Defining and Modeling State-Dependent Dynamic Systems

A state-dependent dynamic system is one in which (1) the marginal effect of x on y at time t ( ) depends on the prior value of the dependent variable , and (2) the persistence of the dependent variable ( ) depends on x t . We present a methodological strategy for dealing with state-dependent dynamic systems and demonstrate the consequences of ignoring state-dependence. As an applied example, we find evidence of state-dependence in the relationship between presidential approval and economic performance: high unemployment rates are most damaging to presidential approval among presidents with the highest initial approval ratings.