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Re: st: rho, sigma_u, sigma_e in xtreg
From
Misha Spisok <[email protected]>
To
[email protected]
Subject
Re: st: rho, sigma_u, sigma_e in xtreg
Date
Fri, 30 Apr 2010 13:55:15 -0700
Here's my take, with some help from the [XT] manual.
The [XT] manual gives the following for the random effects model:
between: corr(x_bar_i*beta_hat, y_bar_i)^2
within: corr{ (x_it - x_bar_i)*beta_hat, y_it - y_bar_i)}^2
overall: corr(x_it*beta_hat, y_it)^2
u refers to the individual component
e refers to the idiosyncratic component
e.g., y_it = alpha + x_it*beta + nu_i + epsilon_it
with u corresponding to nu and e to epsilon.
rho, explained in words in the output, is
rho = (sigma_u)^2/[(sigma_u)^2 + (sigma_e)^2]
sigma_u and sigma_e are estimates of the standard deviation of nu and epsilon.
For example,
display .02692048^2/(.02692048^2 + .0829595^2)
or, more generally,
di e(sigma_u)^2/(e(sigma_u)^2 + e(sigma_e)^2)
ought to give you rho.
On Fri, Apr 30, 2010 at 1:34 PM, Katherine Packman <[email protected]> wrote:
> I have somewhat of a basic question.
>
> I am running xtreg assuming random effects for 150 observations
> (cross-section is 10 and timeseries is 15). I was wondering if anyone could
> explain what rho, sigma_u and sigma_e mean. This is an example of my output:
>
>
> . xtreg pmor dumcov dumuni dum_cu lnprd prduni
>
> Random-effects GLS regression Number of obs =
> 150
> Group variable: session Number of groups =
> 10
>
> R-sq: within = 0.2093 Obs per group: min =
> 15
> between = 0.6968 avg =
> 15.0
> overall = 0.3196 max =
> 15
>
> Random effects u_i ~ Gaussian Wald chi2(5) =
> 50.32
> corr(u_i, X) = 0 (assumed) Prob > chi2 =
> 0.0000
>
> ------------------------------------------------------------------------------
> pmor | Coef. Std. Err. z P>|z| [95% Conf.
> Interval]
> -------------+----------------------------------------------------------------
> dumcov | .1254805 .0344025 3.65 0.000 .0580529
> .1929082
> dumuni | -.0042582 .0392887 -0.11 0.914 -.0812628
> .0727463
> dum_cu | -.1437736 .0444134 -3.24 0.001 -.2308223
> -.0567249
> lnprd | -.077336 .0130727 -5.92 0.000 -.102958
> -.051714
> prduni | .0101917 .002951 3.45 0.001 .0044079
> .0159756
> _cons | .886512 .0343942 25.78 0.000 .8191005
> .9539234
> -------------+----------------------------------------------------------------
> sigma_u | .02692048
> sigma_e | .0829595
> rho | .09526924 (fraction of variance due to u_i)
> ------------------------------------------------------------------------------
>
>
> Any help would be appreciated.
>
> Cheers
>
> --
> Katherine
> University of Alberta
>
>
>
>
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>
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