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Stochastic Logistic Model of the Global Financial Leverage

Author

Listed:
  • Smirnov Alexander D.

    (Department of Applied Macroeconomics, National Research University Higher School of Economics, Moscow, Russia)

Abstract

Debt, as one of basic human relations, has profound effects on economic growth. Debt accumulation in the global economy was modeled by the stochastic logistic equation reflecting causality between leverage and its rate of change. The model, identifying interactions and feedbacks in aggregate behaviour of creditors and borrowers, addressed various issues of macrofinancial stability. Qualitatively diverse patterns, including the Wicksellian (normal) market, the Minsky financial bubbles and the Fisherian debt-deflation, were discerned by appropriate combinations of rates of return, spreads and leverage. The Kolmogorov-Fokker-Plank equation was used to find out the stationary gamma distribution of leverage that was instrumental for the evaluation of appropriate failure and survival functions. Two patterns corresponding to different forms of a stationary gamma distribution were recognized in the long run leverage dynamics and were simulated as scenarios of a possible system evolution. In particular, empirically parameterized asymptotical distribution indicated excessive leverage and unsustainable global debt accumulation. It underlined the necessity of comprehensive reforms aiming to decrease uncertainty, debt and leverage. Assuming these reforms were successfully implemented, global leverage distributions would have converged in the long run to a peaked gamma distribution with the mode identical to the anchor leverage. The latter corresponded to a balanced long run debt demand and supply, hence to fairly evaluated financial assets fully collateralized by real resources. A particular case of macrofinancial Tobin’s q-coefficients following the Ornstein-Ulenbeck process was studied to evaluate a reasonable range of squeezing the bloated world finance. The model was verified on data published by the IMF in Global Financial Stability Reports for the period 2003–2013.

Suggested Citation

  • Smirnov Alexander D., 2018. "Stochastic Logistic Model of the Global Financial Leverage," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 18(1), pages 1-20, January.
    • Handle: RePEc:bpj:bejtec:v:18:y:2018:i:1:p:20:n:3
    DOI: 10.1515/bejte-2016-0009
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    References listed on IDEAS

    as
    1. Ole Peters, 2011. "Optimal leverage from non-ergodicity," Quantitative Finance, Taylor & Francis Journals, vol. 11(11), pages 1593-1602.
    2. Sorin Solomon & Peter Richmond, 2000. "Stability of Pareto-Zipf Law in Non-Stationary Economies," Papers cond-mat/0012479, arXiv.org, revised Jan 2001.
    3. Raymond W. Goldsmith, 1959. "Financial Structure and Development as a Subject for International Comparative Study," NBER Chapters, in: The Comparative Study of Economic Growth and Structure, pages 114-123, National Bureau of Economic Research, Inc.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    leverage; logistic equation; debt collateral; gamma distribution; hazard function;
    All these keywords.

    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates
    • E5 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit
    • G1 - Financial Economics - - General Financial Markets
    • N2 - Economic History - - Financial Markets and Institutions

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