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st: negative Hausman test statistic

From   "Schaffer, Mark E" <>
To   "Galinato, Gregmar" <>, <>
Subject   st: negative Hausman test statistic
Date   Mon, 16 Jul 2007 21:35:08 +0100


From: Galinato, Gregmar [] 
Sent: 16 July 2007 19:11
Cc: Schaffer, Mark E
Subject: negative Hausman test statistic
Dear Prof Schaffer and all stata users,
	Greetings. I came across a stata thread you responded to
regarding negative Hausman test statistics. I am running a simple test
for correlation between the error term and the regressor in RE model to
determine whether to use RE or FE estimates. I am including a short
sample of the code I used in StataSE9:
iis num_pais
xtreg lnbodpappd ngsns50adj lnngtopc nasati lnpaperpc lnngdppc
year1-year15, fe
est store fixed
xtreg lnbodpappd ngsns50adj lnngtopc nasati lnpaperpc lnngdppc
year1-year15, re
hausman fixed 
In the thread, you said "Sometimes the Hausman statistic is guaranteed
to be positive, and if you're getting a negative number it's a sign that
something's wrong.  Other times a negative Hausman statistic is
possible, and can be interpreted as simply being below the relevant
critical value, i.e., you fail to reject the null.  It all depends on
the application."
In this simple example, does a negative Hausman stat mean that I fail to
reject the null hypothesis that there is no correlation between the
error term and the regressor? How does one know if there is something
wrong with the model or you can simply fail to reject the null?
Thank you for your time.


I can offer a two part answer, one pragmatic and one econometric.

The pragmatic answer is that you can download -xtoverid- from ssc-ideas
and run it after your random effects estimation.  It will report a
Hausman test that is guaranteed to be positive definite, and can be made
robust to heteroskedasticity or clustering, unlike the traditional
Hausman stat.

My econometric answer is vaguer.  I've seen somewhere (I think it was
Greene's textbook) a comment that a negative test stat in this context
can be interpreted in the same way as a small test stat, but I can't
recall seeing this worked out formally.  It seems intuitively plausible,

Hope this helps.


Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3296

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