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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>, statalist@hsphsun2.harvard.edu, austinnichols@gmail.com, Alfred.Stiglbauer@oenb.at
Subject   Re: st: RE: Sargen-Hansen and instruments--RE vs. FE--Robust
Date   Tue, 18 Aug 2009 09:28:20 -0600

On Tue, Aug 18, 2009 at 9:27 AM, Steven Archambault<archstevej@gmail.com> wrote:
> This approach is working. I was hoping to calculate the Cragg Donald
> Wald by hand, but it seems I cannot get the  "minimum eigenvalue of
> the Cragg-Donald" statistic from ereturn. Would this be something I
> could calculate another way myself?
>
>
>
>
>
>
> 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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