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

 From JOrsag@access.uzh.ch To statalist@hsphsun2.harvard.edu Subject st: how to interpret sigma_e, sigma_u and rho in xtreg, fe and re Date Tue, 07 Apr 2009 10:14:41 +0200

```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

Greetings,

Jakub Orsag
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```