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

Date |
Wed, 12 Aug 2009 13:44:42 +0100 |

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/

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