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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, dyap82 <dyap82@hotmail.com>
Subject   Re: st: Basic question on Hausman test.
Date   Sat, 27 Sep 2003 22:08:22 +0100 (BST)

Danny,

Quoting dyap82 <dyap82@hotmail.com>:

> 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.

Yes, the Hausman principle is very general, but whether or not it's easy 
to implement in Stata in any particular case is a different question.  In 
some cases you may have to roll your own if you want to do a Hausman test; 
in others, the -hausman- command may be all you need.

--Mark

> 
> 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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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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