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Stability and Bifurcations in Banks and Small Enterprises—A Three-Dimensional Continuous-Time Dynamical System

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  • Desogus, Marco
  • Venturi, Beatrice

Abstract

Here, we discuss a three-dimensional continuous-time Lotka–Volterra dynamical system, which describes the role of government in interactions with banks and small enterprises. In Italy, during the COVID-19 emergency, the main objective of government economic intervention was to maintain the proper operation of the bank–enterprise system. We also review the effectiveness of measures introduced in response to the COVID-19 pandemic lockdowns to avoid a further credit crunch. By applying bifurcation theory to the system, we were able to produce evidence of the existence of Hopf and zero-Hopf bifurcating periodic solutions from a saddle focus in a special region of the parameter space, and we performed a numerical analysis.

Suggested Citation

  • Desogus, Marco & Venturi, Beatrice, 2023. "Stability and Bifurcations in Banks and Small Enterprises—A Three-Dimensional Continuous-Time Dynamical System," MPRA Paper 116598, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:116598
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    1. Caggiano, Giovanni & Castelnuovo, Efrem & Pellegrino, Giovanni, 2017. "Estimating the real effects of uncertainty shocks at the Zero Lower Bound," European Economic Review, Elsevier, vol. 100(C), pages 257-272.
    2. Bernanke, Ben & Gertler, Mark & Gilchrist, Simon, 1996. "The Financial Accelerator and the Flight to Quality," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 1-15, February.
    3. Calcagnini, Giorgio & Giombini, Germana & Travaglini, Giuseppe, 2019. "A theoretical model of imperfect markets and investment," Structural Change and Economic Dynamics, Elsevier, vol. 50(C), pages 237-244.
    4. Petrosky-Nadeau, Nicolas, 2013. "TFP during a credit crunch," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1150-1178.
    5. Stefano Bosi & David Desmarchelier, 2018. "Pollution and infectious diseases," International Journal of Economic Theory, The International Society for Economic Theory, vol. 14(4), pages 351-372, December.
    6. Nishimura Kazuo & Shigoka Tadashi, 2019. "Hopf bifurcation and the existence and stability of closed orbits in three-sector models of optimal endogenous growth," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 23(4), pages 1-21, September.
    7. Jeroen Rozendaal & Yannick Malevergne & Didier Sornette, 2015. "Macroeconomic Dynamics of Assets, Leverage and Trust," Papers 1512.03618, arXiv.org.
    8. Desogus, Marco & Venturi, Beatrice, 2019. "Bank Crashes and Micro Enterprise Loans," MPRA Paper 114469, University Library of Munich, Germany.
    9. Giovanni Bella & Paolo Mattana & Beatrice Venturi, 2022. "Existence and implications of a pitchfork-Hopf bifurcation in a continuous-time two-sector growth model," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(1), pages 259-285, January.
    10. Takeo Hori & Koichi Futagami, 2019. "A Non‐unitary Discount Rate Model," Economica, London School of Economics and Political Science, vol. 86(341), pages 139-165, January.
    11. Marco Bassetto & Marco Cagetti & Mariacristina De Nardi, 2015. "Credit Crunches and Credit Allocation in a Model of Entrepreneurship," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 18(1), pages 53-76, January.
    12. Benhabib, Jess & Miyao, Takahiro, 1981. "Some New Results on the Dynamics of the Generalized Tobin Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(3), pages 589-596, October.
    13. Bi-Huei Tsai, 2017. "Predicting the competitive relationships of industrial production between Taiwan and China using Lotka–Volterra model," Applied Economics, Taylor & Francis Journals, vol. 49(25), pages 2428-2442, May.
    14. repec:zbw:bofrdp:2017_006 is not listed on IDEAS
    15. Peter Ganong & Jeffrey B. Liebman, 2018. "The Decline, Rebound, and Further Rise in SNAP Enrollment: Disentangling Business Cycle Fluctuations and Policy Changes," American Economic Journal: Economic Policy, American Economic Association, vol. 10(4), pages 153-176, November.
