Chaotic Dynamics in Optimal Monetary Policy

摘要

There is by now a large consensus in modern monetary policy. This consensushas been built upon a dynamic general equilibrium model of optimal monetarypolicy as developed by, e.g., Goodfriend and King (1997), Clarida et al.(1999), Svensson (1999) and Woodford (2003). In this paper we extend thestandard optimal monetary policy model by introducing nonlinearity into thePhillips curve. Under the specific form of nonlinearity proposed in our paper(which allows for convexity and concavity and secures closed form solutions),we show that the introduction of a nonlinear Phillips curve into the structureof the standard model in a discrete time and deterministic framework producesradical changes to the major conclusions regarding stability and the efficiencyof monetary policy. We emphasize the following main results: (i) instead of aunique fixed point we end up with multiple equilibria; (ii) instead ofsaddle--path stability, for different sets of parameter values we may havesaddle stability, totally unstable equilibria and chaotic attractors; (iii) forcertain degrees of convexity and/or concavity of the Phillips curve, whereendogenous fluctuations arise, one is able to encounter various results thatseem intuitively correct. Firstly, when the Central Bank pays attentionessentially to inflation targeting, the inflation rate has a lower mean and isless volatile; secondly, when the degree of price stickiness is high, theinflation rate displays a larger mean and higher volatility (but this issensitive to the values given to the parameters of the model); and thirdly, thehigher the target value of the output gap chosen by the Central Bank, thehigher is the inflation rate and its volatility.