Stochastic Logistic Model of the Global Financial Leverage
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Alexander D. Smirnov
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.
Acknowledgements
The author expresses his gratitude to participants of several scientific seminars in Moscow and London where different aspects of the model were discussed.
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Articles in the same Issue
- Bargaining Frictions in Trading Networks
- Competitive Search with Ex-post Opportunism
- Cross-listed Securities and Multiple Exchange Memberships: Demand Differentiability and Equilibrium Existence
- General Equilibrium Model for an Asymmetric Information Economy Without Delivery Upper Bounds
- Optimal Term Structure in a Monetary Economy with Incomplete Markets
- Stochastic Logistic Model of the Global Financial Leverage
- Sharing the Effort Costs in Group Contests
- Pre-contest Communication Incentives
- Conformity Preferences and Information Gathering Effort in Collective Decision Making
- Uncovering the Behavioral Implications of the Rational Addiction Assertion
- Optimism, Pessimism, Audit Uncertainty, and Tax Compliance
- Connected Price Dynamics with Revealed Preferences and Auctioneer’s Discretion in VCG Combinatorial Auction
- Sequential Bidding in Asymmetric First Price Auctions
- Hybrid Invariance and Oligarchic Structures
- A Competitive Optimal Stopping Game
- A Note on Cournot Competition in Differentiated Oligopolies
- How Increasing Supplier Search Cost Can Increase Welfare
- On Reference Dependent Shortlisting Behavior
- Uniform Pricing and Product Innovation
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