Need help to interpret the result of Hausman test

[Ariyo Irhamna]

Dear Statalist Member,

I hope everything is fine.

I am doing a project with 12 variables (data panel which consist of 3 years and 33 provinces dataset). I just perform the Hausman test in order to see if I have to proceed with FE or RE models. Regarding the Hausman test result. This is the result of my Hausman test.

.xtset id year

panel variable: id (strongly balanced)
time variable: year, 2009 to 2014, but with gaps
delta: 1 unit

.xtreg realgdp consumption, fe

Fixed-effects (within) regression Number of obs = 99
Group variable: id Number of groups = 33

R-sq: Obs per group:
within = 0.9623 min = 3
between = 0.9556 avg = 3.0
overall = 0.9135 max = 3

F(1,65) = 1658.24
corr(u_i, Xb) = -0.8232 Prob > F = 0.0000

------------------------------------------------------------------------------
realgdp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
consumption | 1.962263 .0481874 40.72 0.000 1.866026 2.0585
_cons | -7.01e+07 7494447 -9.35 0.000 -8.50e+07 -5.51e+07
-------------+----------------------------------------------------------------
sigma_u | 1.421e+08
sigma_e | 47540049
rho | .89938957 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(32, 65) = 8.64 Prob > F = 0.0000

.estimates store fe_panel

.xtreg realgdp consumption, re

Random-effects GLS regression Number of obs = 99
Group variable: id Number of groups = 33

R-sq: Obs per group:
within = 0.9623 min = 3
between = 0.9556 avg = 3.0
overall = 0.9135 max = 3

Wald chi2(1) = 1002.79
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

------------------------------------------------------------------------------
realgdp | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
consumption | 1.590491 .0502257 31.67 0.000 1.492051 1.688932
_cons | -2.55e+07 1.40e+07 -1.82 0.069 -5.30e+07 1953742
-------------+----------------------------------------------------------------
sigma_u | 40605907
sigma_e | 47540049
rho | .42181724 (fraction of variance due to u_i)
------------------------------------------------------------------------------

.estimates store re_panel

hausman fe_panel re_panel

---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fe_panel re_panel Difference S.E.
-------------+----------------------------------------------------------------
consumption | 1.962263 1.590491 .3717717 .
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg

Test: Ho: difference in coefficients not systematic

chi2(1) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= -689.00 chi2<0 ==> model fitted on these
data fails to meet the asymptotic
assumptions of the Hausman test;
see suest for a generalized test

Regarding hausman test result above, I have a question:

1. Please comment about my dataset availbility, is it good enough to run a panel data?
2. What informations we get from this Hausman test result?
3. How to interpret my Hausman test result?
4. Which one should I choose, RE or FE?

However, i will really appreciate it if my few question can be attended in an easy explanation.

Thanks in Advance

Ariyo DP Irhamna

[Ariyo Irhamna]

Dear Statalist Member,

I hope everything is fine.

I am doing a project with 12 variables (data panel which consist of 3 years and 33 provinces dataset). I just perform the Hausman test in order to see if I have to proceed with FE or RE models. Regarding the Hausman test result. This is the result of my Hausman test.

.xtset id year

panel variable: id (strongly balanced)
time variable: year, 2009 to 2014, but with gaps
delta: 1 unit

.xtreg realgdp consumption, fe

Fixed-effects (within) regression Number of obs = 99
Group variable: id Number of groups = 33

R-sq: Obs per group:
within = 0.9623 min = 3
between = 0.9556 avg = 3.0
overall = 0.9135 max = 3

F(1,65) = 1658.24
corr(u_i, Xb) = -0.8232 Prob > F = 0.0000

------------------------------------------------------------------------------
realgdp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
consumption | 1.962263 .0481874 40.72 0.000 1.866026 2.0585
_cons | -7.01e+07 7494447 -9.35 0.000 -8.50e+07 -5.51e+07
-------------+----------------------------------------------------------------
sigma_u | 1.421e+08
sigma_e | 47540049
rho | .89938957 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(32, 65) = 8.64 Prob > F = 0.0000

.estimates store fe_panel

.xtreg realgdp consumption, re

Random-effects GLS regression Number of obs = 99
Group variable: id Number of groups = 33

R-sq: Obs per group:
within = 0.9623 min = 3
between = 0.9556 avg = 3.0
overall = 0.9135 max = 3

Wald chi2(1) = 1002.79
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

------------------------------------------------------------------------------
realgdp | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
consumption | 1.590491 .0502257 31.67 0.000 1.492051 1.688932
_cons | -2.55e+07 1.40e+07 -1.82 0.069 -5.30e+07 1953742
-------------+----------------------------------------------------------------
sigma_u | 40605907
sigma_e | 47540049
rho | .42181724 (fraction of variance due to u_i)
------------------------------------------------------------------------------

.estimates store re_panel

hausman fe_panel re_panel

---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fe_panel re_panel Difference S.E.
-------------+----------------------------------------------------------------
consumption | 1.962263 1.590491 .3717717 .
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg

Test: Ho: difference in coefficients not systematic

chi2(1) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= -689.00 chi2<0 ==> model fitted on these
data fails to meet the asymptotic
assumptions of the Hausman test;
see suest for a generalized test

Regarding hausman test result above, I have a question:

1. Please comment about my dataset availbility, is it good enough to run a panel data?
2. What informations we get from this Hausman test result?
3. How to interpret my Hausman test result?
4. Which one should I choose, RE or FE?

