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Re: st: sigma_u = 0 in xtreg, re
From
Lloyd Dumont <[email protected]>
To
"[email protected]" <[email protected]>
Subject
Re: st: sigma_u = 0 in xtreg, re
Date
Wed, 31 Aug 2011 09:04:51 -0700 (PDT)
Thank you all very, very much for pondering this for me. You have been extremely helpful. Lloyd
----- Original Message -----
From: John Antonakis <[email protected]>
To: [email protected]
Cc:
Sent: Tuesday, August 30, 2011 2:18 AM
Subject: Re: st: sigma_u = 0 in xtreg, re
OK. Thus, Lloyed might as well use pooled OLS with cluster robust
standard errors, right?
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 30.08.2011 00:05, Schaffer, Mark E wrote:
> 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: [email protected]
>> [mailto:[email protected]] On Behalf Of
>> Stas Kolenikov
>> Sent: 29 August 2011 22:26
>> To: [email protected]
>> 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
>> <[email protected]> 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<[email protected]>
>>>> 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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