3647744   .1033513    -3.53   0.000    -.5680341   -.1615148
      GROWTH |   .0000754   .0000144     5.24   0.000     .0000471    .0001036
         AGE |  -.0052446   .0028572    -1.84   0.067    -.0108638    .0003747
             |
        YEAR |
       1996  |  -.0010936   .0067992    -0.16   0.872    -.0144655    .0122782
       1997  |  -.0120382   .0083081    -1.45   0.148    -.0283776    .0043012
       1998  |  -.0270821   .0080989    -3.34   0.001    -.0430102   -.0111541
       1999  |  -.0263896   .0082888    -3.18   0.002     -.042691   -.0100882
       2000  |  -.0038456   .0066291    -0.58   0.562     -.016883    .0091918
       2001  |          0  (omitted)
             |
       _cons |  -1.486738   .4638209    -3.21   0.001    -2.398929   -.5745472
-------------+----------------------------------------------------------------
     sigma_u |  .27092723
     sigma_e |  .11210781
         rho |  .85380711   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. xtreg LEV COLLAT SIZE PROF GROWTH AGE i.YEAR, re vce (cluster id)

Random-effects GLS regression                   Number of obs     =      1,922
Group variable: id                              Number of groups  =        355

R-squared:                                      Obs per group:
     Within  = 0.0583                                         min =          1
     Between = 0.0373                                         avg =        5.4
     Overall = 0.0304                                         max =          7

                                                Wald chi2(11)     =     120.07
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

                                   (Std. err. adjusted for 355 clusters in id)
------------------------------------------------------------------------------
             |               Robust
         LEV | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
      COLLAT |   .0776448   .0563213     1.38   0.168     -.032743    .1880325
        SIZE |    .035378   .0107094     3.30   0.001     .0143879    .0563682
        PROF |  -.4119617   .1001958    -4.11   0.000    -.6083419   -.2155816
      GROWTH |    .000087   .0000144     6.04   0.000     .0000588    .0001152
         AGE |  -.0005874   .0004855    -1.21   0.226    -.0015389    .0003642
             |
        YEAR |
       1996  |  -.0034985   .0074282    -0.47   0.638    -.0180574    .0110604
       1997  |  -.0122627    .009884    -1.24   0.215     -.031635    .0071095
       1998  |  -.0248749    .010648    -2.34   0.019    -.0457446   -.0040052
       1999  |    -.02639   .0120675    -2.19   0.029     -.050042    -.002738
       2000  |  -.0032863   .0135215    -0.24   0.808     -.029788    .0232154
       2001  |  -.0005919   .0147074    -0.04   0.968     -.029418    .0282341
             |
       _cons |  -.2972312    .181439    -1.64   0.101     -.652845    .0583827
-------------+----------------------------------------------------------------
     sigma_u |  .20109089
     sigma_e |  .11210781
         rho |  .76289041   (fraction of variance due to u_i)
------------------------------------------------------------------------------

[Carlo Lazzaro]

Budu:
collinearity with the fixed effect explains Stata omission.

[Budu Gulo]

Carlo Lazzaro, thanks for the comment. As a panel data beginner, I am a bit lost. Could you please explain it with an example? Thanks!

[Carlo Lazzaro]

Budu:
reading -xtreg- entry in Stata .pdf manual is a good advice.
Please note that panel data regression needs a good knowledge of econometrics over and above its workhorse (that is, OLS).

[Clyde Schechter]

Without knowing what these variables represent, and with no data at hand, it is difficult to give a specific answer here. But I'll take a guess. I see that one of the variables is called AGE. This variable is probably colinear with the year effects in a fixed effects model because when you de-mean the data (as happens in a fixed effects model) the age variable is just a sequence like ...-2 -1 0 1 2... and clearly is linearly related to the calendar year, perhaps with the help of the constant term. By contrast, in the random effects model, the age variable is not demeaned, and the age varies, perhaps considerably, from one id to another. So the combination of the constant term and the year effects is no longer enough information to determine the age variable.

By the way, if you are going to use the fixed-effects model, you should not include the age variable along with the time effects. Use one or the other, but not both: because they are colinear in the fixed effects model, their separate effects are not identifiable, and the coefficients attached to them are meaningless artifacts of the particular way that Stata chose to break the colinearity.

[Budu Gulo]

Clyde Schechter, Thank you so much for the detailed explanation. This is what I was looking for, and I find it very enlightening!
Your guess is correct; AGE is indeed colinear with the year effects.
Thank you again!