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st: Basic question onHausman test.


From   Lucio Vinhas de Souza <lvdesouza@yahoo.com>
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?

Looking forward to your answer and truly yours,

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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