My view on these sorts of modeling questions, for what it's worth
(epsilon, would be my bet), and if I understand your intentions
correctly (I think I do that, at least):
You're fine (statistically), Ben, and you're right, this not a system of
endogenous equations--it's a system of equations in same sense any set
you thought related somehow would be--and its a specific kind of
recursive one, as you say, although I think the label 'recursive' is
often used for a narrower class of similar systems.
An important substantive question that affects how you would want to
specify and estimate these equations, though, is whether you think IV/DV
2, 3, and 4 matter for DV 1 in both their components that are systematic
in IV5-13 and in the non-systematic (i.e., stochastic) parts or by just
one of those paths, and, if both, whether you wanted separate estimates
for the magnitudes of those systematic- and stochastic-component paths.
Depending on your answer to that substantive/theoretical question, a
reasonable strategy here would be to estimate equations 2-4, saving
fitted values and estimated residuals, and either entering just the one
or the other or both to equation 1. A second-order, and wholly
orthogonal question would be whether you want to try to use the fact
that these equations are (substantively) related--so you claim
anyway--to enhance the efficiency of your estimates. If so, SUR or
sometimes labeled SURE for Seemingly Unrelated Regression
(Equations/Estimation), would be a reasonable strategy. Tradeoff there:
enhanced efficiency insofar as specification accurate and equations
actually related vs. errors in specifying one equation either having its
effects isolated to that one or pulled through estimation of all of them
by trying to leverage the cross-equation info for efficiency
enhancement.
Hope this helps, (and hope it sounds right & reasonable to you & to
others reading in...)
Rob
************************************************************************
*
Robert (Rob) J. Franzese, Jr. US Mail: (ISR Room
4246)
Assoc. Prof. Political Science P.O. Box
1248
The University of Michigan Ann Arbor, MI
48106-1248
Research Assoc. Prof. TeleComm:
[log in to unmask]
Center for Political Studies 734-936-1850
(office)
Institute for Social Research, 734-764-3341
(fax)
426 Thompson St., Room 4246
http://www-personal.umich.edu/~franzese
------------------------------------------------------------------------
-
Interim Director, Center for Political Studies,
Institute for Social Research,
University of Michigan, Ann Arbor: Sep 2006-May 2007
************************************************************************
*
> -----Original Message-----
> From: Political Methodology Society [mailto:[log in to unmask]]
On
> Behalf Of Benjamin Appel
> Sent: Thursday, September 14, 2006 11:34 AM
> To: [log in to unmask]
> Subject: [POLMETH] System of Equations Questions
>
> Hi All:
>
> I am having trouble determining if the below problem violates any
> statistical assumptions. Pardon the simplistic notation.
>
> Eq. 1
> DV1=Dem.+IV2 +IV3+IV4+u
>
> Eq. 2
> DV2(which is IV2 in first equation)=Dem.+IV5...IV7+u
>
> Eq.3
> DV3(which is IV3 is first equation)=Dem.+IV8...IV10+u
>
> Eq. 4
> DV4(which is IV4 in the first equation)=Dem.+IV11...IV13+u
>
>
> Basically, Democracy is an IV in the first equation, but is also used
as
> an IV in the other equations (along with various other different/new
> IVs) to explain the IVs in the first equation.
>
> Again, does this problem violate any statistical
properties/assumptions,
> and if so what are the appropriate fixes? It seems somewhat similar to
a
> simultaneous equations problem, but I don't think it is since there
are
> no (non)recursive relationships.
>
> Any suggestions would be greatly appreciated.
>
> Thank you,
>
> Ben Appel
> [log in to unmask]
> Ph.D. Student
> University of Maryland
>
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