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# Re: st: sigma_u = 0 in xtreg, re

 From Stas Kolenikov To statalist@hsphsun2.harvard.edu Subject Re: st: sigma_u = 0 in xtreg, re Date Mon, 29 Aug 2011 15:50:11 -0500

```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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>

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

*
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