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From |
"Mark Schaffer" <[email protected]> |

To |
[email protected] |

Subject |
Re: st: panel data hausman negative |

Date |
Thu, 2 Oct 2003 11:22:28 +0100 |

Vince et al., A couple of follow-up questions to Paula's case and Vince's reply: From: [email protected] (Vince Wiggins, StataCorp) To: [email protected] Subject: Re: st: panel data hausman negative Date sent: Wed, 01 Oct 2003 17:20:49 -0500 Send reply to: [email protected] > Paula Garcia <[email protected]> reports getting different > results from -hausman- and -xthausman-. I recommend that Paula > believe the results from -hausman- and not -xthausman-. The main > reason -xthausman- was undocumented was that it was too easily fooled > by non positive definite (PD) differenced covariance matrices or by > variables with degenerate panel behavior. 1. Vince recommends -hausman- over -xthausman-. In Paula's case, however, -hausman- gives a negative statistic whereas -xthausman- gives a positive one. Is this because -xthausman- is being "fooled"? 2. The degrees of freedom in the fixed vs. random effects version is the number of regressors. In Paula's case, -xthausman- gave the (apparently) correct number, 5, whereas -hausman- reported the degrees of freedom to be 4. Is this because of "degenerate panel behaviour" that is again fooling -xthausman-? I suppose another way of asking the question is whether there are circumstances where -hausman- is fooled but -xthausman- isn't. --Mark > Paula notes that -suest- cannot be easily run because -xtreg- does not > produce scores. If Paula wants another test, I suggest an augmented > regression that is asymptotically equivalent to the Hausman test (see > example below). > > Let me take some wholesale excerpts from an earlier statalist post (I > don't recall the exact day). This post addressed a substantially > similar question from Eric Neumayer. > > ---------------------------------- Begin excerts > -------------------------- > > Eric Neumayer <[email protected]> asks why he is getting different > results from -xthaus- and -hausman- when testing for fixed vs. random > effects after estimation with -xtreg-. [...] > > I believe there are open questions about Hausman tests in situations > like Eric's, see the explanation that follows. > > > Preliminaries > ------------- > > It is hard to discuss the Hausman test without being specific about > how the test is performed. Let B be the parameter estimates from a > fully efficient estimator (random-effects regression in this case) and > b be the estimates from a less efficient estimator (fixed-effects > regression), but one that is consistent in the face of one or more > violated assumptions, in this case that the effects are correlated > with one or more of the regressors. If the assumption is violated > then we expect that the estimates from the two estimators will not be > the same, b~=B. > > The Hausman test is essentially a Wald test that (b-B)==0 for all > coefficients where the covariance matrix for b-B is taken as the > difference of the covariance matrices (VCEs) for b and B. What is > amazing about the test is that we can just subtract these two > covariance matrices to get an estimate of the covariance matrix of > (b-B) without even considering that the VCEs of the two estimators > might be correlated -- they are after all estimated on the same data. > We can just subtract, but only because the the VCE of the fully > efficient estimator is uncorrelated with the VCEs of all other > estimators, see Hausman and Taylor (1981), "panel data and > unobservable individual effects", econometrica, 49, 1337-1398). The > VCE of the efficient estimator will also be smaller than the less > efficient estimator. Taken together, these results imply that the > subtraction of the two VCE (V_b-V_B) will be positive definite (PD) > and that we need not consider the covariance between the two VCEs. > > These results, however, hold only asymtotically. For any given finite > sample we have no reason to believe that (V_b-V_B) will be PD. So, it > is amazing that we can just subtract these two matrices, but the price > we pay is that we can only do so safely if we have an infinite amount > of data. The Hausman test, unlike most tests, relies on asymptotic > arguments not only for its distribution, but for its ability to be > computed! Let's discuss what we do what we do when (V_b-V_B) in not > PD in the context of Eric's results. > > Aside: If anyone is interested in a Hausman-like test that drops the > assumption that either estimator is fully efficient, actually > estimates the covariance between the VCEs, and can always be computed, > see Weesie (2000) "Seemingly unrelated est. and cluster-adjusted > sandwich estimator", STB Reprints Vol 9, pp 231-248. The test > unfortunately requires the scores from