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 [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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