# Re: st: xtabond2 + C test

 From Mark Schaffer <[email protected]> To [email protected], Cordula Stolberg <[email protected]> Subject Re: st: xtabond2 + C test Date Tue, 11 Jan 2005 16:05:54 +0000 (GMT)

Cordula,

Quoting Cordula Stolberg <[email protected]>:

> Dear Statalisters,
>
> I am estimating a dynamic panel with -xtabond2- and suspect that one of
> the regressors might be endogenous. To test for the endogeneity of the
> regressor, I followed the procedure suggested by Mark Schaffer
> (http://www.stata.com/statalist/archive/2004-07/msg00101.html), i.e.
> I first estimated the regression treating the regressor as exogenous
> (which gives me the Sargan statistic S0) and then I estimated the
> regression again treating the regressor as endogenous (which gives me the
> other Sargan statistic S1).
>
> Everything looks ok in those regressions. The problem is that the C test
> would then be calculated as S0-S1. Here, I get a negative number (-0.01)
> and since the statistic is distributed as chi-square, I have a problem.

When you do a difference-in-Sargan statistic "by hand" in this way, you
aren't guaranteed a positive test statistic.  This is because the S0 and S1
aren't using the same covariance matrix of orthogonality conditions, much in
the same way that sometimes a standard Hausman statistic can be guaranteed
to be positive-definite by using a single estimate of the error variance.

This isn't a problem, though.  The difference between S0 and S1 is small,
and the fact that in finite samples it might be so small as to be negative
doesn't negate the fact that it's still small.  You can treat this as a
failure to reject the null, i.e., evidence that the regressor can be treated
as exogneous.  (Assuming, as you said, that everything else is OK, e.g., S0
is itself small enough for the Sargan-Hansen test to be passed.)

Cheers,
Mark

>
> Cordula
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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 +44-131-451-3294
email: [email protected]
web: http://www.sml.hw.ac.uk/ecomes
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