Dynamic theories and models—problems and creative potential

Linear and linearized equations dominate economic and econometric modeling. The gains in terms of solubility and interpretation are considerable. However, important phenomena such as social interactions are then at best subject to informal treatments and at worst relegated to the class of supposedly irrelevant phenomena. This chapter explores the potential of non-linear dynamic theories and models of growth and development. We discuss examples of non-linear phenomena that are amenable to formal analysis such as the spread of infectious diseases, segregation processes and imitative behavior. Multiple equilibria occur frequently in non-linear models. One example is the Kaldor model of business cycles; another is Mees’s model of urban growth and decline. Analyzing the stability of models is central to the study of economic dynamics, where the dynamic stability of an equilibrium requires negative feedback. From the 1960s onward, structural stability became a recurrent catchphrase in dynamic analyses. In this chapter we claim that structural instability is a precondition for creativity in the development of new ideas in science and the arts. It is generally only possible to achieve a new stable equilibrium in conjunction with the completion of a creative process. Realistic dynamic economic models tend to contain a mixture of positive and negative feedback loops, leading to chaotic outcomes. One consequence is deterministic and stochastic processes become indistinguishable in practice. It is for this reason that Benoit Mandelbrot claimed that most “financial analyses” are spurious applications of stochastic theory to situations where fractal models would yield better pattern predictions.