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From |
"Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk> |

To |
"Steven Archambault" <archstevej@gmail.com> |

Subject |
RE: st: RE: Hausman test for clustered random vs. fixed effects (again) |

Date |
Mon, 6 Jul 2009 15:08:04 +0100 |

Steve, > -----Original Message----- > From: Steven Archambault [mailto:archstevej@gmail.com] > Sent: 05 July 2009 01:59 > To: Schaffer, Mark E > Cc: statalist@hsphsun2.harvard.edu > Subject: Re: st: RE: Hausman test for clustered random vs. > fixed effects (again) > > Thanks Mark, > > If I am not mistaken, this old post by Vince Wiggins explains > how one would go about setting up a Hausman test for a select > number of coefficients. I am trying to see how this test > works, and the results compare to just doing a canned > procedure (hausman test, xtoverid hausman test, etc.) > > http://www.stata.com/statalist/archive/2003-10/msg00031.html > > -Steve I think what you're looking for are some later posts by Vince: http://www.stata.com/statalist/archive/2005-08/msg00807.html http://www.stata.com/statalist/archive/2005-08/msg00837.html http://www.stata.com/statalist/archive/2005-08/msg00853.html Note that the last post contains a correction by Vince to his code. Also, if you're interested, here is the last word in the accompanying debate on how to guarantee that a Hausman statistic is non-negative in finite samples. http://www.stata.com/statalist/archive/2005-08/msg00762.html Cheers, Mark NB: Steve, your emails are being posting to Statalist but not showing up here. 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 > > > On Thu, Jul 2, 2009 at 6:17 PM, Schaffer, Mark > E<M.E.Schaffer@hw.ac.uk> wrote: > > Steve, > > > >> -----Original Message----- > >> From: Steven Archambault [mailto:archstevej@gmail.com] > >> Sent: 03 July 2009 00:42 > >> To: Schaffer, Mark E > >> Cc: statalist@hsphsun2.harvard.edu > >> Subject: Re: st: RE: Hausman test for clustered random vs. > >> fixed effects (again) > >> > >> Okay that makes sense. For a second there I thought I was not > >> understanding the test. The different model specifications > I use give > >> p values (from the xtoverid test) of .1 to .25. Do you > think values > >> over say 20% make you less nervous about accepting RE results? My > >> plan is to report both FE and RE models, suggesting that > RE results > >> can be considered valid given the p values. > >> > >> -Steve > > > > Well, like I said, it's really a matter of taste. I'm > perhaps more nervous and less gung ho than your average > applied economist. 20% makes me less nervous than 10%, of > course. But if you want to pursue this seriously, you should > consider going down the route of testing specifically the > subset of coefficients of interest. > > > > --Mark > > > >> On Thu, Jul 2, 2009 at 5:13 PM, Schaffer, Mark > >> E<M.E.Schaffer@hw.ac.uk> wrote: > >> > Steve, > >> > > >> >> -----Original Message----- > >> >> From: Steven Archambault [mailto:archstevej@gmail.com] > >> >> Sent: 03 July 2009 00:01 > >> >> To: Schaffer, Mark E > >> >> Subject: Re: st: RE: Hausman test for clustered random vs. > >> >> fixed effects (again) > >> >> > >> >> Wait a second, I thought with a Chi sq test we reject the > >> null that > >> >> the FE and RE coefficients are different when the critical > >> value is > >> >> such that the p-value is greater or equal to .05. This > >> would give us > >> >> a 5% (or more) significance that the null is rejected. > We get this > >> >> with a lower chi-sq value. > >> >> It was with this logic that I am saying RE is the > preferred model. > >> > > >> > There's nothing sacred about the 5% level. Some people, > >> when constructing tables for their papers, put *s next to > >> coefficients that are significant at the 10% level ... > which happens > >> to be your p-value. > >> > > >> > The bigger the contrasts, the smaller the p-value, and 10% > >> implies contrasts that are large enough to make me nervous. > >> Of course, de gustibus non est disputandum. > >> > > >> > If you want to take this further, you might consider > >> focusing on the coefficients of interest, whatever they are. > >> You may well find that the joint contrast between the RE and FE > >> coefficients of interest is significant at a still smaller p-value > >> (suggesting you dump RE), or is not at all significant > (suggesting RE > >> is preferred on