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RE: st: Hausman error

From   "Glenn Hoetker" <>
To   <>
Subject   RE: st: Hausman error
Date   Thu, 31 Oct 2002 10:59:15 -0600

Hausman & McFadden state that a negative H score can occur when the
difference in the variance matrices I not positive semidefinite.  A
negative H can be taken as strong evidence that IIA holds (Hausman &
McFadden 1984, pg. 1226).


Glenn Hoetker
Assistant Professor of Strategy
College of Commerce & Business Administration
University of Illinois at Urbana-Champaign
(217) 265-4081

-----Original Message-----
[] On Behalf Of Mark Schaffer
Sent: Thursday, October 31, 2002 8:59 AM
Subject: Re: st: Hausman error

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.


Date sent:      	Thu, 31 Oct 2002 09:22:15 -0500
From:           	Marie Olson <>
Organization:   	MTDS
Subject:        	st: Hausman error
Send reply to:

> 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:
> *
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Prof. Mark E. Schaffer
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
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