However, i will really appreciate it if my few question can be attended in an easy explanation.

Thanks in Advance

Ariyo DP Irhamna

[Carlo Lazzaro]

Ariyo:
I would try to re-run -hausman- with the -sigmamore- option.

[Ariyo Irhamna]

Dear Carlo,

Thank you for your prompt reply. I have tried the hausman with -sigmamore- option and here the result.

. hausman fe_panel re_panel, sigmamore

* * * * * * * * *---- Coefficients ----
* * * * * * *| * * *(b) * * * * *(B) * * * * * *(b-B) * * sqrt(diag(V_b-V_B))
* * * * * * *| * *fe_panel * * re_panel * * *Difference * * * * *S.E.
-------------+----------------------------------------------------------------
*consumption | * *1.962263 * * 1.590491 * * * *.3717717 * * * *.0508803
------------------------------------------------------------------------------
* * * * * * * * * * * * * *b = consistent under Ho and Ha; obtained from xtreg
* * * * * * B = inconsistent under Ha, efficient under Ho; obtained from xtreg

* * Test: *Ho: *difference in coefficients not systematic

* * * * * * * * * chi2(1) = (b-B)'[(V_b-V_B)^(-1)](b-B)
* * * * * * * * * * * * * = * * * 53.39
* * * * * * * * Prob>chi2 = * * *0.0000

So back to my first post questions:
1. Please comment about my dataset availbility, is it good enough to run a panel data?
2. What informations we get from this Hausman test result?
3. How to interpret my Hausman test result?
4. Which one should I choose, RE or FE?


Thank you
Ariyo
(Stata 15 SE)

[Carlo Lazzaro]

Ariyo:
all your questions boil down to an unique answer: go -xtreg, fe-.

[Marcos Almeida]

I just wish to add that the output is barely readable. In the forthcoming queries, and according to the FAQ, I recommend to use CODE delimiters so as to make it fully readable.

That said, with regards to "data availability" being "good enough" for panel data analysis, it seems you have a small sample size (groups = 33) and only 3 measures. What is more, there seems to be only one predictor in the model.

Finally, the theme is out of my field. However, if I got it right, the model seems to imply that the predicted values of realgdp would increase according to an increase in consumption, and I wonder whether this is the correct direction, theoretically speaking, or the opposite, I mean, an increase in realgdp leading to an increase in consumption. Who knows...

[Carlo Lazzaro]

Ariyo:
Marcos highlights an important issue, that I ovelooked in my last reply, since I interpreted your example your code lines as an example for getting advice on a possible outcome of -hausman-.
However, if what I figured out is not the case, how can it be that you have 12 variables but one predictor only is included in the right-hand side of your regression model?
Hence, the main question is not whether -hausman. test tells you something substantive about your dataset and points you to the right specification, but whether a simple panel data regression is meaningful at all for your research purposes.
As an aside, Marcos' recommendation about using CODE delimiters is highly commendable.

[Ariyo Irhamna]

Thank you Marcos and Carlo for your reply, I just realised that my output is unreadable.

I have modified my model however I am still not sure about the result. so back to my first post questions:

1. How about my current model, is it good enough to run a panel data with small dataset (which noted by Marcos above)?
2. What informations we get from this Hausman test result?
3. How to interpret my Hausman test result?
4. Which one should I choose, RE or FE? and how to interpret if RE or FE?

Many Thanks,
Ariyo DP Irhamna
(Stata 15 SE)

 xtset id year
       panel variable:  id (strongly balanced)
        time variable:  year, 2009 to 2014, but with gaps
                delta:  1 unit

. xtreg y x1 x2 x3 x4 x7 x10, fe

Fixed-effects (within) regression               Number of obs     =         99
Group variable: id                              Number of groups  =         33

R-sq:                                           Obs per group:
     within  = 0.9815                                         min =          3
     between = 0.8265                                         avg =        3.0
     overall = 0.6453                                         max =          3

                                                F(6,60)           =     529.46
corr(u_i, Xb)  = -0.9701                        Prob > F          =     0.0000

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          x1 |    2361.13   472.2413     5.00   0.000     1416.507    3305.753
          x2 |   1.543548   .3088674     5.00   0.000      .925721    2.161375
          x3 |   .1362727   .5374563     0.25   0.801    -.9387999    1.211345
          x4 |    4030816    1480719     2.72   0.008      1068936     6992695
          x7 |   64866.19   22187.25     2.92   0.005     20485.08    109247.3
         x10 |   -3422031    2744474    -1.25   0.217     -8911796     2067734
       _cons |  -5.47e+08   2.13e+08    -2.57   0.013    -9.72e+08   -1.22e+08
-------------+----------------------------------------------------------------
     sigma_u |  7.396e+08
     sigma_e |   34687884
         rho |  .99780542   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(32, 60) = 9.55                      Prob > F = 0.0000

. estimates store fe_panel

. xtreg y x1 x2 x3 x4 x7 x10, re

Random-effects GLS regression                   Number of obs     =         99
Group variable: id                              Number of groups  =         33

R-sq:                                           Obs per group:
     within  = 0.9734                                         min =          3
     between = 0.9591                                         avg =        3.0
     overall = 0.9503                                         max =          3

