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Revisiting the model of credit cycles with good and bad projects

Author

Listed:
  • Kiminori Matsuyama

    (Northwestern University, USA)

  • Iryna Sushko

    (Institute of Mathematics, National Academy of Science of Ukraine)

  • Laura Gardini

    (DESP University of Urbino "Carlo Bo", Urbino (Italy))

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," Gecomplexity Discussion Paper Series 8, Action IS1104 "The EU in the new complex geography of economic systems: models, tools and policy evaluation", revised Feb 2015.
    • Handle: RePEc:cst:wpaper:8
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    References listed on IDEAS

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    1. Enrique G. Mendoza & Marco E. Terrones, 2008. "An Anatomy Of Credit Booms: Evidence From Macro Aggregates And Micro Data," NBER Working Papers 14049, National Bureau of Economic Research, Inc.
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    16. 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.
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    18. 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.
    19. Sushko, Iryna & Gardini, Laura & Matsuyama, Kiminori, 2014. "Superstable credit cycles and U-sequence," Chaos, Solitons & Fractals, Elsevier, vol. 59(C), pages 13-27.
    20. Giovanni Favara, 2012. "Agency Problems and Endogenous Investment Fluctuations," The Review of Financial Studies, Society for Financial Studies, vol. 25(7), pages 2301-2342.
    21. 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., 2021. "Credit cycles, human capital and the distribution of income," Journal of Economic Behavior & Organization, Elsevier, vol. 183(C), pages 954-975.
    3. Spiros Bougheas & Pasquale Commendatore & Laura Gardini & Ingrid Kubin, 2022. "Financial Development, Cycles and Income Inequality in a Model with Good and Bad Projects," CESifo Working Paper Series 10135, CESifo.
    4. 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.
    5. 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.
    6. 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.
    7. Hashimoto, Ken-ichi & Im, Ryonghun & Kunieda, Takuma & Shibata, Akihisa, 2022. "Financial destabilization," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    8. Matsuyama, Kiminori & Ushchev, Philip, 2022. "Destabilizing effects of market size in the dynamics of innovation," Journal of Economic Theory, Elsevier, vol. 200(C).
    9. Sushko, Iryna & Gardini, Laura & Matsuyama, Kiminori, 2016. "Robust chaos in a credit cycle model defined by a one-dimensional piecewise smooth map," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 299-309.
    10. 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.
    11. Gardini, Laura & Sushko, Iryna & Tramontana, Fabio, 2021. "Dynamics of a two-dimensional map on nested circles and rings," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    12. Hiroshi Fujiu, 2021. "Business Cycles in a Two-Sided Altruism Model," Mathematics, MDPI, vol. 9(17), pages 1-12, August.
    13. Takao Asano & Masanori Yokoo, 2017. "Chaotic Dynamics of a Piecewise Linear Model of Credit Cycles with Imperfect Observability," KIER Working Papers 967, Kyoto University, Institute of Economic Research.
    14. 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.
    15. Takao Asano & Akihisa Shibata & Masanori Yokoo, 2024. "Technology choice, externalities in production, and a chaotic middle-income trap," Journal of Economics, Springer, vol. 141(1), pages 29-56, January.
    16. Ivan Mendieta‐Muñoz & Doğuhan Sündal, 2022. "Business cycles, financial conditions, and nonlinearities," Metroeconomica, Wiley Blackwell, vol. 73(2), pages 343-383, May.
    17. 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.
    18. Gardini, Laura & Radi, Davide & Schmitt, Noemi & Sushko, Iryna & Westerhoff, Frank, 2023. "Sentiment-driven business cycle dynamics: An elementary macroeconomic model with animal spirits," Journal of Economic Behavior & Organization, Elsevier, vol. 210(C), pages 342-359.
    19. Spiros Bougheas & Pasquale Commendatore & Laura Gardini & Ingrid Kubin, 2023. "Dynamic investigations of an endogenous business cycle model with heterogeneous agents," Discussion Papers 2023/02, University of Nottingham, Centre for Finance, Credit and Macroeconomics (CFCM).
    20. repec:zbw:bofrdp:2017_004 is not listed on IDEAS
    21. Takao Asano & Akihisa Shibata & Masanori Yokoo, 2023. "Controlling Chaotic Fluctuations through Monetary Policy," KIER Working Papers 1091, Kyoto University, Institute of Economic Research.
    22. Andrea Caravaggio & Mauro Sodini, 2022. "Environmental sustainability, nonlinear dynamics and chaos reloaded: 0 matters!," Discussion Papers 2022/287, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
    23. Silvo, Aino, 2017. "House prices, lending standards, and the macroeconomy," Research Discussion Papers 4/2017, Bank of Finland.
    24. Silvo, Aino, 2017. "House prices, lending standards, and the macroeconomy," Bank of Finland Research Discussion Papers 4/2017, Bank of Finland.
    25. 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.

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    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;
    All these keywords.

    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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