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


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   "Steven Archambault" <archstevej@gmail.com>
Subject   RE: st: RE: Sargen-Hansen and instruments--RE vs. FE--Robust
Date   Fri, 14 Aug 2009 00:08:24 +0100

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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