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Revisiting the Model of Credit Cycles with Good and Bad Projects

Author

Listed:
  • Kiminori Matsuyama

    (Northwestern University (E-mail:k-matsuyama@ northwestern.edu))

  • Iryna Sushko

    (Institute of Mathematics, National Academy of Science of Ukraine (E-mail: sushko@imath.kiev.ua))

  • Laura Gardini

    (University of Urbino (E-mail:laura.gardini@uniurb.it))

Abstract

The contribution of this paper is twofold. First, it reformulates the model of endogenous credit cycles by Matsuyama (2013, Sections 2-4). It is shown that the same dynamical system that generates the equilibrium trajectory can be obtained under a much simpler set of assumptions. Such a streamlined presentation should help to highlight the key mechanisms through which financial frictions cause instability and persistent fluctuations. Second, it discusses the nature of fluctuations in greater detail for the case where the production function of the final good sector is Cobb-Douglas. For example, the unique steady state possesses corridor stability (i.e., stable against small shocks but unstable against large shocks) for empirically relevant parameter values. This also means that, when a parameter change causes the steady state to lose its stability, its effects are catastrophic and irreversible so that even a small, temporary shock could have large, permanent effects on volatility. Other notable features of the present model include an immediate transition from the stable steady state to a stable asymmetric cycle of period n >= 3, along which n -1 >= 2 consecutive periods of gradual expansion is followed by one period of sharp downturn, or to robust chaotic attractors.

Suggested Citation

  • Kiminori Matsuyama & Iryna Sushko & Laura Gardini, 2015. "Revisiting the Model of Credit Cycles with Good and Bad Projects," IMES Discussion Paper Series 15-E-02, Institute for Monetary and Economic Studies, Bank of Japan.
  • Handle: RePEc:ime:imedps:15-e-02
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    References listed on IDEAS

    as
    1. Baumol, William J & Benhabib, Jess, 1989. "Chaos: Significance, Mechanism, and Economic Applications," Journal of Economic Perspectives, American Economic Association, vol. 3(1), pages 77-105, Winter.
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    Cited by:

    1. Pablo A. Guerron-Quintana & Tomohiro Hirano & Ryo Jinnai, 2019. "Recurrent Bubbles and Economic Growth," CARF F-Series CARF-F-457, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Kubin, Ingrid & Zörner, Thomas O. & Gardini, Laura & Commendatore, Pasquale, 2019. "A credit cycle model with market sentiments," Structural Change and Economic Dynamics, Elsevier, vol. 50(C), pages 159-174.
    3. Laura Gardini & Noemi Schmitt & Iryna Sushko & Fabio Tramontana & Frank Westerhoff, 2019. "Necessary and sufficient conditions for the roots of a cubic polynomial and bifurcations of codimension-1, -2, -3 for 3D maps," Working Papers 1908, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2019.
    4. Kikuchi, Tomoo & Stachurski, John & Vachadze, George, 2018. "Volatile capital flows and financial integration: The role of moral hazard," Journal of Economic Theory, Elsevier, vol. 176(C), pages 170-192.
    5. Deng, Liuchun & Khan, M. Ali, 2018. "On growing through cycles: Matsuyama’s M-map and Li–Yorke chaos," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 46-55.
    6. Ingrid Kubin & Thomas O. Zörner, 2017. "Human Capital in a Credit Cycle Model," Department of Economics Working Papers wuwp251, Vienna University of Economics and Business, Department of Economics.
    7. Silvo, Aino, 2017. "House prices, lending standards, and the macroeconomy," Research Discussion Papers 4/2017, Bank of Finland.
    8. Asano, Takao & Yokoo, Masanori, 2019. "Chaotic dynamics of a piecewise linear model of credit cycles," Journal of Mathematical Economics, Elsevier, vol. 80(C), pages 9-21.
    9. Gardini, Laura & Sushko, Iryna, 2019. "Growing through chaos in the Matsuyama map via subcritical flip bifurcation and bistability," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 52-67.

    More about this item

    Keywords

    borrower net worth; composition of credit flows; financial instability; corridor stability; asymmetric cycles; regime-switching; bifurcation analysis of a piecewise smooth nonlinear dynamical system;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy

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