Optimal banking contracts and financial fragility
We study a finite-depositor version of the Diamond-Dybvig model of financial intermediation in which the bank and all depositors observe withdrawals as they occur. We derive the (constrained) efficient allocation of resources in closed-form and show that this allocation provides liquidity insurance to depositors. The contractual arrangement that decentralizes this allocation has debt-like features and resembles the type of demand deposits commonly offered by banking institutions. We provide examples where this arrangement admits another equilibrium in which some depositors run on the bank, withdrawing funds regardless of their liquidity needs. A bank run in our setting is always partial, with only those depositors who can withdraw sufficiently early participating. Depositors who are late to withdraw during a run suffer significant discounts from the face value of their deposits. The run, while partial, may involve a large number of depositors and result in significant inefficiencies.
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