# Re: st: Hausman test

 From "Mark Schaffer" To statalist@hsphsun2.harvard.edu Subject Re: st: Hausman test Date Thu, 5 Dec 2002 17:16:04 -0000

```Zhehui,

Date sent:      	Thu, 05 Dec 2002 02:00:13 -0500
To:             	statalist@hsphsun2.harvard.edu
From:           	Zhehui Luo <luozhehu@msu.edu>
Subject:        	st: Hausman test
Copies to:      	"Nick Cox" <n.j.cox@durham.ac.uk>

> 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)
article.

> 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
freedom.

<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:

http://fmwww.bc.edu/ec-p/WP545.pdf

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.

--Mark

> 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
>
>
> Zhehui
>
>
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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