My understanding is that this problem can arise in finite samples,
except in certain special cases; it has to do with the matrix
difference (V_b-V_B) not being positive definite. It can happen that
in finite samples the covariance matrix V_B of the efficient
estimator B is "bigger" (in matrix terms) that the cov matrix V_b of
the consistent but inefficient estimator b.
This possibility can be ruled out in special cases. For example, in
the endogeneity test of OLS vs. IV, using a single estimate of the
error variance to construct V_b and V_B will guarantee a positive
test statistic. This can be done *in this case* through the use of
the -sigmamore- option - it will construct the IV and OLS covariance
matrices using the more efficient sigma from OLS, and by doing this
will guarantee that the matrix difference is p.d.
I don't know enough about your application to judge whether the
-sigmamore- option is valid there too ... but I doubt it.
I think there's a place in Greene's econometrics text where quotes
Hausman saying that a negative test statistic can be cautiously
interpreted as a failure to reject the null ... but I'm not sure
about this.
Hope this helps.
--Mark
Date sent: Thu, 31 Oct 2002 09:22:15 -0500
From: Marie Olson <[email protected]>
Organization: MTDS
To: [email protected]
Subject: st: Hausman error
Send reply to: [email protected]
> I am running a series of analyses using xtlogit. In order to identify
> which method of xtlogit is appropriate, I am using the Hausman test
> with xtlogit, fe run first, then xtlogit, re run second. On occasion,
> I run into the problem where the Hausman test produces an assumption
> error indicating the following:
> Test: Ho: difference in coefficients not systematic
>
> chi2( 1) = (b-B)'[(V_b-V_B)^(-1)](b-B)
> = -0.80 chi2<0 ==> model estimated on
> these
> data fails to meet the
> asymptotic
> assumptions of the Hausman test
>
> I was earlier advised to eliminate the cases dropped by the fixed
> effects model (due to lack of variation in the dependent variable) for
> both analyses, but that did not change the error problem. Does anyone
> have any ideas? Thanks in advance, Marie
>
> *
> * 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/
