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Re: st: Hausman test

From   "Mark Schaffer" <[email protected]>
To   [email protected]
Subject   Re: st: Hausman test
Date   Thu, 5 Dec 2002 17:16:04 -0000


Date sent:      	Thu, 05 Dec 2002 02:00:13 -0500
To:             	[email protected]
From:           	Zhehui Luo <[email protected]>
Subject:        	st: Hausman test
Copies to:      	"Nick Cox" <[email protected]>
Send reply to:  	[email protected]

> Dear Listers,
> In Stata manual on Hausman method and formulas, they describe the test as 
> H=(b1-b2)'[V(b1)-V(b2)]^-1(b1-b2). I assume they use the difference of the 
> variances, instead of the variance of the difference. Is that the case?

Yes, that's right.  You can find this in most any graduate 
econometrics textbook, or, of course, in Hausman's original (1978) 

> If 
> so, is it correct to use heteroskedasticity robust standard errors for 
> Hausman test?

This is correct, though you need to beware of two things:

- You might get a negative test statistic.  An interpretation 
problem, though not a big one.

- Stata's -hausman- command deduces the degrees of freedom for the 
test from the rank of the variance-difference matrix.  In the case of 
robust variances, this method might or might not yield the correct 
degrees of freedom.

For example, if you are testing for endogeneity in an IV estimation, 
the correct degrees of freedom will be the number of regressors 
tested.  The rank of the matrix will typically be greater than this, 
however, and hence the method used by -hausman- will typically cause 
it to give you the right test statistic but with too many degrees of 

<Shameless self promotion follows>

This is discussed in the working paper by myself, Kit Baum and Steve 
Stillman, available on the Boston College web site:

If indeed you want to do an endogeneity test for IV estimation with 
robust standard errors, then you can use ivreg2 (also written by us) 
for this and guarantee a positive test stat with the right degrees of 
freedom.  See the paper.

Hope this helps.


> In other words, is it correct to do the following?
> .estimate the less efficient, but consistent model, with robust option
> .hausman, save
> .estimate the fully efficient model, with robust option
> .hausman
> Thanks for any helpful comments.
> Zhehui
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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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