Nonlinear Inflation Expectations and Endogenous Fluctuations

The standard new Keynesian monetary policy problem is presentable as a set of linearized equations, for values of endogenous variables relatively close to their steady-state. As a result, only three possibilities are admissible in terms of long-term dynamics: the equilibrium may be a stable node, an unstable node or a saddle point. Fixed point stability (a stable node) is generally guaranteed for an active monetary policy rule. The benchmark model also considers extremely simple assumptions about expectations (perfect foresight is frequently assumed). In this paper, one inquires how a change in the way inflation expectations are modelled implies a change in monetary policy results, when an active Taylor rule is considered. By assuming that inflation expectations are constrained by the evolution of the output gap, we radically modify the implications of policy intervention: endogenous cycles, of various periodicities, and chaotic motion will be observable for reasonable parameter values.