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From |
Steven Archambault <[email protected]> |

To |
[email protected] |

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 <[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/ > * * 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/

**References**:**st: RE: Sargen-Hansen and instruments--RE vs. FE***From:*"Schaffer, Mark E" <[email protected]>

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