                                                Wald chi2(6)      =    1771.80
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          x1 |   3470.561   580.6697     5.98   0.000     2332.469    4608.653
          x2 |   2.376159   .2812441     8.45   0.000     1.824931    2.927387
          x3 |  -1.820384   .5207132    -3.50   0.000    -2.840963    -.799805
          x4 |    1924600    1669823     1.15   0.249     -1348193     5197393
          x7 |  -6409.437   1667.307    -3.84   0.000    -9677.299   -3141.576
         x10 |   -2085484    2364562    -0.88   0.378     -6719941     2548972
       _cons |  -1.38e+07   1.37e+08    -0.10   0.920    -2.82e+08    2.55e+08
-------------+----------------------------------------------------------------
     sigma_u |   12201677
     sigma_e |   34687884
         rho |  .11010841   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. estimates store re_panel

. hausman fe_panel re_panel

Note: the rank of the differenced variance matrix (4) does not equal the number of coefficients being tested
        (6); be sure this is what you expect, or there may be problems computing the test.  Examine the
        output of your estimators for anything unexpected and possibly consider scaling your variables so
        that the coefficients are on a similar scale.

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |    fe_panel     re_panel      Difference          S.E.
-------------+----------------------------------------------------------------
          x1 |     2361.13     3470.561       -1109.431               .
          x2 |    1.543548     2.376159       -.8326111        .1276747
          x3 |    .1362727    -1.820384        1.956657         .133105
          x4 |     4030816      1924600         2106216               .
          x7 |    64866.19    -6409.437        71275.62        22124.51
         x10 |    -3422031     -2085484        -1336547         1393192
------------------------------------------------------------------------------
                           b = consistent under Ho and Ha; obtained from xtreg
            B = inconsistent under Ha, efficient under Ho; obtained from xtreg

    Test:  Ho:  difference in coefficients not systematic

                  chi2(4) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =        4.70
                Prob>chi2 =      0.3200
                (V_b-V_B is not positive definite)

. estimates table fe_panel re_panel

----------------------------------------
    Variable |  fe_panel     re_panel   
-------------+--------------------------
          x1 |  2361.1301    3470.5611  
          x2 |  1.5435478    2.3761589  
          x3 |   .1362727   -1.8203843  
          x4 |  4030815.5    1924599.9  
          x7 |  64866.185   -6409.4375  
         x10 | -3422031.2   -2085484.1  
       _cons | -5.468e+08    -13760948  
----------------------------------------

[Marcos Almeida]

Well, I gather some if your questions are already answered, at least up to the point of the information given so far.

That said, you may also reflect about the large SEs as well as the quite different coefficients from both models.

[Carlo Lazzaro]

Ariyo:
the missing values in the first column to te right of the -hausman- outcome tables mirrors the evidfence that you have a limited dataset.
You may want to follow -hausman- recommendation and go -xtreg, re-, but consider that the limited sample size probably causes the lack of statistical significance of the -hausman- p-value.

[Guest]

Carlo Lazzaro, I have a similar problem. As you can see below, I tried to perform Hausman test. The null hypothesis is that difference in coefficients is not systematic and the result is Prob > chi2 = 0.0000. Does that mean I have to reject the null and use FE method instead? However, if I use FE model, then my R squared is significantly lower and most coefficients are insignificant. Hence another question - how can I justify the use of RE if I failed the Hausman test?

Thank you very much in advance!

xtreg wages i.high_qual training_hrs i.illness_disability i.sex i.children i.general_health i.region i.age i.sector, fe 

Fixed-effects (within) regression               Number of obs     =     81,014
Group variable: id                              Number of groups  =     45,174

R-squared:                                      Obs per group:
     Within  = 0.0136                                         min =          1
     Between = 0.0765                                         avg =        1.8
     Overall = 0.0675                                         max =          4

                                                F(43,35797)       =      11.45
corr(u_i, Xb) = -0.0383                         Prob > F          =     0.0000

