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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 16:26:26 -0500

```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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```