Oscillations of Money and Debt Dynamics

Abstract

The dynamics of money and debt are modelled as a time-invariant process of economic homeostasis sustained by financial clearing mechanisms. The macrofinancial oscillator model elucidates the behaviour of the aggregate creditor, who compensates for expected losses arising from the expansion of total borrowing. Aperiodic mass sell-offs of debt instruments, known in finance as the "bond vigilante" hypothesis, represent an empirical manifestation of this process. Such debt market reactions can induce significant stress and substantial costs, particularly in the contemporary phase of global economic financialization.

The cyclical dynamics of debt emerge from the interconnected processes of oscillation and rotation within the macrofinancial system. Causal relationships among money, loans, debt, and wealth are unveiled through the solution of the oscillator's ordinary differential equation (ODE) using the Green's function method. Money issuance and its subsequent transformation into new borrowings are modelled via the Dirac delta function. The monetary impulse elicits a fundamental debt market response, enabling the computation of financial system trajectories under diverse monetary and macroprudential conditions. This framework has notably resolved the paradox of "unlimited" money issuance, a phenomenon observed since the 16^th century.

Numerical simulations of the macrofinancial oscillator have accurately replicated the global debt market's response to the money issuance spurred by the COVID-19 pandemic. Further refinement of the model will facilitate the calculation of the total debt volume that can be reliably redeemed by the money supply, consistent with the coherent value of goods and services.