Lascher, Hagen, and Rochlin: Gun behind the door
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Lascher, Hagen, and Rochlin. 1996. Gun behind the door? Ballot initiatives, state policies, and public opinion. Journal of Politics 63:1250-1256.
Fig 2 says it all (p 768): The authors want to know whether initiative states are more responsive than noninitiative states. They use opinion data to give each state a liberalism/conservatism score. They also look at common policy outcomes to give each state a liberalism/conservativism score for its public policy. They find that initiatives do not seem to affect how public opinion is reflected in policy outcomes.
See Fig 1: Initiatives are rarely used (outside CA and OR), and when they are used, initiatives frequently fail. So why should legislators pay attention to them?
Matsusaka (2001) published a brief methodological criticism of this piece. Basically, his point was that it makes no sense to compare the coefficient of X (public opinion) in initiative states to the coefficient in non-initiative states.
Matsusaka's main point: "Unless the researcher know exactly how his or her public opinion variables translate into desired policies [in principle], there is no way to determine whether one institution is doing a better job meeting constituent desires than another" (p 1254).
A possible solution (again, from Matsusaka): We should look for situations where we can observe directly the public's desired policy (as opposed to its general level of conservatism). Find survey questions that ask questions about specific policies (e.g. feeling thermometers about the death penalty), then compare them (in each state) to observed policy outcomes. From this, you might be able to learn whether institutions affect policy responsiveness. Gerber's (1996) approach is another way to resolve Matsusaka's complaint.
In Hagen et al. (2001), the authors respond to Matsusaka, claiming that their approach is perfectly acceptable. It analyzes whether opinion predicts policy better in initiative states than in non-initiative states, and it finds no relationship. Matsusaka was right to suggest looking for public opinion data about specific policies, but that would only work in high-salience issue areas (e.g. death penalty and abortion). When it comes to more arcane policy areas (e.g. precise levels of education spending), it probably makes more sense to compare policies only to general public conservatism/liberalism. Note, however, that their response doesn't seem to address Matsusaka's main point head-on.