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

To |
statalist@hsphsun2.harvard.edu, Lucio Vinhas de Souza <lvdesouza@yahoo.com> |

Subject |
Re: st: Basic question on Hausman test. |

Date |
Sat, 27 Sep 2003 13:05:20 +0100 (BST) |

Lucio, The null is that the two estimation methods are both OK and that therefore they should yield coefficients that are "similar". The alternative hypothesis is that the fixed effects estimation is OK and the random effects estimation is not; if this is the case, then we would expect to see differences between the two sets of coefficients. This is because the random effects estimator makes an assumption (the random effects are orthogonal to the regressors) that the fixed effects estimator does not. If this assumption is wrong, the random effects estimator will be inconsistent, but the fixed effects estimator is unaffected. Hence, if the assumption is wrong, this will be reflected in a difference between the two set of coefficients. The bigger the difference (the less similar are the two sets of coefficients), the bigger the Hausman statistic. A large and significant Hausman statistic means a large and significant difference, and so you reject the null that the two methods are OK in favour of the alternative hypothesis that one is OK (fixed effects) and one isn't (random effects). Your Hausman stat is very big, and you can see why - the differences between some of the coefficients are big enough to be visible to the naked eye, so to speak - and so you can reject random effects as inconsistent and go with fixed effects instead. BTW, xthausman after random effects will do the test for you in one step. Cheers, Mark Quoting Lucio Vinhas de Souza <lvdesouza@yahoo.com>: > Dear all, > > I have a very basic question concerning a Hausman > test. I am comparing a fixed effects panel estimation > with a random effects one (see below). How do I > interpret the results of the Hausman test? Do they > mean that the random effects estimates are > inconsistent? > > Looking forward to your answer and truly yours, > > Lucio Vinhas de Souza > ************************************** > . xtreg ltrade lgdp lpop eud emud trend, fe > > Fixed-effects (within) regression Number > of obs = 57442 > Group variable (i) : ipair Number > of groups = 2611 > > R-sq: within = 0.1548 Obs > per group: min = 22 > between = 0.3077 > avg = 22.0 > overall = 0.2112 > max = 22 > > F(5,54826) = 2008.23 > corr(u_i, Xb) = 0.2545 > Prob > F = 0.0000 > > ------------------------------------------------------- > ltrade | Coef. Std. Err. t P>|t| > [95% Conf. Interval] > -------------+----------------------------------------- > lgdp | .0754704 .0292365 2.58 0.010 > .0181668 .1327741 > lpop | .5473182 .1313844 4.17 0.000 > .2898038 .8048326 > eud | -.2723743 .0951406 -2.86 0.004 > -.4588506 -.085898 > emud | -.9780319 .1085947 -9.01 0.000 > -1.190878 -.7651856 > trend | .1153878 .0018864 61.17 0.000 > .1116905 .1190851 > _cons | -10.33135 2.421705 -4.27 0.000 > -15.07791 -5.584793 > -------------+----------------------------------------- > sigma_u | 2.9860951 > sigma_e | 1.8353774 > rho | .7258032 (fraction of variance due > to u_i) > ------------------------------------------------------- > F test that all u_i=0: F(2610, 54826) = 45.08 > Prob > F = 0.0000 > > . hausman, save > > . xtreg ltrade lgdp lpop eud emud trend > > Random-effects GLS regression Number > of obs = 57442 > Group variable (i) : ipair Number > of groups = 2611 > > R-sq: within = 0.1537 Obs > per group: min = 22 > between = 0.3468 > avg = 22.0 > overall = 0.2963 > max = 22 > > Random effects u_i ~ Gaussian Wald > chi2(6) = 11354.00 > corr(u_i, X) = 0 (assumed) Prob > > chi2 = 0.0000 > > ------------------------------------------------------- > ltrade | Coef. Std. Err. z P>|z| > [95% Conf. Interval] > -------------+----------------------------------------- > lgdp | .2138072 .026484 8.07 0.000 > .1618996 .2657149 > lpop | 1.477494 .0498542 29.64 0.000 > 1.379781 1.575206 > eud | .0097496 .0884326 0.11 0.912 > -.1635752 .1830744 > emud | -1.025233 .1084758 -9.45 0.000 > -1.237842 -.8126247 > trend | .1032162 .001403 73.57 0.000 > .1004664 .105966 > _cons | -25.08318 1.038565 -24.15 0.000 > -27.11873 -23.04763 > -------------+----------------------------------------- > sigma_u | 2.5927197 > sigma_e | 1.8353942 > rho | .66616628 (fraction of variance due > to u_i) > ------------------------------------------------------- > > . hausman > > ---- Coefficients ---- > (b) (B) (b-B) > qrt(diag(V_b-V_B)) > | Prior Current Difference S.E. > -------------+----------------------------------------- > lpop | .5473182 1.477494 -.9301754 > .1215583 > eud | -.2723743 .0097496 -.2821239 > .0350914 > emud | -.9780319 -1.025233 .0472016 > .0050788 > trend | .1153878 .1032162 .0121716 > .001261 > ------------------------------------------------------- > b= less efficient estimates obtained previously from > xtreg > B= fully efficient estimates obtained from xtreg > > Test: Ho: difference in coefficients not systematic > chi2( 5) = (b-B)'[(V_b-V_B)^(-1)](b-B)= 167.24 > Prob>chi2 = 0.0000 > > > > ________________________________________________________________________ > Want to chat instantly with your online friends? Get the FREE > Yahoo! > Messenger http://mail.messenger.yahoo.co.uk > * > * For searches and help try: > * http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > Prof. Mark Schaffer Director, CERT Department of Economics School of Management & Languages Heriot-Watt University, Edinburgh EH14 4AS tel +44-131-451-3494 / fax +44-131-451-3008 email: m.e.schaffer@hw.ac.uk web: http://www.sml.hw.ac.uk/ecomes ________________________________________________________________ DISCLAIMER: This e-mail and any files transmitted with it are confidential and intended solely for the use of the individual or entity to whom it is addressed. If you are not the intended recipient you are prohibited from using any of the information contained in this e-mail. In such a case, please destroy all copies in your possession and notify the sender by reply e-mail. Heriot Watt University does not accept liability or responsibility for changes made to this e-mail after it was sent, or for viruses transmitted through this e-mail. Opinions, comments, conclusions and other information in this e-mail that do not relate to the official business of Heriot Watt University are not endorsed by it. ________________________________________________________________ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Basic question on Hausman test.***From:*"dyap82" <dyap82@hotmail.com>

**References**:**st: Basic question onHausman test.***From:*Lucio Vinhas de Souza <lvdesouza@yahoo.com>

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