----------------------------------------------------------------------------------------------------
                             wages | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-----------------------------------+----------------------------------------------------------------
                         high_qual |
              Other higher degree  |  -.0928267   .4884575    -0.19   0.849    -1.050218    .8645648
                      A-level etc  |   .0182819   .3901527     0.05   0.963    -.7464291    .7829929
                         GCSE etc  |  -.3006534    .506201    -0.59   0.553    -1.292823    .6915159
              Other qualification  |  -.9605771   .7118253    -1.35   0.177    -2.355776     .434622
                 No qualification  |  -2.879779   .8422607    -3.42   0.001    -4.530635   -1.228922
                                   |
                      training_hrs |  -.0000712    .000388    -0.18   0.854    -.0008318    .0006893
                                   |
                illness_disability |
                               no  |  -.0778907   .0936522    -0.83   0.406    -.2614519    .1056704
                                   |
                               sex |
                           female  |   .4485456   2.485943     0.18   0.857    -4.423979     5.32107
                                   |
                          children |
                                1  |   .1282714   .1836384     0.70   0.485    -.2316655    .4882083
                                2  |   .4622015   .2649987     1.74   0.081    -.0572041     .981607
                                3  |   .0442143   .4279878     0.10   0.918    -.7946546    .8830833
                                4  |  -.2602339   .8243079    -0.32   0.752    -1.875902    1.355435
                                5  |  -1.442031   2.088447    -0.69   0.490     -5.53545    2.651389
                                6  |  -5.016402   3.488116    -1.44   0.150    -11.85322    1.820412
                                   |
                    general_health |
                        very good  |  -.0055532   .0923854    -0.06   0.952    -.1866313     .175525
                         or Poor?  |  -.2084222   .2762525    -0.75   0.451    -.7498855    .3330411
                                   |
                            region |
                       North West  |  -.5530689    1.45959    -0.38   0.705    -3.413909    2.307771
         Yorkshire and the Humber  |  -2.145961   1.441226    -1.49   0.137    -4.970808    .6788853
                    East Midlands  |   2.999986   1.523444     1.97   0.049     .0139899    5.985983
                    West Midlands  |   4.373938   1.612606     2.71   0.007     1.213181    7.534694
                  East of England  |   1.498337   1.479719     1.01   0.311    -1.401957    4.398631
                           London  |   1.065125    1.44671     0.74   0.462     -1.77047     3.90072
                       South East  |   1.369021   1.404179     0.97   0.330    -1.383212    4.121254
                       South West  |    .552194   1.506342     0.37   0.714    -2.400282     3.50467
                            Wales  |    1.09009   1.705773     0.64   0.523    -2.253277    4.433457
                         Scotland  |    .915629   1.623863     0.56   0.573    -2.267192     4.09845
                 Northern Ireland  |  -3.344014   3.238417    -1.03   0.302     -9.69141    3.003382
                                   |
                               age |
                  18-19 years old  |   .6114318   .4055764     1.51   0.132    -.1835102    1.406374
                  20-24 years old  |    1.74053   .4566186     3.81   0.000      .845544    2.635517
                  25-29 years old  |   2.709425   .5220407     5.19   0.000      1.68621    3.732641
                  30-34 years old  |   3.427654    .562677     6.09   0.000      2.32479    4.530518
                  35-39 years old  |   4.251303   .5949165     7.15   0.000     3.085249    5.417358
                  40-44 years old  |   4.816463   .6195774     7.77   0.000     3.602072    6.030853
                  45-49 years old  |   5.164924   .6400082     8.07   0.000     3.910488    6.419359
                  50-54 years old  |   5.225232   .6620268     7.89   0.000      3.92764    6.522825
                  55-59 years old  |   5.330005   .6887239     7.74   0.000     3.980085    6.679925
                  60-64 years old  |   5.379775   .7261224     7.41   0.000     3.956553    6.802997
                65 years or older  |   4.311408    .813306     5.30   0.000     2.717303    5.905512
                                   |
                            sector |
managerial & technical occupation  |   1.615665   .3315755     4.87   0.000     .9657667    2.265563
               skilled non-manual  |   .8074404   .3549795     2.27   0.023     .1116698    1.503211
                   skilled manual  |  -2.100734   .3713009    -5.66   0.000    -2.828495   -1.372973
        partly skilled occupation  |   .1310732   .3762136     0.35   0.728    -.6063168    .8684632
             unskilled occupation  |   .0818114   .4849397     0.17   0.866    -.8686851    1.032308
                                   |
                             _cons |   6.510054   1.986823     3.28   0.001     2.615821    10.40429
-----------------------------------+----------------------------------------------------------------
                           sigma_u |  8.5185288
                           sigma_e |  5.1619774
                               rho |  .73142173   (fraction of variance due to u_i)
----------------------------------------------------------------------------------------------------
F test that all u_i=0: F(45173, 35797) = 3.85                Prob > F = 0.0000



. estimates store fe

xtreg wages i.high_qual training_hrs i.illness_disability i.sex i.children i.general_health i.region i.age i.sector, re

Random-effects GLS regression                   Number of obs     =     81,014
Group variable: id                              Number of groups  =     45,174

R-squared:                                      Obs per group:
     Within  = 0.0093                                         min =          1
     Between = 0.2259                                         avg =        1.8
     Overall = 0.2153                                         max =          4

                                                Wald chi2(43)     =   13494.78
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

