The Phillips Curve as a Long-Run Phenomenon in a Macroeconomic Model with Complex Dynamics

After the presentation of the Phillips curve as an empirical regularity (Phillips [1958]) economists and policy makers alike have tried to exploit it for policy purposes. Even before the oil shocks in the seventies and early eighties this has had mixed success only. With the advent of ''stagflation'' the Phillips curve seemed to be definitely dead but nowadays a majority of economists seems to agree that an inverse relationship between inflation and unemployment holds as long as changes in output and prices are demand-driven. Stagflation occurs only when supply-side shocks occur. Recently, new explanations have been advanced both to investigate theoretically and estimate empirically the Phillips curve and to assess its potential for economic policy. (See for example the special issue of the Journal of Monetary Economics (Vol. 44, N.2, 1999) on ''The Return of the Phillips Curve''.) In the present paper we aim to contribute to this discussion by showing that the Phillips curve may be obtained as the image of a chaotic attractor of the state variables of a non-linear dynamical system describing the evolution of an economy. This has two important consequences: on the one hand the Phillips curve in our model is a true long-run phenomenon and, on the other, it cannot be used for policy purposes. Our model is based on an overlapping-generations non-tatonnement approach involving temporary equilibria with stochastic rationing in each period and price adjustment between successive periods. In this way we are able to obtain complex sequences of consistent allocations allowing for recurrent unemployment and inflation.