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Re: st: Hausman error


From   "Mark Schaffer" <M.E.Schaffer@hw.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Hausman error
Date   Thu, 31 Oct 2002 14:58:34 -0000

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 <marie.olson@wayne.edu>
Organization:   	MTDS
To:             	statalist@hsphsun2.harvard.edu
Subject:        	st: Hausman error
Send reply to:  	statalist@hsphsun2.harvard.edu

> 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
> 
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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
*
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*   http://www.ats.ucla.edu/stat/stata/



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