----------------------------------------------------------------------------------------------------
                             wages | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-----------------------------------+----------------------------------------------------------------
                         high_qual |
              Other higher degree  |  -2.226562   .1213105   -18.35   0.000    -2.464326   -1.988797
                      A-level etc  |  -2.750473   .1055585   -26.06   0.000    -2.957363   -2.543582
                         GCSE etc  |  -3.690913   .1114786   -33.11   0.000    -3.909407   -3.472419
              Other qualification  |  -4.429453   .1577683   -28.08   0.000    -4.738673   -4.120232
                 No qualification  |  -5.281472   .1854816   -28.47   0.000     -5.64501   -4.917935
                                   |
                      training_hrs |   .0006149   .0003174     1.94   0.053    -7.30e-06    .0012371
                                   |
                illness_disability |
                               no  |   .1494179   .0684527     2.18   0.029     .0152532    .2835826
                                   |
                               sex |
                           female  |  -1.712939   .0848684   -20.18   0.000    -1.879278     -1.5466
                                   |
                          children |
                                1  |  -.3398704   .1087729    -3.12   0.002    -.5530613   -.1266795
                                2  |  -.2720838   .1282247    -2.12   0.034    -.5233996   -.0207681
                                3  |  -1.174362   .2151139    -5.46   0.000    -1.595978   -.7527469
                                4  |  -1.975734   .4807552    -4.11   0.000    -2.917997   -1.033471
                                5  |  -2.071639   1.181146    -1.75   0.079    -4.386643    .2433645
                                6  |  -4.674262    2.33589    -2.00   0.045    -9.252522   -.0960014
                                   |
                    general_health |
                        very good  |   -.378106   .0689673    -5.48   0.000    -.5132795   -.2429325
                         or Poor?  |  -.9154749   .2117265    -4.32   0.000    -1.330451   -.5004986
                                   |
                            region |
                       North West  |   .2585602   .2247362     1.15   0.250    -.1819145     .699035
         Yorkshire and the Humber  |  -.2284908   .2328341    -0.98   0.326    -.6848373    .2278557
                    East Midlands  |   .0518488   .2331266     0.22   0.824    -.4050709    .5087686
                    West Midlands  |   .5359982   .2331594     2.30   0.022     .0790141    .9929822
                  East of England  |   .9415514   .2282001     4.13   0.000     .4942875    1.388815
                           London  |   1.394893   .2199591     6.34   0.000     .9637811    1.826005
                       South East  |   1.466192   .2183471     6.71   0.000     1.038239    1.894144
                       South West  |  -.0282937   .2312368    -0.12   0.903    -.4815096    .4249222
                            Wales  |  -.2318236   .2358603    -0.98   0.326    -.6941013     .230454
                         Scotland  |   .5588212   .2261004     2.47   0.013     .1156726     1.00197
                 Northern Ireland  |  -.1259098   .2391234    -0.53   0.599    -.5945829    .3427634
                                   |
                               age |
                  18-19 years old  |   .3611545   .2740854     1.32   0.188    -.1760431     .898352
                  20-24 years old  |   .9872718   .2612305     3.78   0.000     .4752694    1.499274
                  25-29 years old  |   2.151108   .2647774     8.12   0.000     1.632154    2.670062
                  30-34 years old  |   3.617456   .2642491    13.69   0.000     3.099537    4.135375
                  35-39 years old  |   4.557396   .2642927    17.24   0.000     4.039391      5.0754
                  40-44 years old  |   4.976156   .2619728    18.99   0.000     4.462698    5.489613
                  45-49 years old  |   5.086969   .2606707    19.51   0.000     4.576063    5.597874
                  50-54 years old  |   4.821479    .261474    18.44   0.000     4.308999    5.333959
                  55-59 years old  |   4.646858   .2659043    17.48   0.000     4.125695    5.168021
                  60-64 years old  |   3.821465   .2773119    13.78   0.000     3.277944    4.364986
                65 years or older  |   1.444498   .3071334     4.70   0.000     .8425278    2.046468
                                   |
                            sector |
managerial & technical occupation  |  -.3820282    .149493    -2.56   0.011     -.675029   -.0890273
               skilled non-manual  |   -2.93446   .1628875   -18.02   0.000    -3.253714   -2.615206
                   skilled manual  |  -6.914072   .1672881   -41.33   0.000    -7.241951   -6.586194
        partly skilled occupation  |  -4.267661     .17175   -24.85   0.000    -4.604285   -3.931038
             unskilled occupation  |  -4.637669   .2287794   -20.27   0.000    -5.086069    -4.18927
                                   |
                             _cons |   13.46299   .3555006    37.87   0.000     12.76622    14.15976
-----------------------------------+----------------------------------------------------------------
                           sigma_u |  6.4843857
                           sigma_e |  5.1619774
                               rho |  .61210157   (fraction of variance due to u_i)
----------------------------------------------------------------------------------------------------

.  estimates store re

hausman fe re, sigmamore

Note: the rank of the differenced variance matrix (42) does not equal the number of coefficients being tested (43); be sure this is
        what you expect, or there may be problems computing the test.  Examine the output of your estimators for anything unexpected
        and possibly consider scaling your variables so that the coefficients are on a similar scale.

