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Re: st: Testing for endogeneity with xtabond


From   Mark Schaffer <M.E.Schaffer@hw.ac.uk>
To   statalist@hsphsun2.harvard.edu, M Quagliariello <mq102@york.ac.uk>
Subject   Re: st: Testing for endogeneity with xtabond
Date   Thu, 17 Jun 2004 21:59:22 +0100 (BST)

Mario,

Quoting M Quagliariello <mq102@york.ac.uk>:

> Hallo!
> 
> I hope someone can help me.
> Suppose I want to estimate a dynamic panel with xtabond having
> three
> sets of variables:
> A) surely endogenous
> B) surely exogenous
> C) maybe endogenous
> 
> I was thinking to test for the endogenity of variables C) in this
> way:
> 1) estimate a model in which variables C are considered as
> exogenous.
> The estimated coefficients should be consistent and efficient if
> the
> variables are actually exogenous, but inconsistent if the variables
> C)
> are endogenous (model1).
> 2) re-estimate the model considering the variables C) as endogenous
> and
> instrumenting them with their lagged levels (as for the lagged
> dependent
> variable and the other enedogenous regressors). The estimated
> coefficients should be always consistent (model2).
> 3) test for endogeneity using -hausman model2 model1- 
> 
> Is it reasonable?

You don't say so explicitly, but it looks like your category C variables 
are regressors.  In that case, what you want is a test of a subset of 
orthogonality conditions.  Because the suspect instruments are regressors, 
the usual GMM "difference-in-Sargan" or "C test" for a subset of 
orthogonality conditions is numerically equivalent to a Hausman test.  See 
Hayashi's (2000) textbook, pp. 233-34, or the 2003 Stata Journal paper I 
did with Kit Baum and Steve Stillman.

You can proceed as you describe, or, since you're using xtabond2, even 
more easily, just calculate the difference of the Sargan-Hansen statistics 
of the two estimations.  This will be distributed as chi-sq with 
dof=number of suspect instruments.

IMPORTANT - you must make sure that every instrument that appears in model 
2 is also an instrument in model 1.  You want to use lagged C variables as 
instruments when estimating model 2, so that means that you have to use 
exactly these lagged variables as instruments when estimating model 1 as 
well (even though the C variables are being treated as exogenous).

--Mark

> 
> Thanks a lot,
> 
> Mario
> 
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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
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