Chaos in macrodynamics: An excursion through the literature

In this paper we critically review that (vast) part of the literature on chaos theory and economic dynamics, in which the final dynamic equation of the model reduces to an equation of the logistic type. To this end, we first characterise and classify existing models in terms of the elements which, in each of them, account for the existence of a fixed (one-period) time-lag and of a unimodal nonlinearity. Second, we show that the procedure followed in these models is something other than the procedure usually used by mathematicians to reduce a higher dimensional dynamical system to a one-dimensional (Poincaré) iterated map. Finally, the problem is investigated in more detail by making reference to Pohjola’s 1981 study of Goodwin’s 1967 growth cycle model as a one-dimensional-map. It is shown that when Pohjola’s simplifications are relaxed – and this is necessary if we want to preserve Goodwin’s original (“symbiotic-conflictual”) spirit of the model – the discrete time version of Goodwin’s model admits chaotic solutions only for parameter values which are not within economically reasonable ranges. From this arises the confirmation of the risk, always present in these kinds of models, of studying dynamically interesting but economically irrelevant models.