With the current financial crisis, the question of the optimality of bank deposit insurance has flared up again. Figuring out how much deposit insurance should cover is not an obvious exercise. Indeed, one has to think this as a game between bank managers, who want to take advantage of moral hazard through excessive risk taking, bank owners, looking maximize bank value, depositors, who decide whether to run and withdraw funds, and regulators, who want to prevents crises, but also want to liquidate banks that should be liquidated.
Michael Manz develops a nice and rich model that attack the problem from the perspective of global games. This has the advantage of resolving the issue of multiple equilibria in the standard bank run models. Among the many results, several stand out. If the bank risk is exogenous, coverage should not be high as it prevents necessary and efficient runs. Also, liquidity requirements are a good substitute to deposit insurance. Finally, coverage should not increase in the event a financial crisis hits. The reason is that the financial risk increases with the scope of deposit insurance because, if I understand right, while higher coverage protects better deposits in banks of systemic importance, it leads to more moral hazard in others and then increases the likelihood of a run on all banks. The only way out is to discriminate coverage by bank, which is a completely different regulatory game.