A reconsideration of Hicks' non-linear trade cycle model

Abstract

The dynamics of Hicks' classical non-linear trade cycle model is reconsidered. The model is an unstable multiplier-accelerator model with an ‘income ceiling’ and an ‘investment floor’. In the simplest two-dimensional version of the model (the basic Hicks model), all consumption lags one period behind income, while all investment outlays are concentrated in the period immediately following the originating change in income. We show that, in addition to stable cycles, so-called ‘quasi-periodic attractors’ can occur in the basic Hicks model. However, in the simplest version of the model, the dynamics are always regular and chaotic income fluctuations do not occur. When consumption and/or investment is distributed over several time periods, higher dimensional versions of the Hicks model are obtained, and the dynamic behaviour can be much more complicated. We show that in the simplest version, the three-dimensional Hicks model, strange-chaotic attractors can occur. The three-dimensional Hicks model also exhibits coexistence of different attractors.