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st: Re: reg3

From   Kit Baum <>
Subject   st: Re: reg3
Date   Mon, 16 Feb 2009 06:56:31 -0500

It would be much easier to figure out the identification status of these equations if you estimated them one at a time with ivregress or ivreg2. As far as I can see the C equation can be estimated with OLS, as there are no RHS endogenous variables. The P equation needs one instrument (for C) and you have both A and G1-G4 available, so it is identified.

You are correct in noting that these products of exogenous and endogenous are not to be considered exogenous. Thus the OS equation is not identified, as you need three instruments and only have two (S2 and B). The D equation is hopelessly unidentified, as P, C, PC, PST, CST and PCST should all be considered endogenous, and the only excluded instruments are S2 and B.

This problem might be dealt with by the method laid out by Wooldridge in Econometric Analysis of Cross Section and Panel Data, 2002, p.231, where he considers the case of a nonlinear function of an exogenous regressor (in this case the square of, for instance, C). You should be able to create additional instruments with powers and cross-products of the exogenous variables in the model -- not merely the excluded S2 and B, but also ST, S, A, and G1-G4 (although powers and cross- products of dummies are not of much use).

I would try estimating just the D equation, explicitly indicating to ivregress or ivreg2 that the PC, PST, CST and PCST are endogenous, and using powers/cross products of _all_ exogenous vars as instruments, and see what you get. As a recent posting of mine points out, there is no need to employ a systems estimator here. It is probably possible to force reg3 to estimate the right equation, but recognize that if you let it figure out what is endogenous, it has created inconsistent estimates of ALL the equations by mistakenly treating the product terms as exogenous.

Kit Baum, Boston College Economics and DIW Berlin
An Introduction to Modern Econometrics Using Stata:

On Feb 16, 2009, at 02:33 , Narasihman wrote:

I was wondering if it is correct to test interactions and non-linear
effects with reg3. My system of equations is as follows. I am trying
to test for non-linear effects in three of the equations.

reg3 (P ST C S S^2 B)
(C ST S S^2 )
(D  A  S G1-4 (categorical) P ST C P*C P*ST C*ST P*C*ST)
(OS ST D C P S A G1-4)

I will appreciate any inputs. What worried me in this set up was that
while the endogenous variables were fine, the interaction terms (of
endogenous variables) are construed as exogenous variables. Also, ST
in my model is an exogenous variable that is not determined by the
model, I have some interaction terms based on ST with some endogenous
variables in the model.

While I am getting some output, and it seems to be theoretically
meaningful, I am wondering if this is correct? I was looking up
examples on the stata manual and I guess it did not explicitly talk
about non-linear models in the manual. I would appreciate if anyone
has inputs to share on this. I am sorry if this question sounds naive.

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