Demand–Deposit Contracts and the Probability of Bank Runs

We study a model of bank runs based on Diamond and Dybvig [1983]. We assume that agents do not have common knowledge regarding the fundamentals of the economy, but rather receive slightly noisy signals. The new model has a unique equilibrium in which the fundamentals determine whether a bank run will occur. This lets us compute the ex-ante probability of a bank run and relate it to the parameters of the demand deposit contract. We find that offering a higher return to agents who demand early withdrawal makes the bank more vulnerable to runs. We construct an optimal demand deposit contract that trades off the benefits from risk sharing against the costs of bank runs. Under this contract, there is a positive probability of panic-based bank runs. Nevertheless, it improves welfare relative to the autarkic regime. Finally, being able to make welfare computations, we assess the desirability of regimes that are intended to prevent bank runs: suspension of convertibility and deposit insurance. We thank Elhanan Helpman for numerous conversations and suggestions, and Joshua Aizenman, Sudipt