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.