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From |
"Schaffer, Mark E" <[email protected]> |

To |
<[email protected]> |

Subject |
RE: st: sigma_u = 0 in xtreg, re |

Date |
Mon, 29 Aug 2011 23:05:38 +0100 |

```
I think it's true in finite samples as well. At least, that's how I read what Baltagi has to say about it in chap 2 of his textbook ("Econometric Analysis of Panel Data" - it's in the section on the random effects model).
--Mark
> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]] On Behalf Of
> Stas Kolenikov
> Sent: 29 August 2011 22:26
> To: [email protected]
> Subject: Re: st: sigma_u = 0 in xtreg, re
>
> John,
>
> certainly so asymptotically when the true sigma_u = 0.
> Whether that is exactly true in finite samples, I don't know,
> although at the face of it, it looks reasonable:
>
> set seed 1234
> set obs 100
> gen id = _n
> gen ni = rpoisson(5) + 1
> expand ni
> gen x = uniform()
> gen y = x + rnormal()
> xtreg y x, i(id)
> reg y x
>
> On Mon, Aug 29, 2011 at 4:14 PM, John Antonakis
> <[email protected]> wrote:
> > One clarification; when rho = 0 aren't these estimates
> simply OLS estimates?
> >
> > Best,
> > J.
> >
> > __________________________________________
> >
> > Prof. John Antonakis
> > Faculty of Business and Economics
> > Department of Organizational Behavior
> > University of Lausanne
> > Internef #618
> > CH-1015 Lausanne-Dorigny
> > Switzerland
> > Tel ++41 (0)21 692-3438
> > Fax ++41 (0)21 692-3305
> > http://www.hec.unil.ch/people/jantonakis
> >
> > Associate Editor
> > The Leadership Quarterly
> > __________________________________________
> >
> >
> > On 29.08.2011 22:50, Stas Kolenikov wrote:
> >>
> >> Note that you have a very decent R^2, especially the
> between one. It
> >> looks, hence, that all of the bewteen-panel variability in Y is
> >> explained by the between-panel variability in X's (the ICC's were
> >> quite similar for each of the variables), so there indeed
> is little
> >> left that needs explaining. -xtsum- is somewhat misleading
> here, as
> >> this is a marginal measure, not a conditional one (which is what
> >> matters for the regression).
> >>
> >> Technically speaking, you are hitting a corner solution
> for sigma_u.
> >> In the simplest form of the estimator for sigma_u, it is formed as
> >> [mean total square] - [mean within square], so substraction of two
> >> non-negative quantities gave you a negative quantity (which was
> >> truncated upwards to zero). More elaborate estimators exist that
> >> guarantee both within and between sigmas to be positive, but for a
> >> vast majority of situations, the simple one should do just
> fine, so
> >> that's what -xtreg, re- does.
> >>
> >> On Mon, Aug 29, 2011 at 1:45 PM, Lloyd
> Dumont<[email protected]>
> >> wrote:
> >>>
> >>> Hello, Statalist.
> >>>
> >>> I am a little confused by the output from an -xtreg, re- estimate.
> >>>
> >>> Basically, I end up with sigma_u = 0, which of course
> yields rho = 0.
> >>> That seems very odd to me. I would guess that that should only
> >>> happen if there is no between-subject variation. But, (I
> think) I
> >>> can tell from examining the data that that is not the case.
> >>>
> >>> I have tried to create a mini example... First, I will
> show the xtreg
> >>> results. Then, I will show you what I think is the evidence that
> >>> there really IS some between-subject variation.
> >>>
> >>> Am I missing something obvious here? Thank you for your help and
> >>> suggestions. Lloyd Dumont
> >>>
> >>>
> >>> . xtreg Y X, re
> >>>
> >>> Random-effects GLS regression Number of
> obs =
> >>> 3133