efficiency grounds). > >> > > >> > -xtoverid- doesn't support tests of subsets of coefficients > >> (I should consider adding this feature, I guess) but you > can do the > >> test by hand. It's described in the Arellano paper in the > help file, > >> and I think Vince Wiggins had a post on Statalist some > time ago that > >> describes how to do it. > >> > > >> > Cheers, > >> > Mark > >> > > >> >> > >> >> -Steve > >> >> > >> >> > >> >> > >> >> On Thu, Jul 2, 2009 at 4:47 PM, Schaffer, Mark > >> >> E<M.E.Schaffer@hw.ac.uk> wrote: > >> >> > Steve, > >> >> > > >> >> >> -----Original Message----- > >> >> >> From: Steven Archambault [mailto:archstevej@gmail.com] > >> >> >> Sent: 02 July 2009 22:41 > >> >> >> To: statalist@hsphsun2.harvard.edu; Schaffer, Mark E > >> >> >> Cc: austinnichols@gmail.com; Alfred.Stiglbauer@oenb.at > >> >> >> Subject: Re: st: RE: Hausman test for clustered random vs. > >> >> >> fixed effects (again) > >> >> >> > >> >> >> Mark, > >> >> >> > >> >> >> I should have commented on this earlier, but when I eye the > >> >> >> coefficients for both the FE and RE results, I see that > >> >> some of them > >> >> >> are quite different from one another. However, the > >> xtoverid result > >> >> >> suggests RE is the one to use. Does anybody see this as > >> a problem? > >> >> >> The numerator of the Hausman wald test is the difference in > >> >> >> coefficients of the two models. Is this not missed in > >> the xtoverid > >> >> >> approach? > >> >> > > >> >> > A few things here: > >> >> > > >> >> > - The "xtoverid approach" in this case is **identical** to > >> >> the traditional Hausman test in concept. They are both > >> >> vector-of-contrast tests, the contrast being between the 9 > >> FE and RE > >> >> coefficients. The **only** difference in this case > >> between the GMM > >> >> stat reported by -xtoverid- and the traditional Hausman > >> stat is that > >> >> the former is cluster-robust. In addition to the > >> references on this > >> >> point that I cited in my previous posting, you should also > >> check out > >> >> Ruud's textbook, "An Introduction to Classical > Econometric Theory". > >> >> > > >> >> > - The test has 9 degrees of freedom because 9 coefficients > >> >> are being contrasted jointly. This means that some can > indeed be > >> >> quite different, but if the others are very similar > then a test of > >> >> the joint contrasts can be statistically insignificant. > >> >> > > >> >> > - The p-value reported by -xtoverid- is 10%, which a little > >> >> worrisome. If you were to do a vector-of-contrast tests > >> focusing on > >> >> a subset of coefficients instead of all 9 (not supported by > >> >> -xtoverid- but do-able by hand), you could well find that > >> you reject > >> >> the null at 5% or 1% or whatever. I don't think it's > >> straightforward > >> >> to conclude that RE is the estimator of choice. > >> >> > > >> >> > Hope this helps. > >> >> > > >> >> > Cheers, > >> >> > Mark > >> >> > > >> >> >> > >> >> >> I am posting my regression results to show what I am > >> talking about > >> >> >> more clearly. > >> >> >> > >> >> >> Thanks for your input. > >> >> >> -Steve > >> >> >> > >> >> >> > >> >> >> Fixed-effects (within) regression Number of obs > >> >> >> = 404 > >> >> >> Group variable: id_code_id Number of > >> >> groups = > >> >> >> 88 > >> >> >> > >> >> >> R-sq: within = 0.2304 Obs per > >> >> >> group: min = 1 > >> >> >> between = 0.4730 > >> >> >> avg = 4.6 > >> >> >> overall = 0.4487 > >> >> >> max = 7 > >> >> >> > >> >> >> F(9,87) > >> >> >> = 2.47 > >> >> >> corr(u_i, Xb) = -0.9558 Prob > F > >> >> >> = 0.0148 > >> >> >> > >> >> >> (Std. Err. adjusted for 88 > >> clusters in > >> >> >> id_code_id) > >> >> >> > -------------------------------------------------------------- > >> >> >> ---------------- > >> >> >> | Robust > >> >> >> lnfd | Coef. Std. Err. t P>|t| > >> >> [95% Conf. > >> >> >> Interval] > >> >> >> > -------------+------------------------------------------------ > >> >> >> ---------- > >> >> >> -------------+------ > >> >> >> lags | -.0267991 .0185982 -1.44 0.153 -.063765 > >> >> >> .0101668 > >> >> >> lagk | .0964571 .0353269 2.73 0.008 > >> >> >> .0262411 .166673 > >> >> >> lagp | .2210296 .1206562 1.83 0.070 > >> >> >> -.0187875 .4608468 > >> >> >> lagdr | -.0000267 .0000251 -1.06 0.291 -.0000767 > >> >> >> .0000232 > >> >> >> laglurb | .3483909 .1234674 2.82 0.006 .102986 > >> >> >> .5937957 > >> >> >> lagtra | .1109513 .1267749 0.88 0.384 > >> >> >> -.1410275 .3629301 > >> >> >> lagte | .0067764 .004166 1.63 0.107 > >> >> >> -.0015039 .0150567 > >> >> >> lagcr | .0950221 .0683074 1.39 0.168 > >> >> >> -.0407463 .2307905 > >> >> >> lagp | .0343752 .1291378 0.27 0.791 > >> >> >> -.2223001 .2910506 > >> >> >> _cons | 4.316618 1.996618 2.16 0.033 > >> >> >> .348124 8.285112 > >> >> >> > -------------+------------------------------------------------ > >> >> >> ---------- > >> >> >> -------------+------ > >> >> >> sigma_u | .44721909 > >> >> >> sigma_e | .0595116 > >> >> >> rho | .98260039 (fraction of variance due to u_i) > >> >> >> > -------------------------------------------------------------- > >> >> >> ---------------- > >> >> >> > >> >> >> > >> >> >> > >> >> >> Random-effects GLS regression Number of obs > >> >> >> = 404 > >> >> >> Group variable: id_code_id Number of > >> >> groups = > >> >> >> 88 > >> >> >> > >> >> >> R-sq: within = 0.1792 Obs per > >> >> >> group: min = 1 > >> >> >> between = 0.5074 > >> >> >> avg = 4.6 > >> >> >> overall = 0.5017 > >> >> >> max = 7 > >> >> >> > >> >> >> Random effects u_i ~ Gaussian Wald chi2(9) > >> >> >> = 48.97 > >> >> >> corr(u_i, X) = 0 (assumed) Prob > chi2 > >> >> >> = 0.0000 > >> >> >> > >> >> >> (Std. Err. adjusted for > >> clustering on > >> >> >> id_code_id) > >> >> >> > -------------------------------------------------------------- > >> >> >> ---------------- > >> >> >> | Robust > >> >> >> lnfd | Coef. Std. Err. z P>|z| > >> >> [95% Conf. > >> >> >> Interval] > >> >> >> > -------------+------------------------------------------------ > >> >> >> ---------- > >> >> >> -------------+------ > >> >> >> lags | -.01138 .0135958 -0.84 0.403 -.0380274 > >> >> >> .0152673 > >> >> >> lagk | .0115314 .0180641 0.64 0.523 > >> >> >> -.0238735 .0469363 > >> >> >> lagp | .2551701 .119322 2.14 0.032 > >> >> >> .0213033 .4890369 > >> >> >> lagdr | -6.17e-06 .0000153 -0.40 0.686 -.0000361 > >> >> >> .0000238 > >> >> >> laglurb | .0657802 .0153923 4.27 0.000 .0356119 > >> >> >> .0959486 > >> >> >> lagtra | .0022183 .0579203 0.04 0.969 > >> >> >> -.1113034 .11574 > >> >> >> lagte | .0048012 .0016128 2.98 0.003 > >> >> >> .00164 .0079623 > >> >> >> lagcr | .1051833 .045994 2.29 0.022 > >> >> >> .0150368 .1953298 > >> >> >> lagp | .184373 .1191063 1.55 0.122 > >> >> >> -.0490711 .4178171 > >> >> >> _cons | 9.071133 .2322309 39.06 0.000 > >> >> >> 8.615968 9.526297 > >> >> >> > -------------+------------------------------------------------ > >> >> >> ---------- > >> >> >> -------------+------ > >> >> >> sigma_u | .10617991 > >> >> >> sigma_e | .0595116 > >> >> >> rho | .76095591 (fraction of variance due to u_i) > >> >> >> > -------------------------------------------------------------- > >> >> >> ---------------- > >> >> >> > >> >> >> . xtoverid; > >> >> >> > >> >> >> Test of overidentifying restrictions: fixed vs > random effects > >> >> >> Cross-section time-series model: xtreg re robust > Sargan-Hansen > >> >> >> statistic 14.684 Chi-sq(9) P-value = 0.1000 > >> >> >> > >> >> >> > >> >> >> > >> >> >> > >> >> >> > >> >> >> 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. > >> >> > > >> >> > > >> >> > >> > > >> > > >> > -- > >> > Heriot-Watt University is a Scottish charity registered > >> under charity > >> > number SC000278. > >> > > >> > > >> > > > > > > -- > > Heriot-Watt University is a Scottish charity registered > under charity > > number SC000278. > > > > > -- 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/

**References**:**Re: st: RE: Hausman test for clustered random vs. fixed effects (again)***From:*Steven Archambault <archstevej@gmail.com>

**RE: st: RE: Hausman test for clustered random vs. fixed effects (again)***From:*"Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>

**RE: st: RE: Hausman test for clustered random vs. fixed effects (again)***From:*"Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>

**Re: st: RE: Hausman test for clustered random vs. fixed effects (again)***From:*Steven Archambault <archstevej@gmail.com>

**RE: st: RE: Hausman test for clustered random vs. fixed effects (again)***From:*"Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>

**Re: st: RE: Hausman test for clustered random vs. fixed effects (again)***From:*Steven Archambault <archstevej@gmail.com>

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