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James B. Wiley
School of Marketing and International Business, Victoria University Wellington, Wellington, New Zealand.
The book consists of a set of refereed and revised papers that were presented at twelfth International Symposia in Economic Theory and Econometrics Conference. The nineteen papers are organised into four sections: Part I considers philosophical and methodological issues; Part II presents several non-linear models of macroeconomic dynamics; Part III presents evolutionary models of single markets, including non-linear cobweb models, genetic algorithms, neural networks, complex systems simulations and cellular automata. Part IV presents approaches for analysing marketing and interdependent behaviours.
I will start with overview sketches of the papers and then abstract what seem to be the most salient aspects for a general reader, adding additional comments on the respective papers as deemed necessary. Comments that are more general are provided in the final paragraph of the review.
Martens ("Toward a generalised Coase Theorem...") argues that neo-classical economic theory, based on perfect competition, implies an idealised "maximum entropy" equilibrium in which, at best, agents exchange the same mix of goods and services at the same prices. The neo-classical model is incomplete and not self-sustainable, he suggests, because it lacks an entropy-decreasing mechanism. Recent scholars have suggested that innovation can provide the required competition reducing economic force. Martens outlines an alternative to the neo-classical paradigm. Individual agents are assumed to have limited information-processing capacity. Claims for the paradigm, which focuses on uncertainty reduction, include a) consistency with evolutionary biology, b) emergence of rule-based (rather than optimising) behaviour, c) emergence of norms, rules and institutions, and d) an explanation for the emergence of trade itself. Though presented at an abstract level, the narrative is provocative and sets an encouraging tone for the book. However, a specific model that implements the paradigm is not advanced.
Nightingale ("Universal Darwinism and social research ...") takes a sceptic's view of the term "evolution" as applied in economics, an issue relevant to many of the papers in the book. I will say more about this in my conclusion. Juniper ("Uncertainty, risk and chaos...") sounds a cautionary note regarding the economic policy implications of chaos. He argues, for example, that economic discussion of chaotic behaviour often is attributed to agents' incomplete knowledge of a system that is implicitly assumed to be structurally determinate. In such cases, conventional interventions by policy makers may arguably prove useful. Complexity, however, provides examples of structurally indeterminate systems. Systems of these sorts are characterised by what Juniper calls fundamental uncertainty. Much of the paper aims to discuss the presence and implications of fundamental uncertainty in the context of Keynes' work.
Standish ("The role of innovation in economics") begins by developing a hierarchy of models. Traditionally, economics has dealt with comparative statics i.e. two equilibria of a dynamic system are compared. Dynamics, in turn, constitute a special case of evolutionary models in which the degrees of freedom for the system are held constant. In the case of evolution, the degrees of freedom for systems are not constant; the condition Juniper calls fundamental uncertainty. Standish then proceeds to an analysis of the dynamic properties of a simple model of an evolving ecology: a generalised Lotka-Volterra equation. Then he provides some suggestions as to how it might be modified to serve as an economic model. In the course of his discussion, he implies that economic work to date has tended to demonstrate that either equilibria of static models may not be stable (resulting in period cycles or chaos) or to conduct studies in the dynamic (rather than the evolutionary) domain. He concludes by suggesting that we should be studying "what might be called open-dimensional dynamic systems," i.e., systems in what he defines to be the evolutionary domain.
The first three papers of this section: a) Keen ("The non-linear economics of debt deflation"), b) Chiarella and Flaschel ("The emergence of complex dynamics...") and c) Barnett and Xu ("Stochastic volatility in interest rates...") adopt analytic based, non-linear equation modelling methodologies generally associated with the literature on chaos. Their aim is to establish the possibility of cyclical, stochastic and/or chaotic behaviour in "traditional," e.g., Keynesian, economic models. The common approach is to advance one or more models, and then demonstrate that previously unanticipated complex dynamic behaviour may be generated. Making such points is useful. However, the behaviour of systems of differential equations is famously (or infamously) dependent on their specification. Useful as such results regarding differential systems may be, the generic next question is: How does one establish that behaviour that appears to be similar to what is observed in "reality," is the "same" as what is observed? The paper by Marks (below) touches on this topic.
The next two papers in this section adopt simulation-based methodologies more commonly associated with the complexity literature. Colin ("A genetic programming based approach to...") applies Genetic Programming to foreign exchange trading. The aim is to identify optimal algorithmic trading models by evolving complex combinations of arithmetic, logical and inequality relations to produce approximations to moving averages, exponential smoothing, directional movement and the like. Lajbcygier et al. ("Hybrid option trading...") use hybrid neural nets to augment (fit residuals) of the Black-Scholes option-pricing model for non-problematic contracts in the somewhat illiquid Australian future options market. As to general applicability, the approaches demonstrated in both papers require a considerable amount of data to "fit" the models. Collecting this data takes time. Wide use of the models in markets, however, presumably results in their "evolution". One wonders whether the approaches ever can "catch up" with changes in a market, even with the evolutionarychange engendered by their own use, given the intrinsic time it would take to collect sufficient data to detect change.
