Assuming that the underlying dimension really is the same for both
initiatives, ordered probit seems appropriate (and preferable to
two-step estimation). The dependent variable would be coded 0 (No on
both), 1 (Yes on 8 only), 2 (Yes on both), 3 (Yes on 13 only). It isn't
clear what an appropriate null hypothesis would be here, but you could
bolster the credibility of the model by rerunning the ordered probit
with alternative orderings of the vote pairs and showing that they fit
the data less well.

Krehbiel and Rivers (AJPS 1988) and Bartels (APSR 1991) have analogous
set-ups.


-----Original Message-----
From: Political Methodology Society [mailto:[log in to unmask]] On
Behalf Of David Hugh-Jones
Sent: Monday, March 06, 2006 6:33 AM
To: [log in to unmask]
Subject: [POLMETH] strategy for pairs of votes

Hi guys

I am examining pairs of initiative votes, such as votes on California's
Propositions 13 and 8 (8 was a counter-initiative placed on the ballot
by the legislature). My basic hypothesis looks like
this:



                                          [=== Yes on 13 ==========...
                           [===== Yes on 8 ====]
<-----------------------------------------------------------------------
------------->
underlying policy preference


I.e. moderates vote yes on 8, and there is some overlap where people
vote yes on both.

As I don't have a nice linear measure of policy preference, my idea was
to (logit) regress support for Proposition 13 against my independent
variables (which are almost all categorical), then to use each
individual's predicted logged odds for support of 13 as a measure of
underlying policy preference. I could then put this predicted value into
a logit on support for Proposition 8, either interacted with actual
support for 13, or in two separate regressions for supporters and
opponents of 13. The expectation would be that the policy variable would
be significant but with opposite signs for yes and no voters on 13.

However, I am worried about endogeneity: if the votes are interrelated,
is using the Yhats for one vote in a regression on the other acceptable?

Any thoughts would be welcome.

Cheers
David Hugh-Jones

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