Macrofinance: The Sigmoidal Dynamics of Money, Debt and Wealth

The compact model of an integrated macro-financial system, proposed in the paper, represents the dynamics of money, debt and wealth. Aristotle had observed the contradictory nature of these economic indicators, which is also evident in the current phase of global financialization, particularly in the use of “deferred” assets accounts by central banks. In the model, macrofinancial assets, liabilities and real wealth are balanced by considering the dual attributes of money, defined as standard for either “deferred” or current payments. The circulation of liquidity between the financial and real segments of the money market links the accumulation of genuine wealth with the formation of macrodebt, representing the expected but unrealized wealth. The volume of financial contracts is measured in the model by the system’s characteristic time, which determines the repayment dates of obligations. Since the financial subsystem does not produce tangible goods, wealth accumulation occurs in the aggregated real market over calendar time. The dynamics of money, debt and wealth dynamics are modeled using logistic ordinary differential equations, resulting in three-dimensional surfaces representing macrofinancial indices such as total, financial and real wealth, as well as credit and “marginal” wealth calculated under full repayment of obligations. The model is parametrized using empirical data and illustrated with numerical examples. The system’s behavior is studied based on initial values of real resources, liquidity, rates of return and money issuance, and average liability maturities. The model demonstrates that finance can indeed multiply social wealth, thereby enhancing the efficiency of money transformation into capital (real resources). Excess liquidity in the financial market can coexist with a deficit in the real segment of the money market, and vice versa. The intersection of surfaces representing general and financial wealth indices corresponds to a state of “money neutrality” characterized by zero growth in real resources. Different combinations of interest rates and money emission ratios can lead to deviations from a balanced trajectory, potentially generating various critical phenomena, including resonance-like effects. The model allows for evaluating some negative consequences of financialization, such as the appearance of a “hump” on the surface of long- term liabilities caused by excessive borrowing.