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

 From John Antonakis To statalist@hsphsun2.harvard.edu Subject Re: st: sigma_u = 0 in xtreg, re Date Mon, 29 Aug 2011 23:14:27 +0200

```Hi Stas:

One clarification; when rho = 0 aren't these estimates simply OLS estimates?

Best,
J.

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Prof. John Antonakis
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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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