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


From   "Martin Weiss" <martin.weiss1@gmx.de>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: AW: how to interpret sigma_e, sigma_u and rho in xtreg, fe and re
Date   Tue, 7 Apr 2009 10:25:54 +0200

<> 



" 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."

Well, they measure different things: -rho- is the share of the estimated
variance of the overall error accounted for by the individual effect u_i.
You can replicate it as in

***
webuse nlswork, clear
generate age2 = age^2
generate ttl_exp2 = ttl_exp^2
generate tenure2 = tenure^2
generate byte black = race==2
xtset idcode
xtreg ln_w grade age* ttl_exp* tenure* black not_smsa south, fe
*replication of rho
di  e(sigma_u)^2/(e(sigma_u)^2+e(sigma_e)^2)
***

The F-test is designed to jointly test that all individual effects u_i are
zero. The answers to both questions need not coincide...

HTH
Martin


-----Ursprüngliche Nachricht-----
Von: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von
JOrsag@access.uzh.ch
Gesendet: Dienstag, 7. April 2009 10:15
An: statalist@hsphsun2.harvard.edu
Betreff: st: how to interpret sigma_e, sigma_u and rho in xtreg, fe and re

Hello everybody,

Can somebody please help me with the following rather beginner problem of 
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


Thank you in advance for any comments and insight.

Greetings,

Jakub Orsag
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