Nonlinear dynamics of a simple behavioral model of inflation

We investigate the nonlinear dynamics of a behavioral model for inflation with boundedly rational agents endowed with heterogeneous expectations. In order to to predict the future rate of inflation, agents choose within a set of linear rules and switch among them using, as a performance measure, the most recent forecast error. A four-dimensional nonlinear map describes the model. Its unique fixed point can be destabilized by a Neimark–Sacker bifurcation, as we analytically prove. Moreover, we also show the Neimark–Sacker bifurcation can be either supercritical or subcritical, with a Chenciner bifurcation that can be associated with it. As a direct consequence, various multistability phenomena arise, highlighting the coexistence of the steady state with an invariant closed curve and cycles of different periodicity.