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RE:st: Part II: An error in the xtabond-description


From   Mark Schaffer <M.E.Schaffer@hw.ac.uk>
To   statalist@hsphsun2.harvard.edu, Giovanni Bruno <giovanni.bruno@uni-bocconi.it>
Subject   RE:st: Part II: An error in the xtabond-description
Date   Mon, 23 Aug 2004 22:20:07 +0100 (BST)

Hi all,

The Sargan-Hansen stat uses residuals in two places.  To abuse the 
sandwich metaphor a bit, it uses residuals in the meat and also in the 
bread (as mustard?).

Arellano-Bond (1991), p. 282, eqn (10) uses the 2-step residuals in both 
the meat and the bread.

The Stata xt manual, p. 32, eqn at the bottom, uses the 2-step residuals 
in the bread and the 1-step residuals in the meat (A2).

It's worth pointing out that although these two definions of the Sargan-
Hansen stat are different, they will both yield valid test statistics, and 
there's no particular econometric reason (at least, one that I'm aware of) 
to favour one over the other.

As for other reasons: the A-B definition has the advantage of being the 
definition in the much-cited A-B paper.  On the other hand it's a little 
more standard with 2-step GMM in general these days to use the definition 
used by Stata (and ivreg2, for that matter); see, e.g., Hayashi (2000), 
pp. 212-13.  I suppose one reason in favour of the latter is that the 2-
step efficient GMM estimator minimizes Hansen's J, and this minimum value 
is given by the Sargan-Hansen stat using the same definition that Stata 
uses (and ivreg2, and Hayashi).

--Mark

Quoting Giovanni Bruno <giovanni.bruno@uni-bocconi.it>:

> David
> 
> I agree that S1 uses 1-step residuals. The problem is about S2 (last
> formula at 
> page 32 in the xt manual), which is based on A2 that necessarily
> uses 1-step 
> residuals. This is not the 2-step Sargan in Arellano and Bond (1991)
> paper, 
> formula (10) p. 282 that employs 2-step residuals.  
> 
> Giovanni
> 
>  
> > While it is possible to define a Sargan statistic that uses the
> one-step
> > moment conditions and the two-step weighting matrix, this is not
> the
> > one-step Sargan test suggested by Arellano and Bond (1991).  The
> one-step
> > Sargan statistic reported by -xtabond- is the s_1 statistic
> suggested by
> > Arellano and Bond (1991) page 282, it uses the one-step
> residuals.
> > 
> > 
> >   --David
> >     ddrukker@stata.com
> > 
> > References
> > 
> > Arellano, M. and Bond, S. (1991) "Some tests of specification for
> panel
> > data:
> > Monte Carlo evidence and an application to Employment Equations",
> The Review
> > of Economic Studies, 58(2) 277-297.
> > *
> > *   For searches and help try:
> > *   http://www.stata.com/support/faqs/res/findit.html
> > *   http://www.stata.com/support/statalist/faq
> > *   http://www.ats.ucla.edu/stat/stata/
> > 
> 
> 
> -- 
> Giovanni Bruno
> Istituto di Economia Politica, UniversitÓ Bocconi
> Via U. Gobbi, 5, 20136 Milano
> Italy
> tel. + 02 5836 5411
> fax. + 02 5836 5438
> *
> *   For searches and help try:
> *   http://www.stata.com/support/faqs/res/findit.html
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
> 



Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3008
email: m.e.schaffer@hw.ac.uk
web: http://www.sml.hw.ac.uk/ecomes
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