# RE: st: how to interpret sigma_e, sigma_u and rho in xtreg, fe and re

 From "Glenn Goldsmith" To Subject RE: st: how to interpret sigma_e, sigma_u and rho in xtreg, fe and re Date Tue, 7 Apr 2009 10:46:15 +0100

```Hi Jakub,

>I particularly do not understand how the F test that all u_i=0 can be
signifikant and at the same time rho to be so large.

Doesn't your F-test is strongly reject the null hypothesis that all u_i=0?
That seems entirely consistent with a large proportion of the variance being
explained by u_i.

HTH

Glenn

JOrsag@access.uzh.ch wrote:

Hello everybody,

mine. Using STATA 8 I have computed couple of Regressions estimating Fixed
and Random effects such as the one, whoch follows bellow. Now I have to
chose few of them to support or decline my theoretical thesis. In doing so I
have used the following parameters:

corr(u_i, Xb)
F-Test / Wald Chi2
F test that all u_i=0
as well as
R-sq

In the following regression seem all of these desicive parameters to be very
good. My question is how to interpret sigma_e, sigma_u and rho or in other
words is it a problem when rho, which is defined as fraction of variance of
the dependet variable due to u_i, is so large (0.9708) as in the case
bellow? I particularly do not understand how the F test that all u_i=0 can
be signifikant and at the same time rho to be so large.

. xtreg xhdi5 mitgl dauer dauer2 openk polis handel aidpc mitgloffgdp, fe

Fixed-effects (within) regression
Group variable (i): landnr

Number of obs = 1794
Number of groups = 71

Obs per group: min = 1
avg = 25.3
max = 30

R-sq: within = 0.5280
between = 0.0070
overall = 0.0394

F(8,1715) = 239.78  Prob > F = 0.0000

corr(u_i, Xb) = -0.1242

----------------------------------------------------------------------------
--
xhdi5 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+--------------------------------------------------------------
--
mitgl | .0270413 .0042603 6.35 0.000 .0186853 .0353973
dauer | .0012923 .0002916 4.43 0.000 .0007204 .0018643
dauer2 | .0000256 4.91e-06 5.21 0.000 .0000159 .0000352
openk | .0001462 .0000495 2.95 0.003 .0000491 .0002434
polis | -.0004915 .0006134 -0.80 0.423 -.0016945 .0007115
handel | .0057409 .0011263 5.10 0.000 .0035319 .00795
aidpc | -.0000454 .0000202 -2.24 0.025 -.0000851 -5.66e-06
mitgloffgdp | .0005159 .0000858 6.02 0.000 .0003477 .000684
_cons | .4023036 .0051096 78.73 0.000 .3922819 .4123253
-------------+--------------------------------------------------------------
--
sigma_u | .16528758
sigma_e | .02866292
rho | .97080605 (fraction of variance due to u_i)
----------------------------------------------------------------------------
--
F test that all u_i=0: F(70, 1715) = 515.05 Prob > F = 0.0000

Greetings,

Jakub Orsag
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