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |       fe           re         Difference       Std. err.
-------------+----------------------------------------------------------------
   high_qual |
          2  |   -.0928267    -2.226562        2.133735        .4754323
          3  |    .0182819    -2.750473        2.768754        .3774327
          4  |   -.3006534    -3.690913         3.39026        .4961182
          5  |   -.9605771    -4.429453        3.468875          .69742
          9  |   -2.879779    -5.281472        2.401693        .8254855
training_hrs |   -.0000712     .0006149       -.0006861        .0002262
2.illness_~y |   -.0778907     .1494179       -.2273086        .0645323
       2.sex |    .4485456    -1.712939        2.161484        2.495736
    children |
          1  |    .1282714    -.3398704        .4681418        .1489867
          2  |    .4622015    -.2720838        .7342853        .2332787
          3  |    .0442143    -1.174362        1.218577        .3722351
          4  |   -.2602339    -1.975734          1.7155        .6741761
          5  |   -1.442031    -2.071639        .6296089        1.733787
          6  |   -5.016402    -4.674262       -.3421401        2.611666
general_he~h |
          2  |   -.0055532     -.378106        .3725528        .0620958
          5  |   -.2084222    -.9154749        .7070527        .1793842
      region |
          2  |   -.5530689     .2585602       -.8116291         1.44886
          3  |   -2.145961    -.2284908        -1.91747        1.428894
          4  |    2.999986     .0518488        2.948138        1.512468
          5  |    4.373938     .5359982         3.83794        1.603026
          6  |    1.498337     .9415514        .5567855        1.468785
          7  |    1.065125     1.394893        -.329768        1.436505
          8  |    1.369021     1.466192       -.0971707        1.393522
          9  |     .552194    -.0282937        .5804877        1.495377
         10  |     1.09009    -.2318236        1.321914        1.697171
         11  |     .915629     .5588212        .3568077        1.615456
         12  |   -3.344014    -.1259098       -3.218104        3.244252
         age |
          3  |    .6114318     .3611545        .2502773        .3014292
          4  |     1.74053     .9872718        .7532585        .3770252
          5  |    2.709425     2.151108        .5583171        .4526458
          6  |    3.427654     3.617456        -.189802        .4996459
          7  |    4.251303     4.557396       -.3060922        .5359862
          8  |    4.816463     4.976156       -.1596928        .5645565
          9  |    5.164924     5.086969         .077955        .5876835
         10  |    5.225232     4.821479         .403753        .6114583
         11  |    5.330005     4.646858        .6831471         .638696
         12  |    5.379775     3.821465         1.55831        .6746319
         13  |    4.311408     1.444498        2.866909        .7570522
      sector |
          2  |    1.615665    -.3820282        1.997693         .297641
          3  |    .8074404     -2.93446          3.7419         .317206
          4  |   -2.100734    -6.914072        4.813338        .3333586
          5  |    .1310732    -4.267661        4.398735        .3366316
          6  |    .0818114    -4.637669        4.719481        .4300662
------------------------------------------------------------------------------
                          b = Consistent under H0 and Ha; obtained from xtreg.
           B = Inconsistent under Ha, efficient under H0; obtained from xtreg.

Test of H0: Difference in coefficients not systematic

   chi2(42) = (b-B)'[(V_b-V_B)^(-1)](b-B)
            = 612.65
Prob > chi2 = 0.0000

[Carlo Lazzaro]

Guest:
I think that there are at last three issues before concerning with -hausman- results:
1) with such a sky-rocketing number of panels, the -vce(cluster panelid)- standard errors are mandatory (BTW: with -xtreg-, unlike -regress-, you can invoke -robust- to have the very same cluster-robust standard errors that you get from -vece(cluster panelid)-. If you go (as I recommend) that way, plese note the you should switch from -hausman- to the community-contributed module -xtoverid-;
2) are you sure that all te relevant predictors and/or interactions were included in the right-hand side of your regression equation?
3) have you checked that the functional form of the regressand is correctly specified?

In addition:
1) when it comes to -fe- we take a look at within R_Sq (that seems low in your case); when it comes to -re-, it's the turn of between R-sq (that seems acceptable);
2) it's good ahabit to include -timevar- among the predictors when we go -fe-;
3) the issue with using -re- when you should go -fe- is a matter of consistency of the estimator.

[Guest]

Thank you for such a prompt response Carlo Lazzaro! I did as you suggested, but I am encountering "1b: operator invalid r(198)" error. I am not sure where I have gone wrong - have I followed your suggestions correctly?

xtreg wages i.high_qual training_hrs i.illness_disability i.sex i.children i.general_health i.region i.age i.sector, re vce(cluster id)

Random-effects GLS regression                   Number of obs     =     81,014
Group variable: id                              Number of groups  =     45,174

R-squared:                                      Obs per group:
     Within  = 0.0093                                         min =          1
     Between = 0.2259                                         avg =        1.8
     Overall = 0.2153                                         max =          4

                                                Wald chi2(43)     =   11825.03
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

