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variable in the valence issue/competence model is valence advantage
2
, which is measured by simply
squaring the valence advantage variable. These competence data were only available for senators who
ran for reelection in 2000 and 2002, so the sample used to estimate this model is much smaller than the
distributive policy valence model (n=52 senators for this model). In the future, I plan to conduct similar
experiments to garner measures of incumbent competence relative to challengers for a greater time
period.
These variables in both the distributive policy and the competence models directly test
propositions (2) and (3) of the Groseclose model detailed earlier. If the valence theories are correct, the
variable valence advantage should predict less deviation from the constituency median, while the valence
advantage
2
variable should predict more deviation from the median. Since the dependent variable is a
measure of legislator divergence from the constituency, then the first variable’s coefficient should be
negative and the second variable’s coefficient should be positive. However, if the alternative hypothesis
of diversionary behavior by legislators is correct and legislators deviate in a monotonic fashion from their
states, then only the first variable should be significant and positive or both variables will be significant
and positive.
Other independent variables that are likely to predict deviation are included in both empirical
models. While these variables are included primarily as controls, some are also tests of other hypotheses
regarding ideological shirking by legislators. Two variables are specified in both models to test for
effects specific to elections: quality challenger in the general election and tough primary. The quality
challenger variable is an indicator denoted “1” if the senator was running for reelection and faced a
general election opponent that was a U.S. House representative or governor. One expectation is that this
would lead to less deviation from the median, though following the logic of valence theories, a quality
challenger may have valence advantages over the incumbent as well and this might alternatively lead to
incumbent divergence. Tough primary is an indicator variable denoting if the senator was running for
reelection and faced a primary where the opponent received 10 percent or more of the vote, and we expect
that tough primaries will lead to divergence between the legislator and the general election state median.
Convention