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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 17:04:57 -0600

Thanks, but I think you misunderstood my question. I would like to
analyze the data with robust standard errors.

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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