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Re: st: Basic question on Hausman test.


From   Mark Schaffer <M.E.Schaffer@hw.ac.uk>
To   statalist@hsphsun2.harvard.edu, Lucio Vinhas de Souza <lvdesouza@yahoo.com>
Subject   Re: st: Basic question on Hausman test.
Date   Sat, 27 Sep 2003 13:05:20 +0100 (BST)

Lucio,

The null is that the two estimation methods are both OK and that therefore 
they should yield coefficients that are "similar".  The alternative 
hypothesis is that the fixed effects estimation is OK and the random 
effects estimation is not; if this is the case, then we would expect to 
see differences between the two sets of coefficients.

This is because the random effects estimator makes an assumption (the 
random effects are orthogonal to the regressors) that the fixed effects 
estimator does not.  If this assumption is wrong, the random effects 
estimator will be inconsistent, but the fixed effects estimator is 
unaffected.  Hence, if the assumption is wrong, this will be reflected in 
a difference between the two set of coefficients.  The bigger the 
difference (the less similar are the two sets of coefficients), the bigger 
the Hausman statistic.

A large and significant Hausman statistic means a large and significant 
difference, and so you reject the null that the two methods are OK in 
favour of the alternative hypothesis that one is OK (fixed effects) and 
one isn't (random effects).

Your Hausman stat is very big, and you can see why - the differences 
between some of the coefficients are big enough to be visible to the naked 
eye, so to speak - and so you can reject random effects as inconsistent 
and go with fixed effects instead.

BTW, xthausman after random effects will do the test for you in one step.

Cheers,
Mark

Quoting Lucio Vinhas de Souza <lvdesouza@yahoo.com>:

> 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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Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3008
email: m.e.schaffer@hw.ac.uk
web: http://www.sml.hw.ac.uk/ecomes

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