Chapter 53 - The Emergence of the Phillips Curve as an Attractor

Abstract

This chapter derives the Phillips curve as the image of a chaotic attractor of the state variables of a nonlinear dynamical system describing the evolution of an economy. This has two important consequences. The Phillips curve in the model is a true long-run phenomenon and it cannot be used for policy purposes. The model is based on an overlapping-generations nontatonnement approach involving temporary equilibria with stochastic rationing in each period and price adjustment between successive periods. In this way, it is possible to obtain complex sequences of consistent allocations allowing for recurrent unemployment and inflation. The occurrence of a Phillips curve as an attractor in the present model requires wages to be sufficiently flexible. Indeed, when wages are rigid downward, the economy typically converges to the market-clearing equilibrium. It is true that convergence is speeded up when wages become flexible downward but when that flexibility is large enough, convergence is destroyed, and irregular behavior emerges. Wage rigidity favors the stability of the economy and its return after a shock to the Walrasian equilibrium, whereas wage flexibility may be destabilizing.