In my view, AKHS 2003 (see
http://gking.harvard.edu/files/akhs.pdf)
contains a good answer to the question. "Logical inconsistency" is not an
issue for applied researchers; the only issue in making ecological
inferences or any other inferences in practice is whether they are
accurate. Most applications of linear regression analysis are "logically
inconsistent" since few dependent variables are entirely unconstrained as
the technique assumes; the only issue there is the validity of the
inferences made from such analyses, which is where ideas like omitted
variable bias, selection bias, etc., come in. AKHS describes the
preferred method we all agree on (the original EI extended model), and for
the two-stage model how far your answers can be from the truth, the fact
that the average width of the bounds and the variance in the width of the
bounds over districts accurately predict errors, and how we know (using
only aggregate data) when the technique will work to recover individual
behavior accurately.
Gary
On Mon, 9 Aug 2004, Gregory Pettis wrote:
Gary,
As an applied researcher, I'm curious as to your reaction to the Herron
and Shotts article in the January 2004 AJPS. They essentially argue that
for any
meaningful application involving EI to employ the extended model, and they
explain how to do so.
Obviously if you have serious disagreements with their argument you cannot
address their points in full in an email to a listserve.
I guess something I'm wondering about in particular is the relationship
between the information contained in the bounds and how EI responds to
aggregation bias. H&S make a convincing argument (as far as I am
concerned, at this point anyway) that this "logical inconsistency" means
aggregation bias will be passed along to contaminate any second-stage EI-R
effect estimates. However, it seems intuitive to me that this problem is
not necessarily absolutely corrupting, but more a matter of degree. They
show with the Burden and Kimball data that in that case this "logical
inconsistency" was a real problem. However, the bounds in that data was
quite atrocious. I can imagine that if you have very informative data (a
la AKHS 2003), and then you run extended models with some covariates, that
these extended models might remove some of the aggregation bias from the
resulting second stage estimates (in fact, that's what they are designed
to do). We don't have Monte Carlo simulations on this question, only one
example with poor data, so the question is open as to the degree to which
this "logical inconsistency" actually matters for the estimates.
I guess I'm wondering if this is logic you might agree with, and I'm
curious as to your other thoughts. I really should have discussed this
with you at PolMeth, but the article only came to my attention later.
Greg
Gregory A. Pettis
ABD, Political Science
UNC Chapel Hill
Polling Fellow, Elon University
CB # 2203
Elon, N.C. 27244
(336) 278-5239
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