Bank runs and privately funded solutions

In a simple extension of the Diamond and Dybvig (J Polit Econ 91:401–419, 1983) environment, we compare three regimes: an explicitly modeled privately funded deposit insurance scheme, an ex-ante funded liquidity insurance scheme, and runs preventing bank contracts without any insurance. It is shown that when the probability of runs is low, both insurance schemes are superior to runs preventing contracts; and in this case, the deposit insurance scheme is socially desirable as long as asset liquidation costs are not excessively high. When liquidation costs are high, the liquidity insurance scheme outperforms the other two regimes. And when the probability of runs is high, the arrangement with runs preventing bank contracts is the best among the three regimes. We also show that when depositors are sufficiently risk averse, the deposit insurance scheme is socially the most desirable among the three regimes. Our main findings remain robust when extended to scenarios with moral hazard and government intervention during insurance fund depletion.