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 <[email protected]>:
> 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:
> * http://www.stata.com/support/faqs/res/findit.html
> * http://www.stata.com/support/statalist/faq
> * http://www.ats.ucla.edu/stat/stata/
>
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: [email protected]
web: http://www.sml.hw.ac.uk/ecomes
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