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RE: st: sigma_u = 0 in xtreg, re


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
> >>>
> >>> .
> >>>
> >>>
> >>> *
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> >>>
> >>
> >>
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> 
> 
> 
> --
> Stas Kolenikov, also found at http://stas.kolenikov.name 
> Small print: I use this email account for mailing lists only.
> 
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> 


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