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Re: st: RE: Sargen-Hansen and instruments--RE vs. FE--Robust


From   Steven Archambault <archstevej@gmail.com>
To   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
Subject   Re: st: RE: Sargen-Hansen and instruments--RE vs. FE--Robust
Date   Thu, 13 Aug 2009 17:12:30 -0600

Oh, yes....now I understand. That makes perfect sense, what a great
way to trick the system!

Thanks!
On Thu, Aug 13, 2009 at 5:08 PM, Schaffer, Mark E<M.E.Schaffer@hw.ac.uk> wrote:
> Steve,
>
>> -----Original Message-----
>> From: Steven Archambault [mailto:archstevej@gmail.com]
>> Sent: 14 August 2009 00:05
>> To: Schaffer, Mark E
>> Cc: statalist@hsphsun2.harvard.edu; austinnichols@gmail.com;
>> Alfred.Stiglbauer@oenb.at
>> Subject: Re: st: RE: Sargen-Hansen and instruments--RE vs. FE--Robust
>>
>> Thanks, but I think you misunderstood my question. I would
>> like to analyze the data with robust standard errors.
>
> I knew exactly what you wanted.  My solution is this:
>
> xtivreg dep `varlist1', re
>
> xtoverid, robust noi
>
> Cheers,
> Mark
>
>>
>> This works,
>>
>> xtivreg2 dep `varlist1', fe robust;
>>
>> But this does not,
>>
>> xtivreg2 dep `varlist1', re robust;
>>
>> I suppose this question is a bit out of the scope of the
>> original subject, but it is definitely related.
>>
>> Thanks!
>>
>> -Steve
>>
>>
>>
>> On Thu, Aug 13, 2009 at 4:57 PM, Schaffer, Mark
>> E<M.E.Schaffer@hw.ac.uk> wrote:
>> > Steve,
>> >
>> >> -----Original Message-----
>> >> From: Steven Archambault [mailto:archstevej@gmail.com]
>> >> Sent: 13 August 2009 23:48
>> >> To: statalist@hsphsun2.harvard.edu
>> >> Cc: austinnichols@gmail.com; Alfred.Stiglbauer@oenb.at; Schaffer,
>> >> Mark E
>> >> Subject: Re: st: RE: Sargen-Hansen and instruments--RE vs.
>> FE--Robust
>> >>
>> >> Is there a way to analyze instrumented panel data using random
>> >> effects and robust standard errors? It seems the current programs
>> >> don't allows this.
>> >
>> > You can used -xtoverid- to do this.  To get an overid stat
>> after -xtivreg- with random effects, -xtoverid- reestimates
>> everything internally, and if you ask for a robust overid
>> stat, that means it reestimates internally with robust SEs.
>> >
>> > If you add the option -noi- (for "noisily") to -xtoverid-
>> after your estimation, you can see the results of the
>> internal reestimation of the random effects model.
>> >
>> > The only problem is ... the variable names in the
>> -xtoverid- output will all be Stata internal macros with
>> names like __0000001 and so forth.  You can tell which is
>> which by matching the values of the coefficients in the
>> -xtoverid- output to the values in the output from your
>> original estimation.  A bit of a hassle but it should work.
>> >
>> > Hope this helps.
>> >
>> > Cheers,
>> > Mark
>> >
>> >> On Wed, Aug 12, 2009 at 10:28 AM, Steven
>> >> Archambault<archstevej@gmail.com> wrote:
>> >> > Mark,
>> >> >
>> >> > Many thanks for  your response, this clears up several
>> >> questions. Yes,
>> >> > I meant having a chi sq value that accepts the null that
>> >> there is no
>> >> > difference between RE and FE coefficients, implying the
>> >> efficient RE
>> >> > model is preferred.
>> >> >
>> >> >  -Steve
>> >> >
>> >> >> On Wed, Aug 12, 2009 at 6:44 AM, Schaffer, Mark E
>> >> <M.E.Schaffer@hw.ac.uk> wrote:
>> >> >>>
>> >> >>> Steve,
>> >> >>>
>> >> >>> I'm not sure exactly what you mean in your question.  For
>> >> one thing,
>> >> >>> rejection of the null means rejection of RE in favour
>> of FE.  But
>> >> >>> assuming that's just a typo, here's an attempt at a
>> >> restatement of
>> >> >>> the question and an answer:
>> >> >>>
>> >> >>> 1.  The difference between FE and RE can be stated in GMM
>> >> terms (see
>> >> >>> Hayashi's "Econometrics" for a good exposition).  The FE
>> >> estimator
>> >> >>> uses only the orthogonality conditions that say the demeaned
>> >> >>> regressor X is orthogonal to the idiosyncratic term
>> e_ij.  The RE
>> >> >>> estimator uses these orthogonality conditions, plus the
>> >> >>> orthogonality conditions that say that the mean of X for
>> >> the panel
>> >> >>> unit is orthogonaly to the panel error term u_j.
>> >> >>>
>> >> >>> 2.  This is why the FE vs RE test is an overid test.  The RE
>> >> >>> estimator uses more orthogonality conditions, and so the
>> >> equation is
>> >> >>> overidentified.  In the special case of classical iid
>> errors, the
>> >> >>> Hausman test is numerically the same as the Sargan-Hansen test.
>> >> >>>
>> >> >>> 3.  Your question is, what happens if some of the Xs are
>> >> endogenous
