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). I 1 2 3 4 5 6 7 8 J D D D D R R R R P eriodI ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... P eriodII ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... P eriodIII ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 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.