Non-linearities in Economics

The term "chaos" has been commonly used to hint non-linear dynamics characterized by an apparent absence of order and therefore incomprehensible and unpredictable behaviour. Instead, through isolated research conducted by scholars out of the scien- tic mainstream, it was shown that a chaotic dynamics is not only ordered [66] and therefore intelligible, but also that it is deterministic and controllable. E. N. Lorenz, a universally recognized forerunner in the study of chaotic phe- nomena, rst discovered in the 1960s a so-called "strange attractor" in a three- dimensional continuous-time dynamic system, when carrying out numerical experi- ments on convection ows [112]. He was able to publish his work in marginal journals only, as the concepts he used were unusual to say the least. Silence about this topic continued until well into late 1970s when in the United States several Physics scho- lars, among whom we remember M. J. Feingelbaum [32] [63], drew the attention of the scientic world to the "strange" results of this type of research. In reality, the problem of chaotic phenomena and more generally of non-linear dynamical systems is their poor permeability to the classical instruments of investiga- tion of dynamics so dominated by the problem of simplicity and regularity. Empirical evidence, on the contrary, shows a dierent world characterized by complexity and disharmony [68]. In economics, dynamics are usually non-linear and characterised by cyclical uc- tuations which are called "business cycles". Burns and Mitchell (1946)[34] dene business cycles as a type of uctuation which "consists of expansions occurring at about the same time in many economic activities, followed by similarly general reces- sions, contractions, and revivals which merge into the expansion phase of the next cycle". Imperfections may be intended as those perturbations of the equilibrium that can lead to recessions or to expansions (Fig. 0-1). The reason why we deal with chaotic models in economics is that, dierently from stochastic models like the so-called "real business cycle" (RBC), the dynamics can be understood and explai- ned in terms of the structural characteristics of the system rather than external and random shocks (i.e. endogenous instead of exogenous).