A Diamond-Dybvig Model in which the Level of Deposits is Endogenous

We extend the Diamond-Dybvig model of bank runs to include a specification of how much to deposit. A contract specifies a deposit level and period 1 withdrawals as a function of the number of previous withdrawals, satisfiying a sequential service constraint. Thus, partial or full suspension of convertibility is allowed. We prove an equivalence result, that the efficient allocation (satisfying resource, IC, and sequential service constraints) can be achieved in equilibrium as long as the deposit level is above a threshold, ∗. However, within this range, the lower the deposit level, the more tempted patient depositors are to withdraw early. We extend the baseline model so that outside investments yield a slightly higher return than bank investments, to capture an administrative cost faced by the bank. Then when the propensity to run is small enough, the optimal contract specifies deposit level near ∗, and it is common for runs to occur on the equilibrium path.