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

Date |
Thu, 2 Jul 2009 23:47:59 +0100 |

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. * * 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>

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