Goodwin: Chaotic Economic Dynamics (1990) PREFACE

 Preface to "Chaotic Economic Dynamics" by Richard M. Goodwin (1990)


THE origin of this collection of short essays was a series of seminars given in 1988 at the European University Institute in Florence, Italy. My aim has been to elaborate the central conceptual framework of the modern industrial economy. In this sense it derives from the formulation of the problem by my teacher and friend Joseph Schumpeter. Though a neoclassical economist, he perceived the essentially evolutionary nature of the industrialized nations.

By comparison with the natural sciences, economics suffers from the lack of a solid empirical foundation based on generally valid experimental data. To make up for this deficiency, an ingenious substitute has been elaborated with great subtlety and considerable success. The method consists in asking what would a rational man (now fashionably called an 'agent') do when confronted by the manifold problems of an economic nature: he is alleged to maximize his utility or his satisfactions, by minimizing his costs and maximizing his profits or his gains of whatever sort he desires.

Under the banner of General Equilibrium Theory, this has been developed into an imposing analytic web of how a system of a large number of such agents would interact in a unified market mechanism. This programme, in an increasingly mathematical form, has produced impressive results, which may be considered 'mainstream' economics. Some tentative efforts at a kind of experimental economics have raised serious doubts about this 'rational' behaviour.
This analysis appeared to work well for a single moment in time, but there always remained the awkward fact that both agents and goods have a future. So while one could in principle solve simultaneously for all prices and quantities at a point of time, one really needed the impossibly difficult set of solutions also over the infinite future! Since the future had to be regarded as unknown and hence uncertain, it all needed to be reformulated as a gambling game. John von Neumann's formulation of game theory proved too weak a tool to resolve such a gigantic problem.

It is at this point that economic dynamics becomes relevant.

It has been proposed, quite naturally but surely unfortunately, to deploy the powerful tool of rationality to decisions in dynamics. One can apply rational choice to known prices and quantities but not to unknown future ones. The subject of these essays is chaotic dynamics, the most arresting consequence of which is that a completely deterministic system produces unpredictable behaviour-unpredictable in the sense that looking at the past and the present one cannot say precisely what the future will be.

Therefore the very basis empirically of rational prediction is destroyed. Yet agents must and do take decisions, and the aim here is to incorporate such evidence as is easily available as to their behaviour into deterministic systems, the nature of which can be analysed and solved for their behaviour over time.
The character of the model developed here is qualitative rather than realistically quantitative. Only if one has a fruitful analytic scheme can one arrive at satisfactory quantitative results. As I see it one needs a system capable of endogenous, irregular, wavelike growth. The recent discovery and elaboration of 'chaotic attractors' seemed to me to provide the kind of conceptualization that we economists need.

I have tried to provide examples of a number of different simple dynamic models, including both difference and differential varieties. Difference equation systems, though of limited applicability to economics, are included because they provide the simplest, reasonably complete introduction to chaotic analysis: in particular, they require no more than one dimension, by contrast with differential equations which require at least three dimensions.

The grave shortcoming of these essays is that they are aggregative. Schumpeter rightly insisted that innovative technology was essentially specific to particular industries or sectors of the economy. However, satisfactory dynamic analysis of such multisectoral systems is a large and difficult task, requiring the kind of quantitative logic deployed by John von Neumann, and well beyond the scope of this short collection of essays.

Unsatisfactory as they are, my hope is that these essays do illuminate the nature of some of the problems, even if not the nature of economic reality.

R.M.G.
Peterhouse, Cambridge
and
University of'Siena
1989