Statalist


[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

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


From   Steven Archambault <archstevej@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: Sargen-Hansen and instruments--RE vs. FE
Date   Wed, 12 Aug 2009 10:28:41 -0600

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-)
>>
>>                > *
>>                > *   For searches and help try:
>>                > *   http://www.stata.com/help.cgi?search
>>                > *   http://www.stata.com/support/statalist/faq
>>                > *   http://www.ats.ucla.edu/stat/stata/
>>                >
>>
>>
>>                --
>>                Heriot-Watt University is a Scottish charity
>>                registered under charity number SC000278.
>>
>>
>>                *
>>                *   For searches and help try:
>>                *   http://www.stata.com/help.cgi?search
>>                *   http://www.stata.com/support/statalist/faq
>>                *   http://www.ats.ucla.edu/stat/stata/
>>
>>
>>
>>
>>
>> --
>> Heriot-Watt University is a Scottish charity
>> registered under charity number SC000278.
>>
>>
>> *
>> *   For searches and help try:
>> *   http://www.stata.com/help.cgi?search
>> *   http://www.stata.com/support/statalist/faq
>> *   http://www.ats.ucla.edu/stat/stata/
>

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/



© Copyright 1996–2014 StataCorp LP   |   Terms of use   |   Privacy   |   Contact us   |   What's new   |   Site index