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RE: st: RE: Hausman test for clustered random vs. fixed effects (again)
Steve,
> -----Original Message-----
> From: Steven Archambault [mailto:[email protected]]
> Sent: 02 July 2009 22:41
> To: [email protected]; Schaffer, Mark E
> Cc: [email protected]; [email protected]
> Subject: Re: st: RE: Hausman test for clustered random vs.
> fixed effects (again)
>
> Mark,
>
> I should have commented on this earlier, but when I eye the
> coefficients for both the FE and RE results, I see that some
> of them are quite different from one another. However, the
> xtoverid result suggests RE is the one to use. Does anybody
> see this as a problem? The numerator of the Hausman wald test
> is the difference in coefficients of the two models. Is this
> not missed in the xtoverid approach?
A few things here:
- The "xtoverid approach" in this case is **identical** to the traditional Hausman test in concept. They are both vector-of-contrast tests, the contrast being between the 9 FE and RE coefficients. The **only** difference in this case between the GMM stat reported by -xtoverid- and the traditional Hausman stat is that the former is cluster-robust. In addition to the references on this point that I cited in my previous posting, you should also check out Ruud's textbook, "An Introduction to Classical Econometric Theory".
- The test has 9 degrees of freedom because 9 coefficients are being contrasted jointly. This means that some can indeed be quite different, but if the others are very similar then a test of the joint contrasts can be statistically insignificant.
- The p-value reported by -xtoverid- is 10%, which a little worrisome. If you were to do a vector-of-contrast tests focusing on a subset of coefficients instead of all 9 (not supported by -xtoverid- but do-able by hand), you could well find that you reject the null at 5% or 1% or whatever. I don't think it's straightforward to conclude that RE is the estimator of choice.
Hope this helps.
Cheers,
Mark
>
> I am posting my regression results to show what I am talking
> about more clearly.
>
> Thanks for your input.
> -Steve
>
>
> Fixed-effects (within) regression Number of obs
> = 404
> Group variable: id_code_id Number of
> groups = 88
>
> R-sq: within = 0.2304 Obs per
> group: min = 1
> between = 0.4730
> avg = 4.6
> overall = 0.4487
> max = 7
>
> F(9,87)
> = 2.47
> corr(u_i, Xb) = -0.9558 Prob > F
> = 0.0148
>
> (Std. Err. adjusted for 88
> clusters in id_code_id)
> --------------------------------------------------------------
> ----------------
> | Robust
> lnfd | Coef. Std. Err. t P>|t| [95%
> Conf. Interval]
> -------------+------------------------------------------------
> ----------
> -------------+------
> lags | -.0267991 .0185982 -1.44 0.153 -.063765
> .0101668
> lagk | .0964571 .0353269 2.73 0.008
> .0262411 .166673
> lagp | .2210296 .1206562 1.83 0.070
> -.0187875 .4608468
> lagdr | -.0000267 .0000251 -1.06 0.291 -.0000767
> .0000232
> laglurb | .3483909 .1234674 2.82 0.006 .102986
> .5937957
> lagtra | .1109513 .1267749 0.88 0.384
> -.1410275 .3629301
> lagte | .0067764 .004166 1.63 0.107
> -.0015039 .0150567
> lagcr | .0950221 .0683074 1.39 0.168
> -.0407463 .2307905
> lagp | .0343752 .1291378 0.27 0.791
> -.2223001 .2910506
> _cons | 4.316618 1.996618 2.16 0.033
> .348124 8.285112
> -------------+------------------------------------------------
> ----------
> -------------+------
> sigma_u | .44721909
> sigma_e | .0595116
> rho | .98260039 (fraction of variance due to u_i)
> --------------------------------------------------------------
> ----------------
>
>
>
> Random-effects GLS regression Number of obs
> = 404
> Group variable: id_code_id Number of
> groups = 88
>
> R-sq: within = 0.1792 Obs per
> group: min = 1
> between = 0.5074
> avg = 4.6
> overall = 0.5017
> max = 7
>
> Random effects u_i ~ Gaussian Wald chi2(9)
> = 48.97
> corr(u_i, X) = 0 (assumed) Prob > chi2
> = 0.0000
>
> (Std. Err. adjusted for
> clustering on id_code_id)
> --------------------------------------------------------------
> ----------------
> | Robust
> lnfd | Coef. Std. Err. z P>|z| [95%
> Conf. Interval]
> -------------+------------------------------------------------
> ----------
> -------------+------
