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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-) > >>> > >>> > * > >>> > * 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/ > >> > > > -- 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/

**Follow-Ups**:**Re: st: RE: Sargen-Hansen and instruments--RE vs. FE--Robust***From:*Steven Archambault <archstevej@gmail.com>

**References**:**Re: st: RE: Sargen-Hansen and instruments--RE vs. FE--Robust***From:*Steven Archambault <archstevej@gmail.com>

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