> >>> Group variable: ID Number of
> groups =
> >>> 31
> >>>
> >>> R-sq: within = 0.4333 Obs per
> group: min =
> >>> 1
> >>> between = 0.8278
> avg =
> >>> 101.1
> >>> overall = 0.4579
> max =
> >>> 124
> >>>
> >>> Wald
> chi2(1) =
> >>> 2644.38
> >>> corr(u_i, X) = 0 (assumed) Prob>
> chi2 =
> >>> 0.0000
> >>>
> >>>
> >>>
> --------------------------------------------------------------------
> >>> ----------
> >>> Y | Coef. Std. Err. z P>|z|
> [95% Conf.
> >>> Interval]
> >>>
> >>>
> -------------+------------------------------------------------------
> >>> -------------+----------
> >>> X | -.0179105 .0003483 -51.42 0.000 -.0185932
> >>> -.0172279
> >>> _cons | 1.004496 .0017687 567.92 0.000 1.001029
> >>> 1.007963
> >>>
> >>>
> -------------+------------------------------------------------------
> >>> -------------+----------
> >>> sigma_u | 0
> >>> sigma_e | .07457648
> >>> rho | 0 (fraction of variance due to u_i)
> >>>
> >>>
> --------------------------------------------------------------------
> >>> ----------
> >>>
> >>>
> >>>
> >>>
> >>> . xtsum X
> >>>
> >>> Variable | Mean Std. Dev. Min Max |
> >>> Observations
> >>>
> >>>
> -----------------+--------------------------------------------+-----
> >>>
> -----------------+--------------------------------------------+-----
> >>>
> -----------------+--------------------------------------------+-----
> >>> -----------------+--------------------------------------------+-
> >>> X overall | 3.277883 3.875116 0
> 42.5 |
> >>> N =
> >>> 3137
> >>> between | 1.286754 0
> 6.890338 | n
> >>> =
> >>> 31
> >>> within | 3.729614 -3.612455
> 42.24883 | T-bar
> >>> =
> >>> 101.194
> >>>
> >>>
> >>>
> >>> . xtsum Y
> >>>
> >>> Variable | Mean Std. Dev. Min Max |
> >>> Observations
> >>>
> >>>
> -----------------+--------------------------------------------+-----
> >>>
> -----------------+--------------------------------------------+-----
> >>>
> -----------------+--------------------------------------------+-----
> >>> -----------------+--------------------------------------------+-
> >>> Y overall | .9457124 .1025887 0
> 1 |
> >>> N =
> >>> 3133
> >>> between | .0315032 .8387879
> 1 | n
> >>> =
> >>> 31
> >>> within | .0985757 -.0235858
> 1.106925 | T-bar
> >>> =
> >>> 101.065
> >>>
> >>> .
> >>>
> >>>
> >>> *
> >>> * For searches and help try:
> >>> * http://www.stata.com/help.cgi?search
> >>> * http://www.stata.com/support/statalist/faq
> >>> * http://www.ats.ucla.edu/stat/stata/
> >>>
> >>
> >>
> > *
> > * For searches and help try:
> > * http://www.stata.com/help.cgi?search
> > * http://www.stata.com/support/statalist/faq
> > * http://www.ats.ucla.edu/stat/stata/
> >
>
>
>
> --
> Stas Kolenikov, also found at http://stas.kolenikov.name
> Small print: I use this email account for mailing lists only.
>
> *
> * For searches and help try:
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> * http://www.stata.com/support/statalist/faq
> * http://www.ats.ucla.edu/stat/stata/
>
--
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registered under charity number SC000278.
*
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```

**Follow-Ups**:**Re: st: sigma_u = 0 in xtreg, re***From:*John Antonakis <[email protected]>

**References**:**st: sigma_u = 0 in xtreg, re***From:*Lloyd Dumont <[email protected]>

**Re: st: sigma_u = 0 in xtreg, re***From:*Stas Kolenikov <[email protected]>

**Re: st: sigma_u = 0 in xtreg, re***From:*John Antonakis <[email protected]>

**Re: st: sigma_u = 0 in xtreg, re***From:*Stas Kolenikov <[email protected]>

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