Danny,
Quoting dyap82 <[email protected]>:
> 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 [email protected], 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: [email protected]
web: http://www.sml.hw.ac.uk/ecomes
________________________________________________________________
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