Cycles and Chaos in Economic Equilibrium

Rating:
Summary: Good introduction to the theory
Review: It was perhaps inevitable that the theory of chaotic dynamical systems would be applied to economics. In an intuitive, everyday sense, economic phenomena is usually perceived as being "chaotic", this notion being equated with a random behavior of sorts. Whether or not economic systems are really random (from a rigorous mathematical standpoint) is the subject of other books. This one addresses the question as to whether chaos does indeed exist in economic systems. Chaos and randomness are of course distinct concepts, and this is brought out clearly by the authors of the articles in the book, the specific theme of which is to shed light on the role of oscillatory dynamics in economic fluctuations. The oscillations are put in the context of chaotic dynamical systems, which, as is well known, have a very rich orbit structure. The emphasis is on theory, but there are some articles that discuss empirical validation of chaotic dynamical system models of time series. What is most interesting about the results in the book is that chaos is a deterministic explanation of the erratic behavior of economic behavior. This is to be contrasted with the situation in financial modeling, where randonmess is thought to be essential because of arbitrage opportunities. It is fascinating to compare the ideas in this book with the ones that are very entrenched in financial modeling. The authors of the articles have been heavily involved in the research of chaotic dynamical systems in economics. Space here permits only a limited review of the contents of the book.

. Before the advent of research in chaos in economics, the complexity of economic phenomena was modeled by linear equations subjected to exogenous shocks. The approach taken in one of the articles discusses to what extent aggregate fluctuations represent endogenous phenomena that are persistent even when there are no random shocks to the economy. Recognizing that chaotic dynamical systems can generate time series that appear irregular or random, discussion is given on the models based on chaos that exhibit the persistence phenomena. Since chaotic systems have countably many periodic orbits, it is natural to ask to what extent these orbits play in models of economic phenomena. One of these considered is the overlapping generations model. A class of robust utility functions, assumed to be constant from one generation to another, are shown to give the existence of bounded trajectories that do not converge to periodic orbits or fixed points, but are also, because of the time scales involved, indistinguishable from periodic orbits of arbitrarily long period, the latter also existing in the model. The existence of these trajectories is interesting, particularly when considering the mechanism by which the trades between generations occur. This mechanism involves the introduction of a central credit authority, and even when the nominal credit expands at a constant rate, the model still exhibits erratic trajectories in the real value of credit. These trajectories appear qualitatively to be very similar to trajectories generated from random processes, and so it is no surprise that statistical techniques and ergodic theory are employed to study their properties.

Another economic model considered in the book is a two-sector growth model that consists of an industry producing consumption goods and another producing capital goods. A dynamical system parametrized by the capital depreciation rate is used to describe the time evolution of the aggregate capital stock over time, and is shown to have chaotic orbits for certain values of the capital depreciation rate. These chaotic orbits exist, interestingly, when capital, but not labor, is very productive in both sectors. An analysis of the relative capital-labor intensities is done to shed light on the oscillatory behavior of the model, this behavior contrary to the expected one of following a smooth averaged path. The latter is expected because of the choice of a concave function for the consumption and investment processes. The model is not shown to be one that could reflect phenomena that exist in the real world. In particular, the time scales needed to observe the chaotic behavior are not discussed.

Another issue taken up in the book deals with the question as to why economic activity exhibits fluctuations, and subsequent attempts to stabilize this activity via fiscal policy. The Judd model, which deals with technical innovation, is adapted to study the economic instabilities that arise from investment activity in such innovation, and the value of fiscal policy in dampening these instabilities. The model is shown to exhibit chaotic dynamics, with this being a consequence of the noncompetitive nature of a market immediately after a new good is introduced into the market. The discussion is reminiscent of arbitrage arguments in finance, since the monopolistic prices charged by the patent holder are wiped out by new innovations. Interestingly, the model shows examples of situations where stabilizing policies are undesirable, and in particular a waste of resources would result.