Stochastic Logistic Model of the Global Financial Leverage

摘要

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