Equilibrium non-panic bank failures

We observe many episodes in which a large number of people attempt to withdraw their deposits from a bank, forcing it to suspend withdrawals or even to fail. In contrast with the view that those episodes are driven by consumers panic or sunspots, we propose to explain them as a consequence of the conjunction of lack of full back up of deposits by banks, and of an unexpectedly high fraction of withdrawers. We validate this view in a version of the standard Diamond and Dybvig [8] model, in which the fraction of impatient consumers is drawn stochastically according to a continuous density function, by showing that: (1) when banks are not allowed to suspend payments, in every symmetric equilibrium where agents deposit banks fail with strictly positive probability, and (2) in every such equilibrium, failure occurs whereas patient consumers find it optimal not to withdraw early. Moreover, we obtain similar results when banks are allowed to suspend payments, and we show that consumers ex-ante welfare is strictly higher compared to when banks cannot suspend payments. Our contribution is therefore two-fold: (1) bank failures driven by large withdrawals can be explained by any fundamental shock that leads to an high fraction of withdrawers, and (2) suspension of payments might be a critical part of the protection of the banking system.