    16. Luc Laeven & FabiÁn Valencia, 2013. "The Real Effects of Financial Sector Interventions during Crises," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(1), pages 147-177, February.
    17. Marasco, A. & Picucci, A. & Romano, A., 2016. "Market share dynamics using Lotka–Volterra models," Technological Forecasting and Social Change, Elsevier, vol. 105(C), pages 49-62.
    18. Nishimura Kazuo & Shigoka Tadashi, 2019. "Hopf bifurcation and the existence and stability of closed orbits in three-sector models of optimal endogenous growth," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 23(4), pages 1-21, September.
    19. Francisco Buera & Roberto Fattal-Jaef & Yongseok Shin, 2015. "Anatomy of a Credit Crunch: From Capital to Labor Markets," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 18(1), pages 101-117, January.
    20. Iyer, Rajkamal & Da-Rocha-Lopes, Samuel & Peydró, José-Luis & Schoar, Antoinette, 2014. "Interbank Liquidity Crunch and the Firm Credit Crunch: Evidence from the 2007-2009 Crisis," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 27(1), pages 347-372.
    21. Giuseppe Castellacci & Youngna Choi, 2014. "Financial instability contagion: a dynamical systems approach," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1243-1255, July.
    22. Degryse, Hans & Van Cayseele, Patrick, 2000. "Relationship Lending within a Bank-Based System: Evidence from European Small Business Data," Journal of Financial Intermediation, Elsevier, vol. 9(1), pages 90-109, January.
    23. Desogus, Marco & Casu, Elisa, 2020. "A Contribution on Relationship Banking. Economic, Anthropological and Mathematical Reasoning, Empirical Evidence from Italy," MPRA Paper 114365, University Library of Munich, Germany.
    24. Sheng Wang & Guixin Hu & Linshan Wang, 2018. "Stability in Distribution of a Stochastic Competitive Lotka-Volterra System with S-type Distributed Time Delays," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1241-1257, December.
    25. Desogus, Marco & Casu, Elisa, 2020. "What Are the Impacts of Credit Crunch on the Bank-Enterprise System? An Analysis Through Dynamic Modeling and an Italian Dataset," MPRA Paper 114349, University Library of Munich, Germany.
    26. Umberto Neri & Beatrice Venturi, 2007. "Stability and bifurcations in IS-LM economic models," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 54(1), pages 53-65, March.
    27. Gert Wehinger, 2014. "SMEs and the credit crunch: Current financing difficulties, policy measures and a review of literature," OECD Journal: Financial Market Trends, OECD Publishing, vol. 2013(2), pages 115-148.
    28. HARRY DeANGELO & RICHARD ROLL, 2015. "How Stable Are Corporate Capital Structures?," Journal of Finance, American Finance Association, vol. 70(1), pages 373-418, February.
    29. Alessio D’Ignazio & Carlo Menon, 2020. "Causal Effect of Credit Guarantees for Small‐ and Medium‐Sized Enterprises: Evidence from Italy," Scandinavian Journal of Economics, Wiley Blackwell, vol. 122(1), pages 191-218, January.
    30. Dimitri O. Ledenyov & Viktor O. Ledenyov, 2012. "On the new central bank strategy toward monetary and financial instabilities management in finances: Econophysical analysis of nonlinear dynamical financial systems," Papers 1211.1897, arXiv.org.
    31. A. Baldini & M. Causi, 2020. "Restoring credit market stability conditions in Italy: evidences on Loan and Bad Loan dynamics," The European Journal of Finance, Taylor & Francis Journals, vol. 26(7-8), pages 746-773, May.
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    More about this item

    Keywords

    Credit crunch; simulation; credit big data; nonlinear analysis; periodic solutions; stability; dynamical system; zero-Hopf bifurcation;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E51 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Money Supply; Credit; Money Multipliers
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation

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