Chaotic dynamics in agricultural markets

Abstract

In a recent article, Chiarella [7] used a nonlinear supply curve with exactly one inflection point in the context of a cobweb model in order to make plausible that chaotic behaviour may result in such a model. There is, however, no exact proof under what conditions chaos can actually show up since Chiarella confines the analysis to a second order approximation to his difference equation. In a somewhat different model (a linear supply and a nonlinear demand curve which can be given a microeconomic foundation) we show that, under the formation of adaptive price expectations, the resulting adjustment mechanism can generate a wide range of dynamic behaviour (depending on the prevailing parameter constellations) such as stability, bifurcations with stable cycles of period 2, 4, 8, ... and, finally, aperiodic time paths, (i.e. we can show that period-3 cycles exist). In a second step, long historical time series of weekly price observations in German agricultural markets are scrutinized with regard to the hypothesis of nonlinearities. We study their correlation dimensions only recently employed by economists as a characteristic measure which allows, under certain conditions, to distinguish between deterministic chaos and random noise. Our results do not provide evidence to reject the hypothesis, although noise infection of the series cannot be ruled out.