                                                      (Std. err. adjusted for 45,174 clusters in id)
----------------------------------------------------------------------------------------------------
                                   |               Robust
                             wages | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-----------------------------------+----------------------------------------------------------------
                         high_qual |
              Other higher degree  |  -2.226562   .1291234   -17.24   0.000    -2.479639   -1.973484
                      A-level etc  |  -2.750473   .1155294   -23.81   0.000    -2.976906   -2.524039
                         GCSE etc  |  -3.690913   .1140873   -32.35   0.000     -3.91452   -3.467306
              Other qualification  |  -4.429453   .1463206   -30.27   0.000    -4.716236    -4.14267
                 No qualification  |  -5.281472   .1727665   -30.57   0.000    -5.620089   -4.942856
                                   |
                      training_hrs |   .0006149   .0002984     2.06   0.039       .00003    .0011998
                                   |
                illness_disability |
                               no  |   .1494179   .0708485     2.11   0.035     .0105575    .2882783
                                   |
                               sex |
                           female  |  -1.712939   .0851025   -20.13   0.000    -1.879737   -1.546141
                                   |
                          children |
                                1  |  -.3398704    .097535    -3.48   0.000    -.5310355   -.1487054
                                2  |  -.2720838   .1301761    -2.09   0.037    -.5272243   -.0169434
                                3  |  -1.174362   .1976833    -5.94   0.000    -1.561814   -.7869101
                                4  |  -1.975734   .3193612    -6.19   0.000    -2.601671   -1.349797
                                5  |  -2.071639   .7868031    -2.63   0.008    -3.613745   -.5295336
                                6  |  -4.674262   1.116908    -4.19   0.000    -6.863361   -2.485162
                                   |
                    general_health |
                        very good  |   -.378106   .0746783    -5.06   0.000    -.5244728   -.2317392
                         or Poor?  |  -.9154749   .1839044    -4.98   0.000    -1.275921   -.5550288
                                   |
                            region |
                       North West  |   .2585602    .177916     1.45   0.146    -.0901486    .6072691
         Yorkshire and the Humber  |  -.2284908   .1794094    -1.27   0.203    -.5801268    .1231452
                    East Midlands  |   .0518488    .189648     0.27   0.785    -.3198545    .4235521
                    West Midlands  |   .5359982   .1955516     2.74   0.006     .1527241    .9192723
                  East of England  |   .9415514   .1921035     4.90   0.000     .5650355    1.318067
                           London  |   1.394893   .1875851     7.44   0.000     1.027233    1.762553
                       South East  |   1.466192   .1884479     7.78   0.000     1.096841    1.835543
                       South West  |  -.0282937   .1922539    -0.15   0.883    -.4051044     .348517
                            Wales  |  -.2318236   .1853624    -1.25   0.211    -.5951273      .13148
                         Scotland  |   .5588212   .1774352     3.15   0.002     .2110545    .9065879
                 Northern Ireland  |  -.1259098   .1794076    -0.70   0.483    -.4775421    .2257226
                                   |
                               age |
                  18-19 years old  |   .3611545   .2141934     1.69   0.092    -.0586569    .7809658
                  20-24 years old  |   .9872718   .2102286     4.70   0.000     .5752312    1.399312
                  25-29 years old  |   2.151108    .201974    10.65   0.000     1.755246     2.54697
                  30-34 years old  |   3.617456   .2031097    17.81   0.000     3.219368    4.015543
                  35-39 years old  |   4.557396   .2068166    22.04   0.000     4.152042    4.962749
                  40-44 years old  |   4.976156   .2035847    24.44   0.000     4.577137    5.375174
                  45-49 years old  |   5.086969   .2029659    25.06   0.000     4.689163    5.484774
                  50-54 years old  |   4.821479   .2027201    23.78   0.000     4.424155    5.218803
                  55-59 years old  |   4.646858   .2161296    21.50   0.000     4.223251    5.070464
                  60-64 years old  |   3.821465   .2433556    15.70   0.000     3.344497    4.298433
                65 years or older  |   1.444498   .3181577     4.54   0.000     .8209206    2.068076
                                   |
                            sector |
managerial & technical occupation  |  -.3820282   .2324561    -1.64   0.100    -.8376337    .0735774
               skilled non-manual  |   -2.93446   .2312363   -12.69   0.000    -3.387675   -2.481245
                   skilled manual  |  -6.914072   .2401358   -28.79   0.000     -7.38473   -6.443415
        partly skilled occupation  |  -4.267661     .23468   -18.19   0.000    -4.727626   -3.807697
             unskilled occupation  |  -4.637669   .2569436   -18.05   0.000     -5.14127   -4.134069
                                   |
                             _cons |   13.46299   .3379914    39.83   0.000     12.80054    14.12544
-----------------------------------+----------------------------------------------------------------
                           sigma_u |  6.4843857
                           sigma_e |  5.1619774
                               rho |  .61210157   (fraction of variance due to u_i)
----------------------------------------------------------------------------------------------------

. xtoverid
1b:  operator invalid
r(198);

[Carlo Lazzaro]

Guest:
my bad indeed. In my previous post I forgot to mention that, being glorious but a bit old-fashioned, the community-contributed module -xtoverid- does not support -fvvarlist- notation.
The usual fix is to prefix your code with -xi:-:

 xi: xtreg wages i.high_qual training_hrs i.illness_disability i.sex i.children i.general_health i.region i.age i.sector, re vce(cluster id)

[Guest]

Thank you for your help Carlo Lazzaro. However I am encountering another type of error - why could that be the case?

xi: xtreg wages i.high_qual training_hrs i.illness_disability i.sex i.children i.general_health i.region i.age i.sector, re vce(cluster id)
i.high_qual       _Ihigh_qual_1-9     (naturally coded; _Ihigh_qual_1 omitted)
i.illness_dis~y   _Iillness_d_1-2     (naturally coded; _Iillness_d_1 omitted)
i.sex             _Isex_1-2           (naturally coded; _Isex_1 omitted)
i.children        _Ichildren_0-9      (naturally coded; _Ichildren_0 omitted)
i.general_hea~h   _Igeneral_h_1-5     (naturally coded; _Igeneral_h_1 omitted)
i.region          _Iregion_1-12       (naturally coded; _Iregion_1 omitted)
i.age             _Iage_1-13          (naturally coded; _Iage_1 omitted)
i.sector          _Isector_1-6        (naturally coded; _Isector_1 omitted)
note: _Ichildren_7 omitted because of collinearity.
note: _Ichildren_8 omitted because of collinearity.
note: _Ichildren_9 omitted because of collinearity.
note: _Iage_13 omitted because of collinearity.

