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 <[email protected]> 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:[email protected]]
>> Sent: 12 August 2009 08:50
>> To: [email protected]; Schaffer, Mark E
>> Cc: [email protected]; [email protected]
>> 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
>> <[email protected]> wrote:
>>
>>
>> Steve,
>>
>> > -----Original Message-----
>> > From: [email protected]
>> > [mailto:[email protected]] On
>> Behalf Of
>> > Steven Archambault
>> > Sent: 27 June 2009 00:26
>> > To: [email protected];
>> [email protected];
>> > [email protected]
>> > 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/
>
*
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