st: Question about using the Hausman test after XTREG, FE and XTREG, RE

[Jeannette Wicks-Lim <janetlim@econs.umass.edu>]

Hi,

I'm trying to run the Hausman test to compare my estimates from XTREG, FE to 
those from XTREG, RE, as described in the STATA 5.0 Reference Manual.

I get the following error message after submitting the xthaus command:

"Estimate of sigma_u = 0, random-effects estimator has degenerated to pooled
OLS and the Wald test from xthausman may not be appropriate.  See [R] 
hausman
for a more general implementation of the Hausman test."

1) Can you tell me why I'm getting this message? Does it indicate that there 
is something wrong with my specification or my data (causing sigma_u to 
equal 0)?
2) Does this message mean that when I use xtreg, re with this model and 
data, the results are actually produced from a pooled OLS estimation?
3) I also tried implementing the test suggested in the FAQ topic "What is 
the between estimator?" that's available from your website. And this seemed 
to work fine (that is, I got no error messages). Does the error message 
above indicate that this test (using "test" to compare coefficients) is not 
valid?

Here's some of my output, in case it helps (please ignore that the dependent 
variable changes from dq10 to dq5 in the two examples, either way, I get the 
same error message). First, the regresion estimates from XTREG, RE followed 
by  XTHAUS. Second, my attempt at implementing the test suggested in the FAQ 
Topic (Title: Between Estimators, Author: William Gould, StataCorp, Date: 
March 2001).

Thanks very much!
Jeannette


**********************************************************************************
. xtreg dq10

> damin1 damin0  propda propida
> , re ;
Random-effects GLS regression                   Number of obs      = 
1900
Group variable (i): gestcen                     Number of groups   = 
50

R-sq:  within  = 0.2076                         Obs per group: min = 
38
      between = 0.1334                                        avg = 
38.0
      overall = 0.2018                                        max = 
38

Random effects u_i ~ Gaussian                   Wald chi2(4)       = 
479.17
corr(u_i, X)       = 0 (assumed)                Prob > chi2        = 
0.0000

------------------------------------------------------------------------------
       dq10 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. 
Interval]
-------------+----------------------------------------------------------------
     damin1 |   .0203958    .036911     0.55   0.581    -.0519485 
.0927401
     damin0 |   .0649504   .0194159     3.35   0.001     .0268959 
.103005
     propda |   .4991502   .0970026     5.15   0.000     .3090285 
.6892719
    propida |   .0449133   .0253814     1.77   0.077    -.0048334 
.0946599
      _cons |   .0269997   .0008809    30.65   0.000     .0252731 
.0287263
-------------+----------------------------------------------------------------
    sigma_u |          0
    sigma_e |  .03232517
        rho |          0   (fraction of variance due to u_i)
------------------------------------------------------------------------------

.
end of do-file

. do "C:\DOCUME~1\JANETL~1.PRO\LOCALS~1\Temp\STD00000000.tmp"

. xthaus
Estimate of sigma_u = 0, random-effects estimator has degenerated to pooled
OLS and the Wald test from xthausman may not be appropriate.  See [R] 
hausman
for a more general implementation of the Hausman test.

**********************************************************************************

. egen avgx1=mean(damin1), by(gestcen)
(40 missing values generated)

. gen deltax1=damin1 -avgx1
(40 missing values generated)

.
. egen avgx2=mean(damin0), by(gestcen)

. gen deltax2=damin0 -avgx2
(23 missing values generated)

.
. egen avgx3=mean(propda), by(gestcen)

. gen deltax3=propda -avgx3
(20 missing values generated)

.
. egen avgx4=mean(propida), by(gestcen)

. gen deltax4=propida -avgx4
(20 missing values generated)

.
. xtreg dq5 avgx1 deltax1 avgx2 deltax2 avgx3 deltax3 avgx4 deltax4, re

Random-effects GLS regression                   Number of obs      = 
1900
Group variable (i): gestcen                     Number of groups   = 
50

R-sq:  within  = 0.1816                         Obs per group: min = 
38
      between = 0.3040                                        avg = 
38.0
      overall = 0.1828                                        max = 
38

Random effects u_i ~ Gaussian                   Wald chi2(8)       = 
422.93
corr(u_i, X)       = 0 (assumed)                Prob > chi2        = 
0.0000

------------------------------------------------------------------------------
        dq5 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. 
Interval]
-------------+----------------------------------------------------------------
      avgx1 |  -.0404122   .2479204    -0.16   0.871    -.5263273 
.445503
    deltax1 |   .2531377   .0551546     4.59   0.000     .1450367 
.3612387
      avgx2 |   .0682897    .386916     0.18   0.860    -.6900517 
.8266311
    deltax2 |   .0726974   .0274479     2.65   0.008     .0189005 
.1264942
      avgx3 |   .6094803   .7170621     0.85   0.395    -.7959356 
2.014896
    deltax3 |   .5501359   .1400594     3.93   0.000     .2756245 
.8246474
      avgx4 |  -.0359376   .1914227    -0.19   0.851    -.4111191 
.339244
    deltax4 |  -.0011282   .0365208    -0.03   0.975    -.0727076 
.0704512
      _cons |   .0312865   .0061887     5.06   0.000      .019157 
.0434161
-------------+----------------------------------------------------------------
    sigma_u |          0
    sigma_e |   .0455745
        rho |          0   (fraction of variance due to u_i)
------------------------------------------------------------------------------

.
end of do-file

. test avgx1 = deltax1

( 1)  avgx1 - deltax1 = 0

          chi2(  1) =    1.35
        Prob > chi2 =    0.2460

. do "C:\DOCUME~1\JANETL~1.PRO\LOCALS~1\Temp\STD00000000.tmp"

.
. test avgx1 = deltax1

( 1)  avgx1 - deltax1 = 0

          chi2(  1) =    1.35
        Prob > chi2 =    0.2460

. test avgx2 = deltax2, accum

( 1)  avgx1 - deltax1 = 0
( 2)  avgx2 - deltax2 = 0

          chi2(  2) =    1.51
        Prob > chi2 =    0.4698

. test avgx3 = deltax3, accum

( 1)  avgx1 - deltax1 = 0
( 2)  avgx2 - deltax2 = 0
( 3)  avgx3 - deltax3 = 0

          chi2(  3) =    2.43
        Prob > chi2 =    0.4882

. test avgx4 = deltax4, accum

( 1)  avgx1 - deltax1 = 0
( 2)  avgx2 - deltax2 = 0
( 3)  avgx3 - deltax3 = 0
( 4)  avgx4 - deltax4 = 0

          chi2(  4) =    5.18
        Prob > chi2 =    0.2697

.
.
end of do-file
**********************************************************************************


Jeannette Wicks-Lim
Department of Economics
University of Massachusetts, Amherst
(413) 577-0820 
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