Nonlinear monetary policy rules in a pure exchange overlapping generations model

The dynamics of a pure exchange overlapping generations model with endogenous money growth rule is investigated. We consider a nonlinear monetary policy rule which, in each period, bounds the money growth rate so that money is determined by the deviation of the inflation rate from its target. More precisely, we introduce such a mechanism through a sigmoidal money adjustment mechanism characterized by the presence of two asymptotes that bound the money variation, and thus the dynamics. It is shown that, depending on the timing of the monetary policy and the degree of reaction of the Central Bank, the target equilibrium may be destabilized via different types of bifurcations. Multistability and coexistence of attractors may also occur and the study of the basins of attraction allows us to analyze the global dynamic properties of the economy under scrutiny. We find that active monetary policy rules may be relevant for their stabilizing properties, but they also may open the door to equilibrium cycles of any periodicity and even chaos.