Optimal Bank Regulation in the Presence of Credit and Run Risk

We modify the 1983 Diamond and Dybvig model so that banks offer liquidity services to depositors, raise equity funding, make risky loans, and invest in safe, liquid assets. Banks monitor borrowers to ensure that they repay loans and they are susceptible to depositor runs. We model the run decision by solving a novel global game. Relative to a social planner, banks opt for a more deposit-intensive capital structure, their assets may be more or less lending intensive, and the level of lending may be higher or lower. Correcting these three distortions requires a package of three regulations.