Deposit Insurance in General Equilibrium

We study the consequences and optimal design of bank deposit insurance in a general equilibrium model. The model involves two production sectors. One sector is financed by issuing bonds to risk-averse households. Firms in the other sector are monitored and financed by banks. Households fund banks through deposits and equity. Deposits are explicitly insured by a de- posit insurance fund. Any remaining shortfall is implicitly guaranteed by the government. The deposit insurance fund charges banks a premium per unit of deposits whereas the government finances any necessary bail-outs by lump-sum taxation of households. When the deposit insurance premium is actuarially fair or higher than actuarially fair, two types of equilibria emerge: One type of equilibria supports the socially optimal (Arrow-Debreu) allo- cation, and the other type does not. In the latter case, bank lending is too large relative to equity and the probability that the banking system collapses is positive. Next, we show that a judicious combination of deposit insurance and reinsurance eliminates all non-optimal equilibrium allocations.