Bayesian Model Fitting Party Influence and Insincere Voting

Revealing Congressional Partisan Effects via Hierarchical Ideal Point Estimation
Ying Lu* and Thomson W. McFarland**
*Assistant Professor, Departments of Political Science and Sociology, University of Colorado at Boulder,
Introduction
Lu & Wang’s Model (2007)
• “Party Effects” in the U.S. Congress are elusive and hard
to separate from ideological preferences of the party of
members.
Let Yij be the observed vote result of house member i on
question j, tij be the perceived score associated with voting “Yea” instead of “Nay”
½
“Yea” 1 if tij ≥ 0
Yij =
“Nay” 0 if tij < 0,
• In particular, voting-based estimates of party effects have
difficulties separating competing factors of ideology and
party (Krehbiel 1993, 2000)
• But effects of party have important consequences: how
polarized are the parties in Congress? What role do parties play? Is “Conditional Party Government” a workable model of parties?
• Problem with existing research
– Party effect is frequently based on party cohesion or
simple additional terms in members’ utility functions.
– Polarization is frequently interpreted as a difference
in the mean or median ideal point across parties.
– Lack of a real measure of ”party effect”, i.e. how
are the voting behaviors of party members being influenced by the party position of each bill given their
ideal points?
Hierarchical Ideal-Point Estimation
• Classical ideal point estimation (the ”null” model) has
been based on upon two unrealistic assumptions:
– House members vote independently from each other;
– Given their ideal points, each house member votes independently.
• Lu and Wang (2007) propose a hierarchical ideal point
estimation framework which can model correlated voting behaviors:
– grouplet: Members of the same party who vote together.
– testlet: Bills voted on during the same House (or same
time period).
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Bayesian Model Fitting
The latent score is modeled,
tij = aj (θi + γid(j)) − ϕp(i)j − bj + ²ij
**Ph.D. Candidate, Department of Political Science, University of Colorado at Boulder
(1)
where ²ij ∼ N (0, 1) independently, γid(j) and ϕp(i)j are
the random testlet and grouplet effects. Moreover,
γik ∼ N(0, σγ2k )
ϕlj ∼ N(µϕl , σϕ2 l )
d(j) = k is the testlet index, k = 1, . . . , K. p(i) = l is the
grouplet index, l = 1, . . . , L.
Extension: Time Varying Party Effect
• In model (1), members of the same party can be view as a
grouplet, σϕ2 l measures the strength of intra-party correlation, aka, “party” effect.
• Extend previous model to further allow “covariates” at grouplet level to model time varying party effect.
ϕljt ∼ N(µϕl,t , σϕ2 l,t )
We fit the proposed model under Bayesian paradigm.
• Data augmentation and Gibbs sampler to simulate the posterior distributions.
• Noninformative priors are assigned to the parameters.
• Parameter expansion and posterior rescaling to identify the
model.
Partisan Effects in House 101-109
• Data source: voteview.com
• Sample 100 roll calls from each House, removed unanimously
voted questions. Total of 809 votes.
• 978 members: 498 Democrats, 480 Republicans.
• Fit random effect ideal point model, 2 grouplets defined by
party, 3 testlets: House 101-103, House 104-106, House 107109. Party effects may vary across different regimes (as defined by testlets.
• No significant testlet effects detected. The ideological values
of individuals are quite consistent under different regimes.
• Significant grouplet effects, aka, intra-party correlations are
detected.
• Democratic members that would otherwise be more conservative are “pulled farther” across the policy space by the party;
same for would-be liberal Republicans.
Party Polarization
• Southern and Central Democrats and Northeast Republicans
are more likely to vote according to the party line than their
sincere ”ideological positions”.
Spatial Logic
Time Varying Party effects
Decision j presentative i makes involves comparing utilities associated with two alternate policy positions,
Yea :
Nay :
Table 1: Intra-party correlation in three different time periods: Unified Democratic Government, Divided Government, Unified Republican Government
Ui(ζj | λi = l) = −(θi − ζj )2 + ωlj + ηij
Ui(ψj | λi = l) = −(θi − ψj )2 + κlj + νij
2
House Pres House
σD2
s.e.
σR
s.e.
101-103
D
D 2.175 0.236 2.058 0.258
D
R 2.189 0.213 3.559 0.335
104-106
107-109
R
R 5.052 0.511 3.973 0.475
θi is the ideal point, zetaj and ψj are ”Yea” and ”Nay” positions, ωlj and κlj are the party ”Yea” and ”Nay” position.
P (yij = 1|λi = l) = P (Ui(ζj | λi = l) > Ui(ψj | λi = l)
= Φ(aj θi − ϕlj − bj )
ϕlj is party l position for decision j.
• A large positive ϕlj would lead to a ”Nay” decision
among party members given their ideal points. A large
negative value of ϕlj would lead to a ”Yea” decision
more likely. close to zero valued ϕlj has very small impact to individual’s decision.
• The larger the variance of a grouplet, σϕl , likely the
larger ϕlj , the more distinct party position on decision
j.
Contact information: Ying Lu: [email protected], 303-492-7030.
Party Influence and Insincere Voting
Conclusion and Discussion
• Idea point estimates without considering party effect exhibit
great polarization between Democratic and Republican representatives.
• Hierarchical Models allow direct estimation of the quantity of interest: Given the ideal point of the member,
what is the effect of being a member of a certain party?
• Less polarization after controlling for party effect. Existence
of liberal Republicans and conservative Democrats.
• Improvement on cohesion-based models or “two-cutpoint”
models of party effects
• Both parties are more heterogeneous ideologically in each House
than null model indicates.
• Results consistent with expectations; party effect on members generally opposed to party position is strong. Also,
polarization overstated in most previous efforts.
• Democratic party consist of members whose ideological values are less cohesive(?) than members of Republican.
Thomson McFarland: [email protected], 303-492-2680.