1

Paper

Generic Tests for a Nonlinear Model of Congressional Campaign Dynamics Mebane, Walter R. Uploaded 08-25-1996 Keywords Congress elections campaigns differential equations Hopf bifurcation non-nested hypothesis tests Cox tests bootstrap nonlinear models Abstract I develop a statistical model based on a generic third-order Taylor series approximation for differential equation systems that exhibit Hopf bifurcation in order to use district-level cross-sectional data to test a nonlinear dynamic formal model of campaign contributions, district service and voting during and after a U.S. House election. The statistical model represents the key nonlinearities of the formal model's Cournot-Nash equilibrium in a highly robust fashion. For data from the years 1984--85 and 1986--87, non-nested hypothesis tests (implemented using a calibrated, parametric bootstrap method) show that under assumptions of multivariate normality, the nonlinear model is vastly superior to the generic linear alternative defined by the sample mean vector and covariance matrix.

2

Paper

Generic Tests for a Nonlinear Model of Congressional Campaign Dynamics Mebane, Walter R. Uploaded 08-25-1996 Keywords Congress elections campaigns differential equations Hopf bifurcation non-nested hypothesis tests Cox tests bootstrap nonlinear models Abstract I develop a statistical model based on a generic third-order Taylor series approximation for differential equation systems that exhibit Hopf bifurcation in order to use district-level cross-sectional data to test a nonlinear dynamic formal model of campaign contributions, district service and voting during and after a U.S. House election. The statistical model represents the key nonlinearities of the formal model's Cournot-Nash equilibrium in a highly robust fashion. For data from the years 1984--85 and 1986--87, non-nested hypothesis tests (implemented using a calibrated, parametric bootstrap method) show that under assumptions of multivariate normality, the nonlinear model is vastly superior to the generic linear alternative defined by the sample mean vector and covariance matrix.

3

Paper

Congressional Campaign Contributions, District Service and Electoral Outcomes in the United States: Statistical Tests of a Formal Game Model with Nonlinear Dynamics Mebane, Walter R. Uploaded 07-22-1997 Keywords congressional elections campaign contributions campaign finance district service intergovernmental transfers formal model game theory Cournot-Nash equilibrium Nash equilibrium differential equations dynamical system nonlinear dynamics Hopf bifurcation normal form Whitney embedding theorem divergence theorem Liouville's theorem multivariate normal distribution maximum likelihood Wald test stability asymptotic stability Abstract Using a two-stage game model of congressional campaigns, the second stage being a system of ordinary differential equations, I argue that candidates, political parties and financial contributors interact strategically in American congressional elections in a way that is inherently nonlinear. Congressional races in which the incumbent faces a challenge are generated by dynamical systems that have Hopf bifurcations: a small change in the challenger's quality or in the type of district service can change a stable incumbent advantage into an oscillating race in which the incumbent's chances are uncertain. The normal form equations for such a system inspire a statistical model that can recover qualitative features of the dynamics from cross-sectional data. I estimate and test the model using data from the 1984 and 1986 election periods for political action committee campaign contributions, intergovernmental transfers and general election vote shares.