Hi everybody. Let me phrase my question a little more precisely.
In a fixed effects estimation using a balanced panel, the usual
estimate of the error variance is RSS * 1/(NT-N-k), where N is the
number of observational units, T is the number of periods, and k is
the number of regressors aside from the fixed effects. The
subtraction of N in the denominator reflects the fact that the N
fixed effects are being estimated (implicitly or explicitly).
The subtraction of k is a standard finite sample adjustment. My
expectation with xtivreg would have been that -small- would use
1/(NT-N-k)
and report t stats, and the default behaviour of xtivreg would be to
use
1/(NT-N)
and report z stats. In fact, 1/(NT-N-k) seems to be used for both,
which is why the same standard errors appear regardless of whether or
not -small- is specified.
This strikes me as odd. Or am I missing something?
--Mark
To: Statalist <[email protected]>
Subject: st: xtivreg question - when is small not small?
Date sent: Fri, 15 Jul 2005 23:30:53 +0100 (BST)
From: Mark Schaffer <[email protected]>
Copies to: Mark Schaffer <[email protected]>
Send reply to: [email protected]
> Hi all. I've just encountered something peculiar about xtivreg (v7 and
> v8.2). According to the manuals and help file,
>
> "small specifies that t statistics should be reported instead of Z
> statistics and F statistics instead of chi-squared statistics."
>
> The peculiar thing is that the t statistics and standard errors are
> numerically identical to the z statistics and SEs. Using the manual dataset,
>
> . xtivreg ln_w age* not_smsa (tenure = union south) , fe i(idcode)
>
> -----------------------------------------------------
> ln_wage | Coef. Std. Err. z P>|z|
> -------------+---------------------------------------
> tenure | .2452291 .0386354 6.35 0.000
>
> . xtivreg ln_w age* not_smsa (tenure = union south) , fe i(idcode) small
>
> -----------------------------------------------------
> ln_wage | Coef. Std. Err. t P>|t|
> -------------+---------------------------------------
> tenure | .2452291 .0386354 6.35 0.000
>
> I had thought that there would be an additional degrees-of-freedom
> adjustment with the -small- option, but apparently not - the only difference
> is that the column heading is "t" instead of "z". Anybody have any idea why?
>
> --Mark
>
> Prof. Mark Schaffer
> Director, CERT
> Department of Economics
> School of Management & Languages
> Heriot-Watt University, Edinburgh EH14 4AS
> tel +44-131-451-3494 / fax +44-131-451-3294
> email: [email protected]
> web: http://www.sml.hw.ac.uk/ecomes
>
> -------------------------------------------------------------------
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>
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>
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>
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Prof. Mark E. Schaffer
Director
Centre for Economic Reform and Transformation
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS UK
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