Preventing bank runs

Abstract

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.

Preventing (panic) bank runs

“…is on. At the same time, it guarantees a high period-2 payoff to the other patient depositor if she keeps the money in the bank, in the spirit of Andolfatto et al (2017). Therefore, if the priority account is chosen while the bank has enough funds, it pays in the second period c pa (pa denoting the priority account), with c pa > c w .…”

“…Hence, announcing a bank run and using the priority account dominates immediate withdrawal. In Andolfatto et al (2017), when the priority account is chosen, convertibility is suspended, which implies that the other patient depositor would receive its promised payoff in period t = 2. In our model, we keep the same incentive scheme through the payoffs associated to the priority account, although we do not introduce suspension of convertibility once the priority account is chosen.…”

“…Arguably, there is evidence of panic bank runs when depositors are affected by what they observe (Kiss et al, 2014a(Kiss et al, ,b, 2018. It is natural to ask whether the mechanism in Andolfatto et al (2017) also prevents panic bank runs. Since the decision to withdraw is not rational in a panic bank run, we do not expect that the priority account increases the likelihood of keeping the funds deposited.…”

“…In particular, we examine depositor behavior when in addition to withdrawing or keeping their money in the bank, depositors are provided with a third option, in the form of a less risky, but also less profitable alternative possibility. The instrument is inspired by Andolfatto et al (2017), who show that bank run is not an equilibrium outcome in a setup in the traditional framework by Diamond and Dybvig (1983) if depositors are offered an adequate mechanism to communicate with the bank, that allows them to avoid a bank run. A potential implementation of the mechanism implies that depositors can communicate an impending run to the bank by relocating their funds to a priority account that yields a (future) payment that is slightly larger than the (immediate) payment that they would receive upon withdrawing.…”

“…There are other advantages of laboratory experiments as well. For example, we know the information that depositors receive when making their choices, thus we can assess whether the mechanism inspired by Andolfatto et al (2017) helps in preventing both sources of bank runs. In addition, we elicit a set of variables in our experiment (e.g., the expectations of depositors that a bank run is underway or the individual characteristics of participants) that cannot always be observed in the field.…”