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st: Hausman Query
From
"Ross, Andrew" <[email protected]>
To
"[email protected]" <[email protected]>
Subject
st: Hausman Query
Date
Wed, 5 Jan 2011 08:50:03 +0000
Hello
I am currently using Stata to investigate new firm formation for 32 Scottish regions over a 10 year period. I was wondering, if you might offer your opinion on a Stata related matter, that I have encountered?
As you can see from the attached output I've run a fixed and random effects model and followed this by the hausman test. However, the hausman highlights a 'note', as you will see from the attached output.
I was wondering, if you could shed any light on this note and what is means? I have asked four other people and they do not know. One suggested it may be a result of over parameterisation given the small size of the panel, but they are not sure.
Many thanks.
Andrew
xtreg Lab_TP Wge_grow Pop_grow Log_unemployed NVQ4_pop House_price LQ_agric LQ_man LQ_b
> s Pop_density Gov_sector Small_bus, fe vce (robust)
Fixed-effects (within) regression Number of obs = 320
Group variable: Region Number of groups = 32
R-sq: within = 0.2061 Obs per group: min = 10
between = 0.0019 avg = 10.0
overall = 0.0030 max = 10
F(11,277) = 3.10
corr(u_i, Xb) = -0.9507 Prob > F = 0.0006
(Std. Err. adjusted for clustering on Region)
------------------------------------------------------------------------------
| Robust
Lab_TP | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------
-------------+------
Wge_grow | -.0265289 .0270548 -0.98 0.328 -.079788 .0267303
Pop_grow | .4054536 .5845519 0.69 0.489 -.7452749 1.556182
Log_unempl~d | 4.109563 4.222209 0.97 0.331 -4.20213 12.42126
NVQ4_pop | -.0295052 .0431429 -0.68 0.495 -.1144348 .0554243
House_price | .0000483 .0000121 3.99 0.000 .0000245 .0000722
LQ_agric | .1687096 .4963323 0.34 0.734 -.8083529 1.145772
LQ_man | -.1523606 .4695697 -0.32 0.746 -1.076739 .7720178
LQ_bs | 2.506032 1.647939 1.52 0.129 -.7380422 5.750107
Pop_density | .0236083 .0110802 2.13 0.034 .0017962 .0454204
Gov_sector | -.0001643 .0309392 -0.01 0.996 -.0610701 .0607415
Small_bus | .3920981 .4383467 0.89 0.372 -.470816 1.255012
_cons | -32.9382 42.48215 -0.78 0.439 -116.5671 50.69067
-------------+----------------------------------------------------------
-------------+------
sigma_u | 17.794849
sigma_e | 2.771809
rho | .9763121 (fraction of variance due to u_i)
------------------------------------------------------------------------------
. estimates store fixed
. xtreg Lab_TP Wge_grow Pop_grow Log_unemployed NVQ4_pop House_price LQ_agric LQ_man LQ
> _bs Pop_density Gov_sector Small_bus, re vce (robust)
Random-effects GLS regression Number of obs = 320
Group variable: Region Number of groups = 32
R-sq: within = 0.1667 Obs per group: min = 10
between = 0.6091 avg = 10.0
overall = 0.4986 max = 10
Random effects u_i ~ Gaussian Wald chi2(12) = 3152.08
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
(Std. Err. adjusted for clustering on Region)
------------------------------------------------------------------------------
| Robust
Lab_TP | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------
-------------+------
Wge_grow | -.0254291 .0298964 -0.85 0.395 -.084025 .0331667
Pop_grow | .8175778 .5211693 1.57 0.117 -.2038953 1.839051
Log_unempl~d | -4.643811 2.993296 -1.55 0.121 -10.51056 1.222941
NVQ4_pop | .008423 .0484623 0.17 0.862 -.0865613 .1034074
House_price | .0000265 .0000108 2.46 0.014 5.39e-06 .0000476
LQ_agric | .7014816 .4126435 1.70 0.089 -.1072848 1.510248
LQ_man | .2703715 .5041589 0.54 0.592 -.7177617 1.258505
LQ_bs | 4.506697 1.720704 2.62 0.009 1.13418 7.879214
Pop_density | .0023373 .0006452 3.62 0.000 .0010727 .0036018
Gov_sector | -.0345817 .034529 -1.00 0.317 -.1022574 .0330939
Small_bus | .6680098 .1846674 3.62 0.000 .3060683 1.029951
_cons | -42.7439 17.37493 -2.46 0.014 -76.79813 -8.689662
-------------+----------------------------------------------------------
-------------+------
sigma_u | 2.2647466
sigma_e | 2.771809
rho | .40033378 (fraction of variance due to u_i)
------------------------------------------------------------------------------
. estimates store random
. hausman fixed random
Note: the rank of the differenced variance matrix (10) does not equal the number of
coefficients being tested (11); be sure this is what you expect, or there may
be problems computing the test. Examine the output of your estimators for
anything unexpected and possibly consider scaling your variables so that the
coefficients are on a similar scale.
---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fixed random Difference S.E.
-------------+----------------------------------------------------------
-------------+------
Wge_grow | -.0265289 -.0254291 -.0010997 .
Pop_grow | .4054536 .8175778 -.4121243 .2647328
Log_unempl~d | 4.109563 -4.643811 8.753374 2.977789
NVQ4_pop | -.0295052 .008423 -.0379283 .
House_price | .0000483 .0000265 .0000218 5.53e-06
LQ_agric | .1687096 .7014816 -.5327721 .2758099
LQ_man | -.1523606 .2703715 -.4227322 .
LQ_bs | 2.506032 4.506697 -2.000664 .
Pop_density | .0236083 .0023373 .021271 .0110614
Gov_sector | -.0001643 -.0345817 .0344174 .
Small_bus | .3920981 .6680098 -.2759117 .3975498
------------------------------------------------------------------------------
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(10) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 5.58
Prob>chi2 = 0.8493
(V_b-V_B is not positive definite)
Andrew Ross
PhD Candidate
School of Accounting, Economics & Statistics
Napier University Business School
Craiglockhart Campus
Room 1/38
EH14 IDJ
Email: [email protected]
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