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Symbolic Dynamics and Control in a Matching Labor Market Model

  • Vivaldo M. Mendes

    ()

    (ISCTE - Department of Economics and UNIDE-ERC)

  • Diana A. Mendes

    ()

    (ISCTE - Department of Quantitative Methods and UNIDE-StatMath)

  • José Sousa Ramos

    (Technical University of Lisbon, IST, Department of Mathematics)

Registered author(s):

    In this paper we apply the techniques of symbolic dynamics and chaos control to the analysis of a labor market model which shows chaotic behavior and large volatility in employment flows. The possibility that chaotic dynamics may arise in modern labor markets had been totally strange to economics until recently. In an interesting paper Bhattacharya and Bunzel [2] have found that the discrete time version of the Pissarides-Mortensen matching model, as formulated in Ljungqvist and Sargent [23], can easily lead to chaotic dynamics under standard sets of parameter values. This paper explores this version of the model with two main objectives in mind: (i) to clarify some open questions raised by Bhattacharya and Bunzel by providing a rigorous proof of the existence of chaotic dynamics in the model; and (ii) to show that this type of dynamics can be easily controlled by linear feedback techniques – the OGY method – without producing modifications to the original model, apart from locally changing its type of stability. These techniques may be of significant importance for the study of economic theory and policy, in particular, if complexity becomes more frequently encountered in the models developed to properly describe the behavior of modern economies, and the view of purely exogenous shocks as explaining cycles and volatility looses its large predominance in contemporary economics.

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    File URL: http://bru-unide.iscte.pt/RePEc/pdfs/ERCwp1308.pdf
    File Function: Third draft, 2008
    Download Restriction: no

    Paper provided by ISCTE-IUL, Business Research Unit (BRU-IUL) in its series Working Papers Series 1 with number ercwp1308.

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    Length: 18 pages
    Date of creation: 15 Mar 2008
    Date of revision:
    Handle: RePEc:isc:iscwp1:ercwp1308
    Contact details of provider: Web page: http://bru-unide.iscte.pt/
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    1. Christopher A. Pissarides & Barbara Petrongolo, 2001. "Looking into the Black Box: A Survey of the Matching Function," Journal of Economic Literature, American Economic Association, vol. 39(2), pages 390-431, June.
    2. Holyst, Janusz A, et al, 1996. "How to Control a Chaotic Economy?," Journal of Evolutionary Economics, Springer, vol. 6(1), pages 31-42, February.
    3. Contini, Bruno & Revelli, Riccardo, 1997. "Gross flows vs. net flows in the labor market: What is there to be learned?," Labour Economics, Elsevier, vol. 4(3), pages 245-263, September.
    4. Chow, Gregory C., 1997. "Dynamic Economics: Optimization by the Lagrange Method," OUP Catalogue, Oxford University Press, number 9780195101928, March.
    5. Michele Boldrin & Michael Woodford, 1988. "Equilibruim Models Displaying Endogenous Fluctuations and Chaos: A Survey," UCLA Economics Working Papers 530, UCLA Department of Economics.
    6. Bullard, James & Mitra, Kaushik, 2002. "Learning about monetary policy rules," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1105-1129, September.
    7. Lucas, Robert Jr. & Prescott, Edward C., 1974. "Equilibrium search and unemployment," Journal of Economic Theory, Elsevier, vol. 7(2), pages 188-209, February.
    8. Kaas, Leo, 1998. "Stabilizing chaos in a dynamic macroeconomic model," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 313-332, January.
    9. Carl Chiarella & Xue-Zhong He, 2000. "Stability of Competitive Equilibria with Heterogeneous Beliefs and Learning," Research Paper Series 37, Quantitative Finance Research Centre, University of Technology, Sydney.
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