re:re: re:st: Hausman test

[Christopher Baum <kit.baum@bc.edu>]

<>
Random-effects GLS regression                   Number of obs      =       416
Group variable: fam                             Number of groups   =         9

R-sq:  within  = 0.1185                         Obs per group: min =        27
       between = 0.8693                                        avg =      46.2
       overall = 0.6005                                        max =        73

                                                Wald chi2(9)       =    610.15
corr(u_i, X)   = 0 (assumed)                    Prob > chi2        =    0.0000

------------------------------------------------------------------------------
        chol |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          l1 |   6.341376   1.317354     4.81   0.000      3.75941    8.923342
          l2 |   -.170823   .0489787    -3.49   0.000    -.2668195   -.0748265
          l3 |   .0016893    .000569     2.97   0.003      .000574    .0028046
       2.sex |    3.77881   .8776635     4.31   0.000     2.058621    5.498999
             |
      marker |
          2  |  -1.579155   1.217692    -1.30   0.195    -3.965788    .8074783
          3  |  -1.128749    1.26016    -0.90   0.370    -3.598617     1.34112
          4  |   1.295496   2.350917     0.55   0.582    -3.312217    5.903209
          5  |  -.8996998   1.409237    -0.64   0.523    -3.661753    1.862353
          6  |   11.06828   3.289858     3.36   0.001     4.620282    17.51629
             |
       _cons |  -16.71301    11.0348    -1.51   0.130    -38.34082    4.914797
-------------+----------------------------------------------------------------
     sigma_u |          0
     sigma_e |  8.1937869
         rho |          0   (fraction of variance due to u_i)
------------------------------------------------------------------------------

You have a corner solution. As you know, the estimates of the two error variances in RE are 'backed out' from
estimates of other forms of the model. In your case, the estimate of sigma_u (and its square) is 0.0. That
is nonsensical, as the FE form of the same model gives a meaningfully positive variance and the F-test for unobserved
heterogeneity shows: 

     sigma_u |  5.0827273
     sigma_e |  8.1937869
         rho |  .27786908   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0:     F(8, 398) =     9.45              Prob > F = 0.0000

indicating that there are significant panel-specific effects (that is, unobserved heterogeneity). A further reason
to disregard the RE estimates, as you can't very well report the error components variances with one of them
equal to zero (which it patently should not be; if it truly was, pooled OLS would be appropriate, but FE says it
surely would not be so). 

This is probably the reason for the singularity of the Hausman VCE.

Cheers
Kit

Kit Baum   |   Boston College Economics & DIW Berlin   |   http://ideas.repec.org/e/pba1.html
                             An Introduction to Stata Programming  |   http://www.stata-press.com/books/isp.html
  An Introduction to Modern Econometrics Using Stata  |   http://www.stata-press.com/books/imeus.html


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