# st: Basic question onHausman test.

 From Lucio Vinhas de Souza To statalist@hsphsun2.harvard.edu Subject st: Basic question onHausman test. Date Sat, 27 Sep 2003 07:37:06 +0100 (BST)

```Dear all,

I have a very basic question concerning a Hausman
test. I am comparing a fixed effects panel estimation
with a random effects one (see below). How do I
interpret the results of the Hausman test? Do they
mean that the random effects estimates are
inconsistent?

Lucio Vinhas de Souza
**************************************
. xtreg ltrade  lgdp lpop eud emud trend, fe

Fixed-effects (within) regression               Number
of obs      =     57442
Group variable (i) : ipair                      Number
of groups   =      2611

R-sq:  within  = 0.1548                         Obs
per group: min =        22
between = 0.3077
avg =      22.0
overall = 0.2112
max =        22

F(5,54826)         =   2008.23
corr(u_i, Xb)  = 0.2545
Prob > F           =    0.0000

-------------------------------------------------------
ltrade |      Coef.   Std. Err.      t    P>|t|
[95% Conf. Interval]
-------------+-----------------------------------------
lgdp |   .0754704   .0292365     2.58   0.010
.0181668    .1327741
lpop |   .5473182   .1313844     4.17   0.000
.2898038    .8048326
eud |  -.2723743   .0951406    -2.86   0.004
-.4588506    -.085898
emud |  -.9780319   .1085947    -9.01   0.000
-1.190878   -.7651856
trend |   .1153878   .0018864    61.17   0.000
.1116905    .1190851
_cons |  -10.33135   2.421705    -4.27   0.000
-15.07791   -5.584793
-------------+-----------------------------------------
sigma_u |  2.9860951
sigma_e |  1.8353774
rho |   .7258032   (fraction of variance due
to u_i)
-------------------------------------------------------
F test that all u_i=0:     F(2610, 54826) =    45.08
Prob > F = 0.0000

. hausman, save

. xtreg ltrade  lgdp lpop eud emud trend

Random-effects GLS regression                   Number
of obs      =     57442
Group variable (i) : ipair                      Number
of groups   =      2611

R-sq:  within  = 0.1537                         Obs
per group: min =        22
between = 0.3468
avg =      22.0
overall = 0.2963
max =        22

Random effects u_i ~ Gaussian                   Wald
chi2(6)       =  11354.00
corr(u_i, X)       = 0 (assumed)                Prob >
chi2        =    0.0000

-------------------------------------------------------
ltrade |      Coef.   Std. Err.      z    P>|z|
[95% Conf. Interval]
-------------+-----------------------------------------
lgdp |   .2138072    .026484     8.07   0.000
.1618996    .2657149
lpop |   1.477494   .0498542    29.64   0.000
1.379781    1.575206
eud |   .0097496   .0884326     0.11   0.912
-.1635752    .1830744
emud |  -1.025233   .1084758    -9.45   0.000
-1.237842   -.8126247
trend |   .1032162    .001403    73.57   0.000
.1004664     .105966
_cons |  -25.08318   1.038565   -24.15   0.000
-27.11873   -23.04763
-------------+-----------------------------------------
sigma_u |  2.5927197
sigma_e |  1.8353942
rho |  .66616628   (fraction of variance due
to u_i)
-------------------------------------------------------

. hausman

---- Coefficients ----
(b)        (B)        (b-B)
qrt(diag(V_b-V_B))
|     Prior       Current  Difference    S.E.
-------------+-----------------------------------------
lpop | .5473182     1.477494     -.9301754
.1215583
eud |  -.2723743     .0097496    -.2821239
.0350914
emud |  -.9780319    -1.025233    .0472016
.0050788
trend |   .1153878     .1032162   .0121716
.001261
-------------------------------------------------------
b= less efficient estimates obtained previously from
xtreg
B= fully efficient estimates obtained from xtreg

Test:  Ho:  difference in coefficients not systematic
chi2(  5) = (b-B)'[(V_b-V_B)^(-1)](b-B)=   167.24
Prob>chi2 =     0.0000

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