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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>, <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: Sargen-Hansen and instruments--RE vs. FE--Robust
Date   Thu, 13 Aug 2009 23:57:33 +0100

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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