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e-JEMED - Issue 3


This issue has been published on May 10, 2005.


All articles in this issue have been peer-viewed through a double-blind referee system.

Article 1047: Volatility, Heterogeneous Agents and Chaos
by Orlando Gomes

Agent heterogeneity, alongside several types of learning rules, has been used in recent economic literature to justify nonlinear dynamics for the time paths of aggregate economic variables. In this paper, the mechanism through which heterogeneous agents leads to chaotic motion is explained.Adding to a system with initial behavior heterogeneity an adaptive learning rule based on discrete choice theory, one is able to encounter a reasonable explanation for nonlinear motion. The adaptive learning / bounded rationality rule is not the only ingredient necessary for the absence of a long run steady state; heterogeneity must also imply that the several behavior possibilities alternate as the best behavioral choice. Only in such circumstances heterogeneity persists and an unpredictable outcome is likely to arise.After a review of the literature, the paper develops two models. The first is a generic approach that exemplifies how heterogeneity concerning the volatility of two stochastic processes may lead to chaotic motion; the second is a utility maximization setup, where the source of heterogeneity is investment decisions. For the utility problem, we find that the time path concerning consumption growth tends to stabilize around a constant value (a constant expected value is observable), but the steady state will be characterized by periods of low volatility that alternate with periods of high volatility.

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Article 1048: "S-shaped" Economic Dynamics. The Logistic and Gompertz curves generalized
by Gloria Jarne, Julio Sánchez-Chóliz, Francisco Fatás-Villafranca


Over the years "S-shaped" evolutions have regularly been incorporated in economic models, and indeed in those of other sciences, by way of the logistic or Gompertz equations. However, both equations have noteworthy shortcomings when fitting some empirical features of economic growth: the logistic equation is characterized by strong symmetries, whilst the growth rate is decreasing in the case of both equations. In this paper, we have set out to overcome these limitations by defining a family of unimodal differential equations which includes the logistic and Gompertz equations and covers practically the whole spectrum of sigmoid curves. We have identified three sub-families of these differential equations, all offering good mathematical expressions. Using these, it is possible to obtain an acceptable fit for any S-shaped curve. The results are applied to various economic series, successfully replicating certain well-known economic phenomena. Mathematical analysis: Unimodal differential equations. Empirical analysis: Non-linear adjustment to the USA Capacity Index time series. We have defined a family of unimodal differential equations covering practically the whole spectrum of "S-shaped" curves. We have selected three sub-families mathematically manageable and which depend on five easily interpretable parameters. It is shown that any one of them may adequately replicate empirically relevant S-shaped phenomena (overcoming certain limitations of the logistic and Gompertz curves). In order to assess the power of these families to replicate real economic events we have calculate the fit with the USA Capacity Index for Total Industry (1967/02-2003/01) and the US Capacity Index series for Durables, Manufacturing, Computers and Primary processing. Then, we have drawn conclusions on capital accumulation and investment patterns in the period that would appear to be in line with recent historical facts in the US economy.

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Article 1053: Book Review: "Time Strategies, Innovation and Environmental Policy" and edited by Christian Sartorius and Stefan Zundel (Edward Elgar Publishing, 2005)
by Maïder Saint-Jean

The aim is to provide a critical evaluation of the book entitled 'Time, Strategies, Innovation and Environmental Policy' and edited by Christian Sartorius and Stefan Zundel. The main emphasis is on the theoretical work developed in the book rather than the empirical part. Indeed twelve case studies are constituting the main part of the book and are used to test the hypothesis underlying the conceptual framework. But since each case is evaluated in the light of the main common concepts (path-dependence, lock-in, windows of opportunity)we find it more suitable to focus the review on the theoretical framework. The book makes a significant contribution to the important issue of sustainability and transition management through the analysis of technological competition case studies involving new environmentally improved technologies. Some general issues of transition management are addressed in the book, which are of particular relevance to many problems of sustainability. These issues concern: i) the importance of a systemic perspective to account for the interplay between different subsystems, ii) the variety of possible schemes and sequence of windows of opportunity in the societal subsystems, iii) the importance of time and history in the success or failure of environmental innovation policy and iv) the influential interplay between short term policy actions and long term planning but also between global and local environmental regulations that affect the international diffusion of environmental technologies and give rise to competitive (dis)advantage to firms and countries.


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