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From |
"Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

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: owner-statalist@hsphsun2.harvard.edu > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of > Stas Kolenikov > Sent: 29 August 2011 22:26 > To: statalist@hsphsun2.harvard.edu > 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 > <John.Antonakis@unil.ch> 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<lloyddumont@yahoo.com> > >> 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: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > -- Heriot-Watt University is a Scottish charity registered under charity number SC000278. * * 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/

**Follow-Ups**:**Re: st: sigma_u = 0 in xtreg, re***From:*John Antonakis <John.Antonakis@unil.ch>

**References**:**st: sigma_u = 0 in xtreg, re***From:*Lloyd Dumont <lloyddumont@yahoo.com>

**Re: st: sigma_u = 0 in xtreg, re***From:*Stas Kolenikov <skolenik@gmail.com>

**Re: st: sigma_u = 0 in xtreg, re***From:*John Antonakis <John.Antonakis@unil.ch>

**Re: st: sigma_u = 0 in xtreg, re***From:*Stas Kolenikov <skolenik@gmail.com>

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