From Catastrophe to Chaos: A General Theory of Economic Discontinuities.

Professor Rosser set out to create a single-volume encyclopedia covering the broad sweep of economic applications for bifurcation theory (the field encompassing the non-linear math specialties of catastrophe and chaos), and to a great extent he has succeeded. For the economist wanting an introduction to this promising new field, Rosser's work is a boon. The research into the non-linear aspects of economics is actually quite extensive, but a paucity of cross-references obscured that range before the emergence of this volume. Rosser studied virtually all the various aspects of this research in economics, then organized them into a consistent presentation that gives linear economists easy access to up-to-date non-linear research in their specialties. Even practicing non-linear economists will find in his volume a useful bibliographic reference in their specialty, a source of inspiration in its scope and perhaps even some useful new ideas. Despite a title that makes our dismal science sound even more dismal, Rosser's book is a great service to the profession.

After a brief introduction motivating the use of bifurcation theory in economics and a mathematical review that nicely balances the non-specialist's needs for both accessibility and rigor, Rosser's book goes on to cover the broad scope of applications. Starting with macroeconomics, he looks at potential routes to bifurcation ranging from preferences to expectations to lags. He then focuses in on speculative bubbles, devoting two chapters to an extensive review of this contentious phenomenon. The first of these chapters examines irrational bubbles, the second looks at rational and semi-rational bubbles. As a student of irrational bubbles, I can highly recommend his discussion as both sensitive and fairly comprehensive within the space constraints.

Turning from microeconomics, Rosser focuses on catastrophe and chaos in macroeconomics models and macroeconomies. He shows how the mathematics of these models can produce bifurcations and chaotic dynamics, and discusses the ongoing econometric search for chaos evidence in macroeconomic variables. After micro ad macro, Rosser illuminates a number of individual topics, including capital theory, urban and regional economics, interfaces between ecology and economy, foreign exchange rates and the world economy. Without the specific focus of bifurcation theory, such a wide array of topics would inevitably lead to a vapid discussion by even the most capable author, but Rosser's attention to bifurcations allows him to make cogent observations in each of these diverse areas.

As Rosser observes, the direction that non-linear analysis will take from here is unclear. Some students of economic bifurcations seem content to place their analysis in the belt of auxiliary hypotheses surrounding the Lakatosian core of neoclassical economics. Others feel that economic catastrophes and chaos point out the need for a fundamentally different metaphor to understand the economy. One of the greatest virtues of Rosser's book is his evenhanded presentation of models from both the mainstream neoclassicals and the alternative postmodern evolutionary economists.

In fact, by discussing both research programs without denigrating either, Rosser makes a contribution unique among books addressing these topics. More typical are Dosi et al. in their Technical Change and Economic Theory |2~, in which postmodern evolutionary economists are unequivocal in their criticism of the general equilibrium metaphor, and Brock, Hsieh and LeBaron's Nonlinear Dynamics, Chaos and Instability |1~ in which neoclassicals do not even deign to discuss evolutionary self-organization theories, giving those theories the ultimate denigration in scientific circles. However, if Rosser's book reflects anything back to the economics profession from whence it springs, it is the potential for that profession's seemingly linear development to encounter a bifurcation that shifts the mainstream out of the general equilibrium metaphor's basin with just on big self-organizing bandwagon. Whichever course the economics profession eventually follows, Rosser's book provides the interested economist with an excellent overview of bifurcation theory's economic applications.

References

1. Brock, William A., David A. Hsieh and Blake LeBaron. Nonlinear Dynamics, Chaos and Instability: Statistical Theory and Economic Evidence. Cambridge, Mass.: The MIT Press, 1991.

2. Dosi, Giovanni, Christopher Freeman, Richard Nelson, Gerald Silverberg and Luc Soete, editors. Technical Change and Economic Theory. London: Pinter Publishers, 1988.