Discretely proceeding from cycle to chaos on Goodwin's path

Abstract

Goodwin's [Goodwin, R.M., 1951. The nonlinear accelerator and the persistence of business cycles. Econometrica 19, 1–17; Goodwin, R.M., 1955. A model of cyclical growth. In: Lundberg, E. (Ed.), The Business Cycle in the Post-war World. Macmillan, London, pp. 203–221] nonlinear multiplier–accelerator model, worked out in continuous-time, is a recognised contribution to business cycle theory. It is rarely observed that its first version was a linear model formulated in discrete-time [Goodwin, R.M., 1946. Innovations and the irregularity of economic cycles. Review of Economics and Statistics 28, 95–104]. A few decades later, he restated the fully-fledged nonlinear version of the model in discrete-time showing that such a version may account better for the complex behaviour of empirical time series [e.g., Goodwin, R.M., 1985. An irregular, asymmetric oscillator, or The discrete charm of erraticism, Mimeo, Siena (reproduced, with the title The discrete charm of erraticism, in Goodwin, R.M., 1989. Essays in Nonlinear Economic Dynamics. Peter Lang, Frankfurt am Main, pp. 139–156); Goodwin, R.M., 1988. The multiplier/accelerator discretely revisited. In: Ricci, G., Velupillai, K. (Eds.), Growth Cycles and Multisectoral Economics: The Goodwin Tradition. Springer-Verlag, Berlin, pp. 19–29]. The article reconstructs the evolution of the multiplier–accelerator model in Goodwin's thought with special emphasis on the early and late discrete version. First, the genesis of the model is considered in some depth in order to clarify its foundations based on the constraints of a monetary economy. Second, the results of Goodwin's late contributions are amended and generalised. Finally, the path followed by Goodwin is reconstructed and appraised in the light of the dialectics between continuity and discontinuity, regularity and irregularity, stability and instability that steered its direction. The main conclusion is that Goodwin's path should be further pursued as an effective alternative to the equilibrium business cycle models.