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| From | Clive Nicholas <clivelists@googlemail.com> |
| To | statalist@hsphsun2.harvard.edu |
| Subject | Re: st: fixed vs random effect model |
| Date | Mon, 5 Jul 2010 01:32:14 +0100 |
Martin Weiss replied:
> What`s your rule of thumb then, Steve, for the RE model to be considered? In
> this case, you have -.15, do you still use RE? If you -bootstrap- the thing,
> the CI covers 0 comfortably...
>
>
> ***********
> webuse grunfeld, clear
> xtset company year
> bs e(corr), reps(200) seed(32456): xtreg invest mvalue kstock, i(company) fe
> ***********
For me -- speaking as an idiot non-econometrican -- the key, as I
implied earlier, would be to use both -hausman- and that indicator in
-xtreg, fe- together:
. webuse grunfeld, clear
. xtreg invest mvalue kstock, i(company) fe
Fixed-effects (within) regression Number of obs = 200
Group variable (i): company Number of groups = 10
R-sq: within = 0.7668 Obs per group: min = 20
between = 0.8194 avg = 20.0
overall = 0.8060 max = 20
F(2,188) = 309.01
corr(u_i, Xb) = -0.1517 Prob > F = 0.0000
^^^^^^^^^
------------------------------------------------------------------------------
invest | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mvalue | .1101238 .0118567 9.29 0.000 .0867345 .1335131
kstock | .3100653 .0173545 17.87 0.000 .2758308 .3442999
_cons | -58.74393 12.45369 -4.72 0.000 -83.31086 -34.177
-------------+----------------------------------------------------------------
sigma_u | 85.732501
sigma_e | 52.767964
rho | .72525012 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(9, 188) = 49.18 Prob > F = 0.0000
. est store fixed
. qui xtreg invest mvalue kstock, re
. est store random
. hausman fixed .
---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fixed random Difference S.E.
-------------+----------------------------------------------------------------
mvalue | .1101238 .1097811 .0003427 .0055213
kstock | .3100653 .308113 .0019524 .0024516
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg
Test: Ho: difference in coefficients not systematic
chi2(2) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 2.33
Prob>chi2 = 0.3119
^^^^^^^^^
Here, the two statistics reinforce the same conclusion: an RE model
could be fit to this data. But lucky is the researcher who has such
data to play with; certainly not me.
An alternative example (although one could say this is a selective
model, but imagine it was the only data we had):
. webuse nlswork
. xtreg ln_wage age nev_mar south union tenure hours wks_ue wks_work,
i(idcode) fe
Fixed-effects (within) regression Number of obs = 13550
Group variable (i): idcode Number of groups = 4001
R-sq: within = 0.1325 Obs per group: min = 1
between = 0.2106 avg = 3.4
overall = 0.1744 max = 11
F(8,9541) = 182.14
corr(u_i, Xb) = 0.1774 Prob > F = 0.0000
^^^^^^^^
------------------------------------------------------------------------------
ln_wage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .0046006 .0006602 6.97 0.000 .0033066 .0058947
nev_mar | -.0295329 .0118592 -2.49 0.013 -.0527794 -.0062863
south | -.0514096 .0169021 -3.04 0.002 -.0845412 -.018278
union | .1249207 .0089688 13.93 0.000 .1073399 .1425015
tenure | .0206019 .001053 19.56 0.000 .0185378 .0226661
hours | -.0015052 .0003538 -4.25 0.000 -.0021987 -.0008117
wks_ue | -.0001856 .0004326 -0.43 0.668 -.0010336 .0006624
wks_work | .0011162 .0001514 7.37 0.000 .0008193 .001413
_cons | 1.500244 .0237174 63.26 0.000 1.453753 1.546735
-------------+----------------------------------------------------------------
sigma_u | .39638065
sigma_e | .26223304
rho | .69556838 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4000, 9541) = 5.85 Prob > F = 0.0000
. est store fixed
. qui xtreg ln_wage age nev_mar south union tenure hours wks_ue wks_work, re
. hausman fixed .
---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fixed . Difference S.E.
-------------+----------------------------------------------------------------
age | .0046006 .0029873 .0016134 .0002999
nev_mar | -.0295329 -.01738 -.0121529 .0066411
south | -.0514096 -.1348857 .0834761 .0135749
union | .1249207 .1377239 -.0128032 .0039118
tenure | .0206019 .0254651 -.0048631 .0004508
hours | -.0015052 -.0001432 -.001362 .0001495
wks_ue | -.0001856 -.0008195 .0006339 .0001434
wks_work | .0011162 .0016362 -.00052 .0000481
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg
Test: Ho: difference in coefficients not systematic
chi2(8) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 440.74
Prob>chi2 = 0.0000
^^^^^^^^^
There's not much more difference in -corr(u_i, Xb)- than that observed
in the Grunfeld data, and yet the Hausman test suggests a
statistically significant difference between the two models fit to
this data, this time favouring FE. No doubt the specialist
econometricians will have more to say about this if they feel more
needs to be said, which they probably will.
--
Clive Nicholas
[Please DO NOT mail me personally here, but at
<clivenicholas@hotmail.com>. Please respond to contributions I make in
a list thread here. Thanks!]
"My colleagues in the social sciences talk a great deal about
methodology. I prefer to call it style." -- Freeman J. Dyson.
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