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Re: st: Basic question on Hausman test.


From   "dyap82" <dyap82@hotmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Basic question on Hausman test.
Date   Sat, 27 Sep 2003 16:03:47 -0000

I have a personal question on the Hausman test. Can it be 
generalised to different forms of models, in particular a 
simultaneous equations model where the endogenous variables (which 
incidentally are the dependent variables) are binary.

Thanks

Danny

--- In statalist@yahoogroups.com, Mark Schaffer <M.E.Schaffer@h...> 
wrote:
> 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@y...>:
> 
> > 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@h...
> web: http://www.sml.hw.ac.uk/ecomes
> 
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