Minsky Financial Instability, Interscale Feedback, Percolation and Marshall-Walras Disequilibrium

We study analytically and numerically Minsky instability as a combination of top-down, bottom-up and peer-to-peer positive feedback loops. The peer-to-peer interactions are represented by the links of a network formed by the connections between firms; contagion leading to avalanches and percolation phase transitions propagating across these links. The global parameter in the top-bottom – bottom-up feedback loop is the interest rate. Before the Minsky Moment, in the “Minsky loans accelerator” stage the relevant “bottom” parameter representing the individual firms' micro-states is the quantity of loans. After the Minsky Moment, in the “Minsky crisis accelerator” stage, the relevant “bottom” parameters are the number of ponzi units/quantity of failures/defaults. We represent the top-bottom, bottom-up interactions on a plot similar to the Marshall-Walras diagram for quantity-price market equilibrium (where the interest rate is the analog of the price). The Minsky instability is then simply emerging as a consequence of the fixed point (the intersection of the supply and demand curves) being unstable (repulsive). In the presence of network effects, one obtains more than one fixed point and a few dynamic regimes (phases). We describe them and their implications for understanding, predicting and steering economic instability