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


From   Steven Archambault <archstevej@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: Sargen-Hansen and instruments--RE vs. FE--Robust
Date   Thu, 13 Aug 2009 16:47:55 -0600

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.


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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>>
>

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