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Re: st: endogeneity and IV


From   Mark Schaffer <M.E.Schaffer@hw.ac.uk>
To   statalist@hsphsun2.harvard.edu, sistoand80 <sistoand80@libero.it>
Subject   Re: st: endogeneity and IV
Date   Fri, 29 Oct 2004 15:32:43 +0100 (BST)

Andrea,

I'm not an xtabond(2) expert, but ...

One way to think about the Sargan stat in xtabond(2) is that it indicates 
that your instrumenting is OK from the point of satisfying the 
orthogonality conditions.  That is, your instruments are "valid".

It does *not* tell you directly about what regressors, if any, actually 
need any instrumenting in the first place.

In the simple IV context, this second question can be addressed using a Wu-
Hausman endogeneity test, or, equivalently in this context, a C or 
difference-in-Sargan test.

In your xtabond(2) application, you could also do a difference-in-Sargan 
test "by hand".  Say you have two specifications.  One treats more 
variables as endogenous, and passes the Sargan test.  You want to know if 
you can treat some of these variables as exogenous, and so you have a 
second specification that does this but is otherwise identical (same 
number of obs, same variables, etc - but note this can be tricky to get 
right in practice).  You run this second spec and take the difference 
between its Sargan and the Sargan from the first spec.  If the difference 
is "big" (i.e., reject the null if it's above a chi-sq critical value with 
#dofs=#vars being tested for exogeneity), you conclude that these 
variables are endogenous and needed instrumenting after all.  If the 
difference is small, then you didn't need to instrument them and you can 
go with your second spec.

Hope this helps.

--Mark

Quoting sistoand80 <sistoand80@libero.it>:

> Dear Mark,
> i need some suggestions about the problem of over-identifying
> restrictions. If I tape
> 
> xtabond y X
> 
> stata instruments Ld.y with its own lags (in level) from t-3 to t
> and, if you think at X as a vector of exogenous variables, d.X. The
> degree of freedom of sargan test is the number of instruments minus
> 1 (the variable instrumented). If, in this case, the sargan reject
> the null hypothesis, it would mean that X are not fully exogenous or
> I would expect this result as the lagged dependent variable has been
> instrumented only with its own lags?
> 
> If I tape
> 
> xtabond y, pre(X)
> 
> stata would instrument Ld.y with lags of y and X in level (y from
> t-3 and X from t-2). In this case, if Sargan test does not reject
> the null, it means that X variables are not predetermined and it may
> be considered as strictly exogenous covariates? And if the Sargan
> rejectes the null, it means that these variables are endogenous?
> (I've already red about the small power of Sargan test that tends to
> overreject the null in presence of heteroskedasticity).
> Thank You very much for your kindly reply,
> best regards
> 
> Andrea Sisto
> University of Eastern Piedmont
> ---------- Initial Header -----------
> 
> >From      : owner-statalist@hsphsun2.harvard.edu
> To          : statalist@hsphsun2.harvard.edu,"Katarina Lynch"
> ferkel999@hotmail.com
> Cc          : 
> Date      : Fri, 29 Oct 2004 13:42:30 +0100 (BST)
> Subject : Re: st: endogeneity and IV
> 
> > Katarina,
> > 
> > Quoting Katarina Lynch <ferkel999@hotmail.com>:
> > 
> > > Dear Statalist,
> > > 
> > > I am trying to inroduce instrumental variables to fix the
> > > endogeneity
> > > problem caused by fixed and random effects regressions. How can
> I
> > > determine
> > > which independent variables are endogenous, i.e. correlated with
> the
> > > error
> > > term? I simply gave the command "pw resid var1 var2 var3 var4"
> and
> > > it gave a
> > > matrix where one of the variables showed a correlation with
> resid.
> > 
> > That's not how you test for endogeneity.  You want use either a
> Sargan-
> > Hansen statistic or the Hausman approach (these are sometimes
> equivalent, 
> > depending on the application).
> > 
> > > Does it
> > > mean that this variable is endogenous or is there any other way?
> The
> > > reason
> > > I am asking this, perhaps, strange question is, in STATA7, the
> > > xtabond
> > > command requires predetermined variables in the sense that
> E(x,
> > > error) is
> > > nonzero.
> > 
> > The Sargan(-Hansen) stat at the bottom of the xtabond output is a
> test of 
> > your orthogonality conditions, i.e., that your exogenous
> independent 
> > variables and instruments are indeed exogenous.
> > 
> > Hope this helps.
> > 
> > --Mark
> > 
> > > 
> > > Thank you,
> > > 
> > > Katarina
> > > 
> > >
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> > 
> > 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
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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
________________________________________________________________

DISCLAIMER:

This e-mail and any files transmitted with it are confidential
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whom it is addressed.  If you are not the intended recipient
you are prohibited from using any of the information contained
in this e-mail.  In such a case, please destroy all copies in
your possession and notify the sender by reply e-mail.  Heriot
Watt University does not accept liability or responsibility
for changes made to this e-mail after it was sent, or for
viruses transmitted through this e-mail.  Opinions, comments,
conclusions and other information in this e-mail that do not
relate to the official business of Heriot Watt University are
not endorsed by it.
________________________________________________________________
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