Moral hazard, bank runs and contagion

We study banking with ex ante moral hazard. Resolving the misalignment of the incentives between banks and depositors requires early liquidation with positive probability : efficient risk-sharing between depositors is no longer implementable. In a closed region with a single bank, we show that (i) with costless and perfect monitoring, contracts with bank runs of the equilibrium path of play improve on contracts with transfers, (ii) when the bank’s actions are non-contractible, equilibrium bank runs driven by incentives are linked to liquidity provision by banks. With multiple regions linked via an interbank market, with local moral hazard, we show that implementing second-best allocations requires both ex-ante trade in inter-bank markets and contagion after realization of liquidity shocks.