Modeling contagion in the Eurozone crisis via dynamical systems

We recently (Castellacci and Choi, 2013) formulated a theoretical framework for the modeling of financial instability contagion using the theories of dynamical systems. Here, our main goal is to model the Eurozone financial crisis within that framework. The underlying system comprises many economic agents that belong to several subsystems. In each instantiation of this framework, the hierarchy and nesting of the subsystems is dictated by the nature of the problem at hand. We describe in great detail how a suitable model can be set up for the Eurozone crisis. The dynamical system is defined by the evolution of the wealths of the individual agents and can be estimated by solving a nonlinear programming problem that incorporates features of prospect theory. Contagion is formulated in terms of how the market instability indicators for the different subsystems and the global system behave. We present several scenarios tailored to recent financial developments in the Eurozone and discussed within our model. These all point to the key role played by the elasticity coefficients of the wealth dynamical system. Accordingly, we put forward general recommendations on how regulators or other super-systemic agents may act to prevent and forestall the spreading of financial distress.