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Revisiting the Model of Credit Cycles with Good and Bad Projects


  • Kiminori Matsuyama

    (Northwestern University (E-mail:k-matsuyama@

  • Iryna Sushko

    (Institute of Mathematics, National Academy of Science of Ukraine (E-mail:

  • Laura Gardini

    (University of Urbino (


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

    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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    3. Philippe Aghion & Abhijit Banerjee & Thomas Piketty, 1999. "Dualism and Macroeconomic Volatility," The Quarterly Journal of Economics, Oxford University Press, vol. 114(4), pages 1359-1397.
    4. Moritz Schularick & Alan M. Taylor, 2012. "Credit Booms Gone Bust: Monetary Policy, Leverage Cycles, and Financial Crises, 1870-2008," American Economic Review, American Economic Association, vol. 102(2), pages 1029-1061, April.
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    6. Marco Terrones & Enrique G. Mendoza, 2008. "An Anatomy of Credit Booms; Evidence From Macro Aggregates and Micro Data," IMF Working Papers 08/226, International Monetary Fund.
    7. Kiminori Matsuyama, 2008. "Aggregate Implications of Credit Market Imperfections," NBER Chapters, in: NBER Macroeconomics Annual 2007, Volume 22, pages 1-60, National Bureau of Economic Research, Inc.
    8. Francois Melese & William Transue, 1986. "Unscrambling Chaos Through Thick and Thin," The Quarterly Journal of Economics, Oxford University Press, vol. 101(2), pages 419-423.
    9. Pietro Reichlin & Paolo Siconolfi, 2004. "Optimal debt contracts and moral hazard along the business cycle," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(1), pages 75-109, July.
    10. Kiminori Matsuyama, 2007. "Credit Traps and Credit Cycles," American Economic Review, American Economic Association, vol. 97(1), pages 503-516, March.
    11. Alberto Martin, 2004. "Endogenous credit cycles," Economics Working Papers 916, Department of Economics and Business, Universitat Pompeu Fabra, revised Aug 2008.
    12. Myerson, Roger B., 2014. "Moral-hazard credit cycles with risk-averse agents," Journal of Economic Theory, Elsevier, vol. 153(C), pages 74-102.
    13. Matsuyama, Kiminori, 2013. "The good, the bad, and the ugly: An inquiry into the causes and nature of credit cycles," Theoretical Economics, Econometric Society, vol. 8(3), September.
    14. Bernanke, Ben & Gertler, Mark, 1989. "Agency Costs, Net Worth, and Business Fluctuations," American Economic Review, American Economic Association, vol. 79(1), pages 14-31, March.
    15. Iryna Sushko & Laura Gardini & Kiminori Matsuyama, 2014. "Chaos in a Model of Credit Cycles with Good and Bad Projects," Working Papers 1405, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2014.
    16. Roger B. Myerson, 2012. "A Model of Moral-Hazard Credit Cycles," Journal of Political Economy, University of Chicago Press, vol. 120(5), pages 847-878.
    17. Giovanni Favara, 2012. "Agency Problems and Endogenous Investment Fluctuations," Review of Financial Studies, Society for Financial Studies, vol. 25(7), pages 2301-2342.
    18. Gardini, Laura & Sushko, Iryna & Naimzada, Ahmad K., 2008. "Growing through chaotic intervals," Journal of Economic Theory, Elsevier, vol. 143(1), pages 541-557, November.
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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


    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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