Schnabl ("Evolutionary patterns of multi-sectoral growth dynamics") describes an approach in which economic input/output tables are converted into directed graphs. As regards complexity or evolution, this paper is probably better conceived of as a visualisation technique than an approach to complexity or evolutionary modelling. Foster and Wild ("The detection of change in evolutionary patterns...") provide one of the papers in the collection that deals with detection of chaotic behaviour. They discuss spectral analysis of time series and develop arguments that processes (which satisfy their conditions for evolutionary processes) should show characteristic spectral patterns. The argument is presented in the context of a (presumably complete) series generated by a logistic diffusion model.
The next three papers deal with cobweb models. Matsumotot ("Ergodic chaos in...") notes that actual markets exhibit a broader range of dynamic behaviour than the three types that traditional cobweb models may exhibit. He then demonstrates that modifying traditional linear models by introducing upper and lower bounds results in models that may exhibit a wide spectrum of dynamic behaviour. Two papers make use of genetic algorithms (GA). The narrow objective of Gaffney et al. ("The cobweb model and a modified genetic algorithm") is to modify a previously formulated GA with the aim of achieving stable convergence. Pearce ("The convergence of genetic learning algorithms ...") extends the Gaffney et al. paper by providing a more general parenting scheme and provides proofs of convergence. The papers establish that GA can solve cobweb models of the sort formulated in the papers. However, Gaffney et al. point to a larger question, which is whether GA provide "a natural model for learning in society", e.g. do they provide insight into how "real" agents operate? Whether this broader objective is achieved by the demonstrations provided is unclear.
Johnson and Betts ("A complex-systems approach...") compare a simplified inventory control system populated by two types of agents, 1) reactive ("just in time') and 2) proactive ("planners"). A multi-agent simulation is used to evaluate the relative effectiveness of the two types of agents in several environments. The results indicate that the prevalence of proactive agents increases in stable markets and with larger minimal stocks. Yao and Darwen ("Genetic algorithms and evolutionary games") generalise 2-person, Iterated Prisoner's Dilemma games to populations as high as 16. Generalising to the larger populations is possible because the problem is reformulated so that only the numbers of co-operators in previous rounds are stored, rather than the actions of individual parties. Results indicate that evolution of co-operation becomes more difficult in larger groups, but it may nonetheless evolve. A finding that deserves further investigation is that adding non co-operating agents to a co-evolving system of agents may produce agents that co-operate with one another, but resist exploitation by non co-operators.
Marks ("Evolved perception and validation...") begins with a pithy summary that well characterises both the field and the contents of the book. He notes there are two basic strategies for exploring non-additivity in economic systems: non-linear dynamics (which looks for necessary conditions) and simulation, which asks questions such as "What are the consequences in the aggregate of individual agents behaving just so - what assumptions at the micro level are sufficient for the emergence of a specific pattern of economic phenomena?" Marks then points out that a neglected area in both approaches, but especially in the simulation approach, is that of validation using historical data. He suggests a partial solution to an aspect of the validation issue, which is to reduce the number of feasible states in the validation problem through partitioning i.e. combining states to be "fit" in validation exercises. Three partitioning schemes are discussed.
Oda et al. ("The application of cellular automata and agent models...") criticise consumer demand models that ignore the fact that the choices of other consumers influence a consumer's behaviour. They then develop a model in which consumer choice is influenced by price and the number of "neighbours" who purchased the product in the previous period. A simulation is used to explore the impact of the number of neighbours on system behaviour. Equilibrium values are not assured with their model. Cycles and other dynamic phenomena are likely outcomes.
Gans ("Engendering change") considers the case in which economies may be characterised by multiple Pareto ranked equilibria. A problem in such economies is that they may become "trapped" in lower equilibria and the question is how external parties (e.g. governments) may intervene to co-ordinate efforts to reach a more efficient equilibrium. Two general strategies are proposed to changing the beliefs that support the inefficient equilibrium: broad-effect or individually targeted policies. Within the context of the employment discrimination example used, Gans concludes that the best strategy depends on the nature of the beliefs: broad-effect strategies are best for inflexibly held beliefs; individually targeted strategies are best for flexible beliefs.
The 19 papers in this book provide a good representation of approaches in the field i.e. non-linear dynamics and simulation (including neural nets, cellular automata, cobweb models and GA). When the papers get to technical details, however, the presentations are generally too condensed for a reader first coming to the respective techniques, although explanations that are more transparent may be found in references provided. Interspersed throughout the book are some insightful philosophical discussions and critical analysis of the application of complexity/chaos concepts to economics and commerce. Regarding critical analysis, the Nightingale and Standish papers stand out. It is not a criticism of the papers in the book to say that Standish's observation that work tends to focus on the interface between statics and dynamics (or on dynamics proper) rather than what he calls open-dynamic systems does seem to be reflected in the papers selected. Nightingale's discussion as to what exactly constitutes an "evolutionary" phenomenon is also pertinent. It is evident from the papers that several uses of the term "evolution" occur in economic narrative. For example, it may refer to the "reality" (organisms, firms and/or relationships amongst them); or it may refer to a model of the reality. The models used to represent organisms/firms and/or relationships amongst them (whether they are evolving or not) may or may not be evolutionary; and regardless of whether they are evolutionary, they may or may not exhibit chaotic properties. Most of these uses may be found in the papers in this book.
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© Copyright Journal of Artificial Societies and Social Simulation, 2003