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Dynamical Coupling, Nonlinear Accelerator and the Persistence of Business Cycles

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  • Stefano Zambelli

Abstract

Many of the research questions and research programs that were posed and suggested by Richard Goodwin are still highly relevant for various methodological, empirical and theoretical reasons. In this paper, we address the issue of whether highly articulated and complex economic interactions can be represented by a simplified low dimensional model. We follow the valuable insight offered by Goodwin (1947) concerning the importance of dynamical coupling and the potential role of analog and/or digital computers in studying them fruitfully. Here, we extend the nonlinear, flexible accelerator - dynamic multiplier model of business cycle by Goodwin (1951), to the case in which these economies are coupled through trade. The dynamics implied by the coupling are studied in analogy with the well known Fermi-Pasta-Ulam problem (Fermi et al., 1955). We show that for nonlinear economies, even when they are exactly the same, i.e. having the same structural behavioral equations, the very rich dynamics depend crucially on the initial conditions. This result is somewhat unexpected.

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Bibliographic Info

Paper provided by ASSRU - Algorithmic Social Science Research Unit in its series ASSRU Discussion Papers with number 1214.

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Date of creation: 2012
Date of revision:
Handle: RePEc:trn:utwpas:1214

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Keywords: Business cycles; coupled economies; analog and digital computations; Fermi-Pasta-Ulam problem; computable economics; algorithmic social sciences; Richard Goodwin; analogy and induction;

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References

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  1. Stefano Zambelli, 2011. "Flexible Accelerator Economic Systems As Coupled Oscillators," Journal of Economic Surveys, Wiley Blackwell, vol. 25(3), pages 608-633, 07.
  2. Velupillai Kumaraswamy Vela, 2008. "The Mathematization of Macroeconomics. A Recursive Revolution," Economia politica, Società editrice il Mulino, issue 2, pages 283-316.
  3. Stefano Zambelli, 2007. "A Rocking Horse That Never Rocked: Frisch's “Propagation Problems and Impulse Problems”," History of Political Economy, Duke University Press, vol. 39(1), pages 145-166, Spring.
  4. Kumaraswamy Velupillai, 2003. "Economics and the complexity vision: chimerical partners or elysian adventurers," Department of Economics Working Papers 0307, Department of Economics, University of Trento, Italia.
  5. repec:ept:journl:v:4:y:2011:i:323en:p:39-62 is not listed on IDEAS
  6. Stefano Zambelli, 2010. "Coupled Dynamics in the Phillips Machine Model of the Macroeconomy," ASSRU Discussion Papers 1011, ASSRU - Algorithmic Social Science Research Unit.
  7. K. Vela Velupillai, 2005. "The impossibility of an Effective Theory of Policy in a Complex Economy," Working Papers 0094, National University of Ireland Galway, Department of Economics, revised 2005.
  8. Velupillai, K. Vela, 1998. "The vintage economist," Journal of Economic Behavior & Organization, Elsevier, vol. 37(1), pages 1-31, September.
  9. V. Ragupathy & K. Vela Velupillai, 2012. "Existence Proofs in Nonlinear Endogenous Theories of the Business Cycle on the Plane -- The Origins," ASSRU Discussion Papers 1210, ASSRU - Algorithmic Social Science Research Unit.
  10. Kumaraswamy Velupillai, . "The Computable Approach to Economics," Working Papers _005, University of California at Los Angeles, Center for Computable Economics.
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