Preventing bank runs

The work of Diamond and Dybvig, 1983 is commonly understood as a theory of bank runs driven by self-fulfilling prophecies. Their contribution may alternatively be interpreted as a theory for preventing these bank runs. Absent aggregate risk over liquidity demand, they show that a simple scheme that suspends withdrawls when a target level of bank reserves is reached implements the efficient allocation as the unique equilibrium. Uniqueness implies that there cannot be a bank-run equilibrium. Unfortunately, this scheme cannot implement the efficient allocation when there is aggregate uncertainty over every possible liquidity demand because any realization of liquidity demand may, in this case, be determined by fundamentals instead of psychology. When there is aggregate risk, Peck and Shell, 2003 demonstrate that the constrained efficient allocation can be implemented by a direct mechanism as an equilibrium. They show that the same mechanism can also implement a bank-run equilibrium, which suggests that Diamond and Dybvig, 1983 can be understood as a theory of bank runs. The use of direct mechanisms, however, imposes a severe restriction on communications. We propose an indirect mechanism that (i) permits depositors to communicate their beliefs, not just their types, (ii) incentivizes depositors to communicate 'rumors' of an impending bank run, and (iii) threatens to suspend payments conditional on what is revealed in these communications. We demonstrate that if commitment is possible, then under some weak parameter restrictions our indirect mechanism uniquely implements an allocation that can be made arbitrarily close to the the constrained efficient allocation as an equilibrium. In other words, our mechanism prevents bank runs.