Random-effects GLS regression                   Number of obs     =     81,014
Group variable: id                              Number of groups  =     45,174

R-squared:                                      Obs per group:
     Within  = 0.0093                                         min =          1
     Between = 0.2259                                         avg =        1.8
     Overall = 0.2153                                         max =          4

                                                Wald chi2(43)     =   11825.03
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

                                 (Std. err. adjusted for 45,174 clusters in id)
-------------------------------------------------------------------------------
              |               Robust
        wages | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
--------------+----------------------------------------------------------------
_Ihigh_qual_2 |  -2.226562   .1291234   -17.24   0.000    -2.479639   -1.973484
_Ihigh_qual_3 |  -2.750473   .1155294   -23.81   0.000    -2.976906   -2.524039
_Ihigh_qual_4 |  -3.690913   .1140873   -32.35   0.000     -3.91452   -3.467306
_Ihigh_qual_5 |  -4.429453   .1463206   -30.27   0.000    -4.716236    -4.14267
_Ihigh_qual_9 |  -5.281472   .1727665   -30.57   0.000    -5.620089   -4.942856
 training_hrs |   .0006149   .0002984     2.06   0.039       .00003    .0011998
_Iillness_d_2 |   .1494179   .0708485     2.11   0.035     .0105575    .2882783
      _Isex_2 |  -1.712939   .0851025   -20.13   0.000    -1.879737   -1.546141
 _Ichildren_1 |  -.3398704    .097535    -3.48   0.000    -.5310355   -.1487054
 _Ichildren_2 |  -.2720838   .1301761    -2.09   0.037    -.5272243   -.0169434
 _Ichildren_3 |  -1.174362   .1976833    -5.94   0.000    -1.561814   -.7869101
 _Ichildren_4 |  -1.975734   .3193612    -6.19   0.000    -2.601671   -1.349797
 _Ichildren_5 |  -2.071639   .7868031    -2.63   0.008    -3.613745   -.5295336
 _Ichildren_6 |  -4.674262   1.116908    -4.19   0.000    -6.863361   -2.485162
 _Ichildren_7 |          0  (omitted)
 _Ichildren_8 |          0  (omitted)
 _Ichildren_9 |          0  (omitted)
_Igeneral_h_2 |   -.378106   .0746783    -5.06   0.000    -.5244728   -.2317392
_Igeneral_h_5 |  -.9154749   .1839044    -4.98   0.000    -1.275921   -.5550288
   _Iregion_2 |   .2585602    .177916     1.45   0.146    -.0901486    .6072691
   _Iregion_3 |  -.2284908   .1794094    -1.27   0.203    -.5801268    .1231452
   _Iregion_4 |   .0518488    .189648     0.27   0.785    -.3198545    .4235521
   _Iregion_5 |   .5359982   .1955516     2.74   0.006     .1527241    .9192723
   _Iregion_6 |   .9415514   .1921035     4.90   0.000     .5650355    1.318067
   _Iregion_7 |   1.394893   .1875851     7.44   0.000     1.027233    1.762553
   _Iregion_8 |   1.466192   .1884479     7.78   0.000     1.096841    1.835543
   _Iregion_9 |  -.0282937   .1922539    -0.15   0.883    -.4051044     .348517
  _Iregion_10 |  -.2318236   .1853624    -1.25   0.211    -.5951273      .13148
  _Iregion_11 |   .5588212   .1774352     3.15   0.002     .2110545    .9065879
  _Iregion_12 |  -.1259098   .1794076    -0.70   0.483    -.4775421    .2257226
      _Iage_2 |  -1.444498   .3181577    -4.54   0.000    -2.068076   -.8209206
      _Iage_3 |  -1.083344   .2938119    -3.69   0.000    -1.659204   -.5074829
      _Iage_4 |  -.4572263   .2795858    -1.64   0.102    -1.005204    .0907518
      _Iage_5 |   .7066099   .2763311     2.56   0.011     .1650109    1.248209
      _Iage_6 |   2.172958   .2788041     7.79   0.000     1.626512    2.719404
      _Iage_7 |   3.112897   .2813211    11.07   0.000     2.561518    3.664277
      _Iage_8 |   3.531657   .2780079    12.70   0.000     2.986772    4.076543
      _Iage_9 |    3.64247   .2767357    13.16   0.000     3.100078    4.184862
     _Iage_10 |   3.376981   .2751978    12.27   0.000     2.837603    3.916359
     _Iage_11 |    3.20236   .2804129    11.42   0.000     2.652761    3.751959
     _Iage_12 |   2.376967   .2801664     8.48   0.000     1.827851    2.926083
     _Iage_13 |          0  (omitted)
   _Isector_2 |  -.3820282   .2324561    -1.64   0.100    -.8376337    .0735774
   _Isector_3 |   -2.93446   .2312363   -12.69   0.000    -3.387675   -2.481245
   _Isector_4 |  -6.914072   .2401358   -28.79   0.000     -7.38473   -6.443415
   _Isector_5 |  -4.267661     .23468   -18.19   0.000    -4.727626   -3.807697
   _Isector_6 |  -4.637669   .2569436   -18.05   0.000     -5.14127   -4.134069
        _cons |   14.90749     .39036    38.19   0.000     14.14239    15.67258
--------------+----------------------------------------------------------------
      sigma_u |  6.4843857
      sigma_e |  5.1619774
          rho |  .61210157   (fraction of variance due to u_i)
-------------------------------------------------------------------------------

. xtoverid
o. operator not allowed
r(101);

.