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


From   Mark Schaffer <M.E.Schaffer@hw.ac.uk>
To   statalist@hsphsun2.harvard.edu, Jeannette Wicks-Lim <janetlim@econs.umass.edu>
Subject   Re: st: Question about using the Hausman test after XTREG, FE and XTREG, RE
Date   Sat, 25 Sep 2004 09:50:04 +0100 (BST)

Jeannette,

This questions comes up from time to time on Statalist, e.g.,

http://www.stata.com/statalist/archive/2004-02/msg00644.html

The answers to your questions are: (1) this can happen with finite samples 
and doesn't necessarily mean there's anything "wrong"; (2) yes; and (3) 
because xtreg,re is degenerating to OLS, your test is a test of the 
difference between the between-effects estimator and OLS.

If you use the -sa- option with xtreg,re, you might get an estimate of 
sigma_u > 0.  Worth a try.

--Mark

Quoting 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 
> 
> *
> *   For searches and help try:
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> 



Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3008
email: m.e.schaffer@hw.ac.uk
web: http://www.sml.hw.ac.uk/ecomes
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