# RE: st: What distribution are the coefs of Random-effects GLS regression ?

 From "Feiveson, Alan H. (JSC-SK311)" To Subject RE: st: What distribution are the coefs of Random-effects GLS regression ? Date Thu, 9 Mar 2006 11:48:33 -0600

```We often make the assumption that these coeficient estimates are
normally distributed with the given standard errors as SD, but this is
only true aymptotically. For a finite number of clusters, almost any
distribution is possible. If the number of clusters is small (say under
50), getting the empirical distribution of the coeffs via bootstrap is
probably a better apporach than assuming normality.

Al Feiveson

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Austin
Nichols
Sent: Thursday, March 09, 2006 9:48 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: What distribution are the coefs of Random-effects GLS
regression ?

The heading on each column of the table of estimates shown in your post
gives the answer: z implies std normal in most settings.
.di 2*(1-norm(abs(-1.45)))
gives an approx. answer, subject to rounding error in z.
. di 2*(1-norm(abs(-.2144353 /.1475938))) would do better, and . di
2*(1-norm(abs(_b[grant]/_se[grant])))
better still, I would guess.

On 3/9/06, ronggui <ronggui.huang@gmail.com> wrote:
> . xtreg  lscrap d88 d89 grant grant_1,re i(fcode)
>
------------------------------------------------------------------------
------
>      lscrap |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
> -------------+--------------------------------------------------------
> -------------+--------
>       grant |  -.2144353   .1475938    -1.45   0.146    -.5037139
.0748433

> I thought it was T-distribution, but I can't get the exact result with

> the output.
> for example, the coef of grant.
> . dis ttail(157,1.45)*2
> .14905327

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```