the estimator, and -xtreg, fe- > does not directly produce these. > > <Note, a version of -suest- command is now official> > > > Of Inverses and Hausman Statistics > ---------------------------------- > > The reason that -xthaus- and -hausman- produce different statistics on > Eric's models is that they take different inverses of this non-PD > matrix. -xthaus- uses Stata's -syminv()- which zeros out columns and > rows to form a sub-matrix that is PD and inverts that matrix, whereas > -hausman- uses a Moore-Penrose generalized inverse. Most of the > literature on Hausman tests suggests that a generalized inverse such > as Moore-Penrose be used when the matrix is not PD, however, I have > not seen a foundation of this suggestion (and would appreciation a > reference if anyone knows of one). > > Two of us at Stata have independently run some informal simulations, > where non-PD matrices are common, to determine if either of these > inverses has nominal coverage for a true null. While these > simulations are not complete enough to share or publish, we both found > that neither inverse performs well. This doesn't seem too surprising > to me, if the information in our sample is insufficient to produce a > PD "VCE" then the basis of the test would seem to be in question. > > -xthaus- does not make it clear when the matrix is not PD. I recall > having read, though I cannot now find the reference, that in the case > of random vs. fixed effects that the matrix was either always PD. > This may have been the thinking in excluding this check from > -xthausman-. Regardless, it is clearly not impossible and is not even > unlikely. Simulations show that non-PD matrices are quite common. > > > An Alternative > -------------- > > Even in their early work, Hausman and Taylor (1981) discuss an > asymptotically equivalent test for random vs. fixed effects using an > augmented regression. There are actually several forms of the > augmented regression, all of which are asymptotically equivalent to > the Hausman test. All of these augmented regression tests are based > on estimating an augmented regression that nests both the random- and > fixed-effects models. They are parameterized in such a way that we > can perform a simple Wald test of a set of the jointly estimated > coefficients. They have fewer of the mechanical and interpretation > problems associated with the Hausman test. > > I have include below my signature a block of code that will perform an > augmented regression test for Eric's model (it also performs the > Hausman test using -xthause- and -hausman-). It can easily be adapted > to any model by changing the depvar and varlist macros. > > If I have given the impression that I don't much care for the Hausman > test, good. I don't. In ad hoc simulations I have found that in > addition to its proclivity to be uncomputable, the test has low power > for the current problem, for tests of engodeniety in instrumental > variables regression, and for tests of independence of irrelvant > alternatives (IIA) in choice models. > > Regardless, the test is a staple in econometrics and it will stay in > Stata. > > > > -- Vince > [email protected] > > > Note: Paula should be able to easily adapt this code. > > ---------------------------------- BEGIN --- foreric.do --- CUT HERE > ------- local id myid local depvar lnuncs local varlist lngdp ecrise > ecfall urban lnhouse femalepa male1544 /* > */ lndiscr lnfree lnpts latin ssa deathp rulelaw protest cathol /* > */ muslim transiti lnethv oecd war year89 year92 year95 > > xtreg `depvar' `varlist', re > hausman, save > xthaus > > xtreg `depvar' `varlist', fe > hausman, less > > tokenize `varlist' > local i 1 > while "``i''" != "" { > qui by `id': gen double mean`i' = sum(``i'') / _n > qui by `id': replace mean`i' = mean`i'[_n] > qui by `id': gen double diff`i' = ``i'' - mean`i' > local newlist `newlist' mean`i' diff`i' > > local i = `i' + 1 > } > > xtreg `depvar' `newlist' , re > > qui test mean1 = mean1 , notest /* clear test */ > local i 2 > while "``i''" != "" { > if `b'[1,colnumb(`b', "mean`i'")] != 0 & /* > */ `b'[1,colnumb(`b', "diff`i'")] != 0 { > qui test mean`i' = diff`i' , accum notest > } > local i = `i' + 1 > } > test > > ---------------------------------- END --- foreric.do --- CUT HERE > ------- > > * > * 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 E. Schaffer Director Centre for Economic Reform and Transformation Department of Economics School of Management & Languages Heriot-Watt University, Edinburgh EH14 4AS UK 44-131-451-3494 direct 44-131-451-3008 fax 44-131-451-3485 CERT administrator http://www.som.hw.ac.uk/cert * * 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/

**References**:**Re: st: panel data hausman negative***From:*[email protected] (Vince Wiggins, StataCorp)

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