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 Marshal-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.
Download