Martín Puchet Anyul

Coding economic dynamics to represent regime dynamics. A teach-yourself exercise

Abstract Much of the recent economic history of various countries, regions and/or sectors in the world economy can usefully be reconstructed as sequences of repeated, basically endogenously induced, changes of growth regimes. Coded dynamics (CD) is proposed hereafter as the appropriate tool for the analysis of such multi-regime dynamics, i.e. dynamics where switches between growth regimes represent structural changes, or in other words, abrupt alterations in an economys qualitative dynamics . On a theoretical tone, one of our arguments in favor of the adoption of a CD approach derives from the lesson that can be drawn from the complex dynamics literature. Often, some form of regularity, while it cannot be found in the punctual analysis of motion across states, can be recovered from the systems dynamics over a partition of its state space. This dynamics can be represented by strings of symbols (instead of real numbers), or symbolic trajectories . The 2-fold purpose of this paper is to introduce the formalism and terminology of multi-regime dynamics, and to try our hand with the technique of coding through a set of simple exercises. In fact, we consider only cases with two and three regimes, instead of the six of the Framework Space introduced in the Preface. Via such exercises, we also trace the origins of the multi-regime framework in the tradition of classical macrodynamics.

Coding Economic Dynamics to Represent Regime Dynamics

In this paper a new approach to the analysis of the dynamics of economies is presented; applications to time series will also be suggested. In such applications, computational experiments may play a central role to provide a different heuristics and to explore data information. The approach is based upon ideas emerging in the literature on complex and chaotic dynamics, which imply that one can no longer rely on the fine description of classical dynamical systems: the state space structure breaks down, and instead of simple orbits, we should be satisfied with a description based upon symbolic trajectories, each symbol being associated with a partition of the original state space. Such partition can be induced by the introduction of the qualitative notion of regimes and of regime dynamics as a dynamics allowing for regime shifts. It can otherwise be suggested by preliminary data screening. Starting from a pre-set model, a regime is a set of dynamical paths generated by the same ?canonical model? with parameters. By identifying bifurcation values in the parameter space, one can classify a finite collection of realizations of such canonical model. A symbolic dynamical model reproduces dynamics across such sets of realisations, and can be tested against available empirical data. A preliminary exploration of some simple models yielding a finite (low-)number of regimes with a complex cross-regimes dynamics is presented, to motivate the move towards a discrete space dynamics and as a step towards the building of a general approach to multidimensional dynamical models.

Coevolution of science and technology and innovation: a three stage model of policies based on the Mexican case

The purpose of this paper is to discuss the coevolution between two arenas, on one side the Science and Technology (S&T)1, and on the other the Innovation (Innov), from a developing countrys perspective. It argues that in the context of the knowledge economy, the coevolution of these arenas is crucial for this type of countries to transit to a development process. The discovery that some Japanese firms as well as firms from Korea and other newly industrializing countries could compete successfully with their United States counterparts contributed to focus the attention of scholars and policy makers on the conditions of a successful catching up process. From the 1980s there has been a sudden increase of books and papers focusing on the function of science, technology and innovation (STI), and on their interrelations, for the development processes.

A Dynamic Extension of the Classical Model of Production Prices Determination

This paper generalizes the classical model of determination of production prices for two good by introducing a dynamics generated by the possibility that the profit rate is computing using prices of different periods. In this theoretical framework, the prices show a codependency between the two sectors, given by the rate of profit, and inter-industry transactions. In this setup and using discrete time, the model can be represented by a nonlinear two dimensional dynamical system of difference equations of second order. The study shows that the dynamical system admits a unique solution for any initial condition and that there is a unique nontrivial equilibrium. In addition, it can be shown that locally the dynamical system can be represented in the canonical form xt 1 = f(xt) and that the stability of the equilibrium depends on the technological parameters of the production process. Future research includes the extension of the model to the case of several commodities and the closed solution of the stability of the two goods version of the model.

Regímenes De Desempeño Económico Y Dualismo Estructural En La Dinámica De Las Entidades Federativas De México, 1970-2006 (Regimes of Economic Performance and Structural Dualism in the Dynamics of States of Mexico, 1970-2006)

This paper describes the dynamics of the economic performance of the sub-national Mexican states from 1970 to 2006; the used state variables are the levels and the growth rates of the GDP per capita. The authors situate his approach in a conceptual and methodological panorama of the existent literature. Starting by the regime concept, the paper introduces a distance notion for to compare the observed paths and the clustering of the economies whose evolution is studied. The analysis shows that have existed two fundamental clusters: One of high and another of low performance, in addition of other transitory groups. In the cluster of high performance increases the number of members while in the cluster of low performance diminishes; at the same time, the article shows that the sub-national states that belong to the first cluster have had performances each time more similar. Also it confirms that the subnational states move starting from the cluster of low performance to arrive to the cluster of high performance and that the distance between both clusters has increased. These facts are interpreted basing in the concept of dual economy proposed by the development theory.

Can Catastrophe Theory Become a New Tool in Understanding Singular Economies

The aim of this paper is to show that economic systems must be characterized by their possible singularities rather than by their regularities. Changes in parameters of a regular economy imply only small changes in the optimal choice of the agents, i.e. the economic system is structurally stable, and they are consistent with one another minor changes. But in a singular economy, small changes in parameters affect the choice of the agents in a relevant way. The equilibria, after and before the changes, are radically different states, i.e. the economic system is structurally unstable. Catastrophe theory and Morse theory are used here to characterize singular economies. These are classical theories in mathematics but nevertheless, they are new tools to help understand the behavior of an economic system. Also the approach of Negishi is followed, and this allows us to consider in a unified way economies with finitely or infinitely many goods.