We present a New Keynesian model in which a fraction n of agents are fully rational, and a fraction 1 − n of agents are bounded rational. After deriving a simple reduced form, we demonstrate that the Taylor condition is sufficient for determinacy and stability , both when the proportion of fully rational agents is held fixed, and when it is allowed to vary according to reinforcement learning. However, this result relies on the absence of persistence in the monetary policy rule, and we demonstrate that the Taylor condition is not sufficient for determinacy and stability in the presence of interest rate smoothing. For monetary policy rules that imply indeterminacy, we demonstrate the existence of limit cycles via Hopf bifurcation, and explore a rational route to randomness numerically. Our results support the broader literature on behavioural New Keynesian models, in which the Taylor condition is known to be a useful guide to monetary policy, despite not always being sufficient for determinacy and/or stability.
Levine, P., Calvert Jump, R., & Hommes, C. (2019). Learning, heterogeneity, and complexity in the New Keynesian model. Journal of Economic Behavior and Organization, 166, 446-470. https://doi.org/10.1016/j.jebo.2019.07.014