Dynamical coupling, the non-linear accelerator and the persistence of business cycles

Many of the research questions and programmes that were posed and suggested by Richard Goodwin remain highly relevant today for various methodological, empirical and theoretical reasons. This paper addresses the issue of whether highly articulated and complex economic interactions can be represented by a simplified low-dimension model. We follow the valuable insight offered by Goodwin in 1947, concerning the importance of dynamical interactions (coupling) and the potential role of analogue and/or digital computers in studying them fruitfully. The non-linear, dynamic multiplier–flexible accelerator model of the business cycle proposed in 1951 is extended to the case in which these economies are coupled through trade. The dynamics implied by the coupling are studied by analogy with the well-known Fermi–Pasta–Ulam problem. It is shown that for non-linear economies, even when they are exactly the same, i.e. having the same structural behavioural equations, the very rich dynamics depend crucially on the initial conditions. This result is somewhat unexpected.