>> >> >>> and you have some Zs as instruments?  The answer is
>> that the same
>> >> >>> GMM framework encompasses this.  You remove some of the
>> >> demeaned Xs
>> >> >>> from the orthogonality conditions and add some
>> demeaned Zs to the
>> >> >>> orthogonality conditions, and if you are using an RE
>> >> estimator, you
>> >> >>> also remove the panel unit means of the Xs from the
>> orthogonality
>> >> >>> conditions and add some panel unit means of Zs to
>> them.  (This is
>> >> >>> the case for the EC2SLS RE estimator - it's a bit
>> >> different for the
>> >> >>> G2SLS estimator.  The reason is that the G2SLS using a single
>> >> >>> quasi-demeaned instrument Z instead of the demeaned Z and
>> >> panel unit
>> >> >>> mean Z separately, which is what EC2SLS does.  I think
>> >> the intuition
>> >> >>> for EC2SLS is easier to get.)
>> >> >>>
>> >> >>> 4.  If the FE model is overidentified, you'll now have
>> an overid
>> >> >>> test stat for it that tests the validity of the demeaned
>> >> Zs as instruments.
>> >> >>> If you're estimating an RE model, the overid test will
>> test the
>> >> >>> validity of the demeaned and panel unit means of the Zs
>> >> and also the
>> >> >>> panel unit means of the exogenous Xs.
>> >> >>>
>> >> >>> 5.  If the overid test with endogenous regressors
>> rejects the RE
>> >> >>> model, you have a standard GMM problem: which of your
>> >> orthogonality
>> >> >>> conditions is invalid?  It could be the demeaned Zs,
>> or the panel
>> >> >>> unit means of the Xs, or both, or whatever.  In that
>> >> case, you can
>> >> >>> do a "GMM distance test" (aka "C test",
>> >> "Difference-in-Sargan test",
>> >> >>> etc.) where you compare the Sargan-Hansen test stat (from
>> >> >>> -xtoverid-) after estimation with and without the orthognality
>> >> >>> conditions that you think are the likely culprits.  But
>> >> you have to
>> >> >>> decide ex ante which are the dubious ones - econometric
>> >> theory can't tell you.
>> >> >>>
>> >> >>> Hope this helps.
>> >> >>>
>> >> >>> Yours,
>> >> >>> Mark
>> >> >>>
>> >> >>> Prof. Mark Schaffer FRSE
>> >> >>> Director, CERT
>> >> >>> Department of Economics
>> >> >>> School of Management & Languages
>> >> >>> Heriot-Watt University, Edinburgh EH14 4AS tel
>> +44-131-451-3494 /
>> >> >>> fax +44-131-451-3296 http://ideas.repec.org/e/psc51.html
>> >> >>>
>> >> >>>
>> >> >>>
>> >> >>>
>> >> >>>
>> >> >>> ________________________________
>> >> >>>
>> >> >>>        From: Steven Archambault [mailto:archstevej@gmail.com]
>> >> >>>        Sent: 12 August 2009 08:50
>> >> >>>        To: statalist@hsphsun2.harvard.edu; Schaffer, Mark E
>> >> >>>        Cc: austinnichols@gmail.com; Alfred.Stiglbauer@oenb.at
>> >> >>>        Subject: Sargen-Hansen and instruments--RE vs. FE
>> >> >>>
>> >> >>>
>> >> >>>        A while back we discussed the use of the
>> >> Sargen-Hansen test
>> >> >>> to check if RE was an appropriate analysis to use for
>> >> panel data. My
>> >> >>> question now is regarding suspected endogeneity
>> problems. If the
>> >> >>> Sargen-Hansen statistic is such that you reject the null,
>> >> in favor
>> >> >>> of using the RE, does it follow that we do not need to
>> >> worry about
>> >> >>> explanatory variables being endogenous? My feeling is
>> >> yes, here is
>> >> >>> the logic. If I were to use xtivreg I would call the same over
>> >> >>> identification test to see if my instruments are valid.
>> >> So, if the
>> >> >>> test already rejects before adding instruments, I
>> should not need
>> >> >>> the instruments.
>> >> >>>
>> >> >>>        If I do use instruments, what is then a valid test to
>> >> >>> determine if RE is an appropriate model to use (over FE)?
>> >> >>>
>> >> >>>        Is my question clear?
>> >> >>>
>> >> >>>        Thanks,
>> >> >>>        Steve
>> >> >>>
>> >> >>>
>> >> >>>
>> >> >>>        On Sat, Jun 27, 2009 at 11:31 AM, Schaffer, Mark E
>> >> >>> <M.E.Schaffer@hw.ac.uk> wrote:
>> >> >>>
>> >> >>>
>> >> >>>                Steve,
>> >> >>>
>> >> >>>                > -----Original Message-----
>> >> >>>                > From: owner-statalist@hsphsun2.harvard.edu
>> >> >>>                >
>> [mailto:owner-statalist@hsphsun2.harvard.edu] On
>> >> >>> Behalf Of
>> >> >>>                > Steven Archambault
>> >> >>>                > Sent: 27 June 2009 00:26
>> >> >>>                > To: statalist@hsphsun2.harvard.edu;
>> >> >>> austinnichols@gmail.com;
>> >> >>>                > Alfred.Stiglbauer@oenb.at
>> >> >>>                > 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-)
>> >> >>>
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