# st: RE: Help needed in interpreting the C-statistics in -ivreg2, orthog-

 From Bo MacInnis To "Schaffer, Mark E" , Subject st: RE: Help needed in interpreting the C-statistics in -ivreg2, orthog- Date Tue, 27 Jun 2006 18:07:19 -0700

Mark,

Thank you very much. You are right to point out the discrepancy between the model I referred to and the test statistics I cited. The model that corresponded to is:

ivreg2 y x2 (x1 = z1 z2 z3 z4 z5 z6) X, orthog(x2)

So, x2 "should" be modelled as "exogenous"?

Thank you!
Bo

At 05:53 PM 6/27/2006, Schaffer, Mark E wrote:

Bo,

> -----Original Message-----
> From: Bo MacInnis [mailto:bo@macinnis.org]
> Sent: 28 June 2006 01:39
> To: statalist@hsphsun2.harvard.edu
> Subject: Help needed in interpreting the C-statistics in
> -ivreg2, orthog-
>
> Dear StataListers,
>
> I'd really appreciate if you would help me on a really simple
> question about the -orthog- option in the -ivreg2- command.
>
> Suppose:
>
> ivreg y (x1 x2 = z1 z2) X
>
> Now I want to test whether x2 is endogenous. So I use:
>
> ivreg2 y x2 (x1 = z1 z2) X, orthog(x2)
>
> I get the following statitics:
>
> -orthog- option:
> Hansen J statistic (eqn. excluding suspect orthog.
> conditions):          4.559
>                                                     Chi-sq(4)
> P-val =    0.3356
> C statistic (exogeneity/orthogonality of suspect
> instruments):           1.865
>                                                     Chi-sq(1)
> P-val =    0.1720
>
> Question: Does it mean I fail to reject the null where the
> null is that x2 is endogenous?

That's right.  The first Hansen J stat is a test that the 4
overidentifying restrictions are jointly valid.  The second J stat is a
test that the one specified orthogonality condition is valid, i.e., the
variable is exogenous.

In your case, you find that the 4 overid restrictions are valid (so that
you don't reject the null that they're invalid, i.e., they're OK), and
that the one specified orthogonality condition is valid (so that you
don't reject the null that that it's exogneous/valid).

BTW, I assume the results you are reporting are not for the example
above, since in the model estimated by

ivreg2 y x2 (x1 = z1 z2) X, orthog(x2)

there is only one overidentifying restriction, and so you don't have
enough degrees of freedom to test the exogeneity of just x2 (roughly
speaking, the C stat would have zero degrees of freedom).

Cheers,
Mark

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
email: m.e.schaffer@hw.ac.uk
web: http://www.sml.hw.ac.uk/ecomes

> Thank you so much,
> Bo MacInnis
>
>
>
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