# st: Re: overidentification test after reg3

 From Kit Baum To statalist@hsphsun2.harvard.edu Subject st: Re: overidentification test after reg3 Date Sun, 1 Oct 2006 07:13:13 -0400

Valerie,

I don't think that the reg3 syntax you are using will properly handle the notion that a nonlinear transformation of a LHS variable should be considered endogenous. The alternative syntax -- with the endog() option -- will allow you to specify that those d ln p variables are to be treated as endogenous. But the default syntax of reg3 (see help reg3) causes Stata to take the LHS variables as endogenous and treat all others as exogenous. You will probably get quite different results from your reg3 if you correct this. I would suggest estimating the system without constraints, as you have it and as it should be, to analyse the differences, before reimposing the constraints appropriate from economic theory.

Others may want to comment on the notion of an instrumental variables estimator in which some of the endogenous variables to be instrumented are nonlinear transformations of the LHS variables.

The Wooldridge formula you quoted for the Sargan test should then give you a somewhat more sensible d.f. if all the references to d ln p variables are taken as endogneous variables rather than exogenous variables.

Kit Baum, Boston College Economics
http://ideas.repec.org/e/pba1.html
An Introduction to Modern Econometrics Using Stata:
http://www.stata-press.com/books/imeus.html

On Oct 1, 2006, at 2:33 AM, statalist-digest wrote:

Thank you for your trying to help me. What I didn't mentionned (and that's =
why
it was unclear) is that the

dlnp`i' with i =3D1, 2, 3, 4 which are on the RHS of the first 4 equations
correspond to the p`i' (dlnp`i' are just in log and in difference).
ddeflexp is also a tranformed form for exp.
So the variables I supposed to be endogeneous are the four dlnp`i' and exp,
that's why I have written 5 equations of instrumentation.

val=E9rie

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```From   Kit Baum <baum@bc.edu>
```
To statalist@hsphsun2.harvard.edu
Subject st: Re: overidentification test after reg3
Date Thu, 28 Sep 2006 11:00:47 -0400

- ---------------------------------------------------------------------- -----=
- -----
It is not apparent that this system is simultaneous. The dependent variable=
s are
dw1,dw3, dw3, exp, p1, p2, p3, p4 =3D 7. I do not see any of those variable=
s on
the RHS of other equations. If that is the case, there is no simultaneity h=
ere,
and each equation can be estimated by OLS (or, with constraints across
equations, as a SUR via sureg).

If there is no simultaneity, there is no question of identification, and th=
us no
need for a test of overidentifying restrictions. It is not surprising that =
the
routine referenced should come up with a huge number of d.f., as the number=
of
exogenous variables is huge, and that will be multiplied by 7. By my count
you're estimating 48 RHS coefficients (plus constant terms) minus 6
constraints, or 42. Somehow, I knew the answer should be 42.

Kit Baum, Boston College Economics
http://ideas.repec.org/e/pba1.html
An Introduction to Modern Econometrics Using Stata:
http://www.stata-press.com/books/imeus.html

On Sep 28, 2006, at 2:33 AM, Valerie wrote:

am trying to run an over identification test for a constrained
simultaneaous model (with reg3). It is the following :

/*symmetry*/
constraint 1 [dw1]dlnp2 =3D [dw2]dlnp1
constraint 2 [dw1]dlnp3 =3D [dw3]dlnp1
constraint 3 [dw2]dlnp3 =3D [dw3]dlnp2
/*homogeneity*/
constraint 4 [dw1]dlnp1 + [dw1]dlnp2 + [dw1]dlnp3 + [dw1]dlnp4 =3D0
constraint 5 [dw2]dlnp1 + [dw2]dlnp2 + [dw2]dlnp3 + [dw2]dlnp4 =3D0
constraint 6 [dw3]dlnp1 + [dw3]dlnp2 + [dw3]dlnp3 + [dw3]dlnp4 =3D0

reg3(dw1 ddeflexp dlnp1 dlnp2 dlnp3 dlnp4 period dlnyear) /*
*/ (dw2 ddeflexp dlnp1 dlnp2 dlnp3 dlnp4 period dlnyear)/*
*/ (dw3 ddeflexp dlnp1 dlnp2 dlnp3 dlnp4 period dlnyear) /*
*/ (exp explag PIB period)/*
*/ (p1 pxlaitcomteinterp pxlaitcomteinterplag1 ind_sal_interp
pourc_vol_ean_1 pourc_vol_MDDHD_1)/* */ (p2 pxlaitstandinterp
pxlaitstandinterplag1 ind_sal_interp pourc_vol_ean_2 pourc_vol_MDDHD_2)/*
*/ (p3 pxlaitcomteinterp pxlaitcomteinterplag1 pxlaitstandinterp
pxlaitstandinterplag1 ind_sal_interp pourc_vol_ean_3 pourc_vol_MDDHD_3
pourc_vol_parm pourc_vol_beauf) /*
*/ (p4 pxlaitstandinterp pxlaitstandinterplag1 ind_sal_interp
pourc_vol_ean_4 pourc_vol_MDDHD_4), cons(1-6)

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```