st: hausman speficiation test using both xthaus and hausman

["Jun Xu" <mystata@hotmail.com>]

Why the results from the two commands xthaus (old command) and hausman (new 
command in version 8) are different in the following example even though the 
two columns of estiamtes and the third column of differences in estiamtes 
are the same, but the chi2 test statistic is completely different.  Thanks a 
lot.

Jun Xu
Department of Sociology
Indiana University at Bloomington

****************************************************************
* fixed effects
. xtreg lcrmrte lprbarr lprbconv lprbpris lavgsen lpolpc /*

>    */ d82 d83 d84 d85 d86 d87, fe
Fixed-effects (within) regression               Number of obs      =       
630
Group variable (i): county                      Number of groups   =        
90

R-sq:  within  = 0.4342                         Obs per group: min =         
7
      between = 0.4066                                        avg =       
7.0
      overall = 0.4042                                        max =         
7

                                               F(11,529)          =     
36.91
corr(u_i, Xb)  = 0.2068                         Prob > F           =    
0.0000

------------------------------------------------------------------------------
    lcrmrte |      Coef.   Std. Err.      t    P>|t|     [95% Conf. 
Interval]
-------------+----------------------------------------------------------------
    lprbarr |  -.3597944   .0324192   -11.10   0.000    -.4234806   
-.2961083
   lprbconv |  -.2858733   .0212173   -13.47   0.000    -.3275538   
-.2441928
   lprbpris |  -.1827812   .0324611    -5.63   0.000    -.2465496   
-.1190127
    lavgsen |  -.0044879   .0264471    -0.17   0.865    -.0564421    
.0474663
     lpolpc |   .4241142   .0263661    16.09   0.000     .3723191    
.4759093
        d82 |   .0125802   .0215416     0.58   0.559    -.0297373    
.0548977
        d83 |  -.0792813   .0213399    -3.72   0.000    -.1212027   
-.0373598
        d84 |  -.1177281   .0216145    -5.45   0.000    -.1601888   
-.0752673
        d85 |  -.1119561   .0218459    -5.12   0.000    -.1548715   
-.0690407
        d86 |  -.0818268   .0214266    -3.82   0.000    -.1239185   
-.0397352
        d87 |  -.0404704   .0210392    -1.92   0.055    -.0818011    
.0008602
      _cons |  -1.604135   .1685739    -9.52   0.000    -1.935292   
-1.272979
-------------+----------------------------------------------------------------
    sigma_u |  .43487416
    sigma_e |  .13871215
        rho |  .90765322   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0:     F(89, 529) =    45.87             Prob > F = 
0.0000

.
. * version 8
. estimates store fixed

.
. * random effects
. xtreg  lcrmrte lprbarr lprbconv lprbpris lavgsen lpolpc /*

>    */ d82 d83 d84 d85 d86 d87, re
........random effects output..........
.......................................
.......................................
.
. * version 8
. estimates store random

.
. * Hausman specification test
. xthaus
(Warning:  xthausman is no longer a supported command; use -hausman-.  For 
instructions, see help hausman.)


Hausman specification test

               ---- Coefficients ----
            |      Fixed       Random
    lcrmrte |    Effects      Effects       Difference
-------------+-----------------------------------------
    lprbarr |  -.3597944    -.4252097         .0654153
   lprbconv |  -.2858733    -.3271464         .0412731
   lprbpris |  -.1827812    -.1793507        -.0034305
    lavgsen |  -.0044879    -.0083696         .0038816
     lpolpc |   .4241142     .4294148        -.0053005
        d82 |   .0125802     .0137442         -.001164
        d83 |  -.0792813     -.075388        -.0038933
        d84 |  -.1177281    -.1130975        -.0046306
        d85 |  -.1119561    -.1057261          -.00623
        d86 |  -.0818268    -.0795307        -.0022962
        d87 |  -.0404704    -.0424581         .0019876

   Test:  Ho:  difference in coefficients not systematic

                chi2( 11) = (b-B)'[S^(-1)](b-B), S = (S_fe - S_re)
                          =   121.31
                Prob>chi2 =     0.0000

.
. * version 8
. hausman fixed random

                ---- Coefficients ----
            |      (b)          (B)            (b-B)     
sqrt(diag(V_b-V_B))
            |     fixed        random       Difference          S.E.
-------------+----------------------------------------------------------------
    lprbarr |   -.3597944    -.4252097        .0654153        .0059393
   lprbconv |   -.2858733    -.3271464        .0412731        .0032245
   lprbpris |   -.1827812    -.1793507       -.0034305               .
    lavgsen |   -.0044879    -.0083696        .0038816               .
     lpolpc |    .4241142     .4294148       -.0053005        .0033778
        d82 |    .0125802     .0137442        -.001164               .
        d83 |   -.0792813     -.075388       -.0038933               .
        d84 |   -.1177281    -.1130975       -.0046306               .
        d85 |   -.1119561    -.1057261         -.00623               .
        d86 |   -.0818268    -.0795307       -.0022962               .
        d87 |   -.0404704    -.0424581        .0019876               .
------------------------------------------------------------------------------
                          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(11) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                         =   -36.92    chi2<0 ==> model fitted on these
                                       data fails to meet the asymptotic
                                       assumptions of the Hausman test;
                                       see suest for a generalized test





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