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Dynamical Coupling, Nonlinear Accelerator and the Persistence of Business Cycles

Listed author(s):
  • Stefano Zambelli

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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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
Handle: RePEc:trn:utwpas:1214
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  1. Stefano Zambelli, 2010. "Coupled Dynamics in the Phillips Machine Model of the Macroeconomy," ASSRU Discussion Papers 1011, ASSRU - Algorithmic Social Science Research Unit.
  2. Velupillai Kumaraswamy Vela, 2008. "The Mathematization of Macroeconomics. A Recursive Revolution," Economia politica, Società editrice il Mulino, issue 2, pages 283-316.
  3. 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.
  4. 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.
  5. Stefano Zambelli, 2011. "Flexible Accelerator Economic Systems As Coupled Oscillators," Journal of Economic Surveys, Wiley Blackwell, vol. 25(3), pages 608-633, 07.
  6. 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.
  7. Kumaraswamy Velupillai, "undated". "The Computable Approach to Economics," Working Papers _005, University of California at Los Angeles, Center for Computable Economics.
  8. Ragnar Frisch, 1932. "Capital Production and Consumer-Taking: A Final Word," Journal of Political Economy, University of Chicago Press, vol. 40, pages 694-694.
  9. Ragnar Frisch, 1931. "The Interrelation Between Capital Production and Consumer-Taking," Journal of Political Economy, University of Chicago Press, vol. 39, pages 646-646.
  10. K. Vela Velupillai & Stefano Zambelli, 2011. "Computing in Economics," Chapters,in: The Elgar Companion to Recent Economic Methodology, chapter 12 Edward Elgar Publishing.
  11. Ragnar Frisch, 1932. "Capital Production and Consumer-Taking: A Rejoinder," Journal of Political Economy, University of Chicago Press, vol. 40, pages 253-253.
  12. Velupillai, K. Vela, 1998. "The vintage economist," Journal of Economic Behavior & Organization, Elsevier, vol. 37(1), pages 1-31, September.
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