Financial Crisis and Contagion: A Dynamical Systems Approach

We use a multi-agent-based model to investigate and analyze financial crises where agents are large aggregates of the economic system under consideration. We analyze financial crises as the breakage of a dynamic financial equilibrium. We suggest that when the equilibrium is stable, a small perturbation is absorbed by the market. On the other hand, when the market becomes unstable, perturbations propagate and amplify through the system, and contagion and systemic risk occur, resulting in a global financial crisis. The market instability indicator is the spectral radius of the Jacobian matrix of a dynamical system driving the evolution of the economy. Entries of this Jacobian matrix can be computed by estimating the elasticities of flows of funds between aggregate agents. The higher the elasticities, the larger the entries of the Jacobian matrix and the more unstable the economy. High leverage and borrowing capacity constraints increase elasticities and make the market unstable as soon as the market instability indicator is above the critical value 1. In order to avoid deflation and economic collapse in 2008, the US government had a very strong reaction with Quantitative Easing and TARP. This put the market under rapid oscillations of very high amplitude and chaotic behavior, making long term forecasts inefficient. By correctly monitoring and utilizing elasticities, governments facing a major crisis may be able to optimize the efficiency of monetary and fiscal policies and accurately allocate their support to the various sectors of the economy, as opposed to being part of the origination of market chaos by inappropriate allocation of government resources.