Runs, Panics and Bubbles: Diamond Dybvig and Morris Shin reconsidered

Numerous papers following seminal work of Diamond and Dybvig have attempted to analyze self-generated market failures such as bank runs and currency attacks within a framework of self-consistent expectations. The common feature of these models is an initial committed move, which can benefit agents if they pool resources, but which leaves them open to a risk of coordination failure (the bank run) with an outcome worse than remaining out of the pool. The static equilibrium analysis of the bank run is unsatisfying: the agents who create a run based on expectations were only rational to enter the pool if they “expected” that the run would not occur. The origin of time-inconsistent expectations was formalized by Morris and Shin using an extensive-form game and a correlated-equilibrium solution concept. They derived the result that in the presence of arbitrarily small noise in the agents’ perceptions of the correlating signal, the Diamond/Dybvig multiple equilibrium is replaced by a unique equilibrium. Bank runs and similar coordination failures could not then be explained by models of this form. The Morris/Shin equilibrium has a formal singularity, however: the unique equilibrium exists for arbitrarily small observation noise, but is undefined if signals are exact. We argue that such removable singularities signal fragile solution concepts. To formalize this idea, we make the solution concept dynamical using a stochastic replicator. We show that, with large observation noise, the Morris/Shin equilibrium is recovered, while in an open interval around zero noise the multiple equilibria of Diamond and Dybvig can be recovered in some situations. We show in this context how to compute the expected risk of failures, which determines whether entering the pool is rational Runs, Panics and Bubbles: Diamond Dybvig and Morris Shin reconsidered