> lags | -.01138 .0135958 -0.84 0.403 -.0380274
> .0152673
> lagk | .0115314 .0180641 0.64 0.523
> -.0238735 .0469363
> lagp | .2551701 .119322 2.14 0.032
> .0213033 .4890369
> lagdr | -6.17e-06 .0000153 -0.40 0.686 -.0000361
> .0000238
> laglurb | .0657802 .0153923 4.27 0.000 .0356119
> .0959486
> lagtra | .0022183 .0579203 0.04 0.969
> -.1113034 .11574
> lagte | .0048012 .0016128 2.98 0.003
> .00164 .0079623
> lagcr | .1051833 .045994 2.29 0.022
> .0150368 .1953298
> lagp | .184373 .1191063 1.55 0.122
> -.0490711 .4178171
> _cons | 9.071133 .2322309 39.06 0.000
> 8.615968 9.526297
> -------------+------------------------------------------------
> ----------
> -------------+------
> sigma_u | .10617991
> sigma_e | .0595116
> rho | .76095591 (fraction of variance due to u_i)
> --------------------------------------------------------------
> ----------------
>
> . xtoverid;
>
> Test of overidentifying restrictions: fixed vs random effects
> Cross-section time-series model: xtreg re robust
> Sargan-Hansen statistic 14.684 Chi-sq(9) P-value = 0.1000
>
>
>
>
>
> On Sat, Jun 27, 2009 at 11:31 AM, Schaffer, Mark
> E<[email protected]> wrote:
> > Steve,
> >
> >> -----Original Message-----
> >> From: [email protected]
> >> [mailto:[email protected]] On Behalf Of Steven
> >> Archambault
> >> Sent: 27 June 2009 00:26
> >> To: [email protected]; [email protected];
> >> [email protected]
> >> Subject: st: Hausman test for clustered random vs. fixed effects
> >> (again)
> >>
> >> Hi all,
> >>
> >> I know this has been discussed before, but in STATA 10
> (and versions
> >> before 9 I understand) the canned procedure for Hausman test when
> >> comparing FE and RE models cannot be run when the data
> analysis uses
> >> clustering (and by default corrects for robust errors in STATA 10).
> >> This is the error received
> >>
> >> "hausman cannot be used with vce(robust), vce(cluster cvar), or
> >> p-weighted data"
> >>
> >> My question is whether or not the approach of using xtoverid to
> >> compare FE and RE models (analyzed using the clustered and
> by default
> >> robust approach in STATA 10) is accepted in the literature. This
> >> approach produces the Sargan-Hansen stat, which is typically used
> >> with analyses that have instrumentalized variables and need an
> >> overidentification test. For the sake of publishing I am
> wondering if
> >> it is better just not to worry about heteroskedaticity, and avoid
> >> clustering in the first place (even though
> heteroskedaticity likely
> >> exists)? Or, alternatively one could just calculate the
> Hausman test
> >> by hand following the clustered analyses.
> >>
> >> Thanks for your insight.
> >
> > It's very much accepted in the literature. In the -xtoverid- help
> > file, see especially the paper by Arellano and the book by Hayashi.
> >
> > If you suspect heteroskedasticity or clustered errors,
> there really is
> > no good reason to go with a test (classic Hausman) that is
> invalid in
> > the presence of these problems. The GMM -xtoverid- approach is a
> > generalization of the Hausman test, in the following sense:
> >
> > - The Hausman and GMM tests of fixed vs. random effects
> have the same
> > degrees of freedom. This means the result cited by Hayashi
> (and due
> > to Newey, if I recall) kicks in, namely...
> >
> > - Under the assumption of homoskedasticity and independent
> errors, the
> > Hausman and GMM test statistics are numerically identical.
> Same test.
> >
> > - When you loosen the iid assumption and allow
> heteroskedasticity or
> > dependent data, the robust GMM test is the natural generalization.
> >
> > Hope this helps.
> >
> > Cheers,
> > Mark (author of -xtoverid-)
> >
> >> *
> >> * For searches and help try:
> >> * http://www.stata.com/help.cgi?search
> >> * http://www.stata.com/support/statalist/faq
> >> * http://www.ats.ucla.edu/stat/stata/
> >>
> >
> >
> > --
> > Heriot-Watt University is a Scottish charity registered
> under charity
> > number SC000278.
> >
> >
> > *
> > * For searches and help try:
> > * http://www.stata.com/help.cgi?search
> > * http://www.stata.com/support/statalist/faq
> > * http://www.ats.ucla.edu/stat/stata/
> >
>
--
Heriot-Watt University is a Scottish charity
registered under charity number SC000278.
*
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/