Chaotic banking crises and regulations

We study a model where limited liability and enforcement permits bank owners to shift the risk of their asset portfolios to the depositors. Incentive-compatible equilibria require the franchise value of the bank to exceed the value that the bank owners can obtain by undertaking excessively risky investments, and defaulting on deposits when investment returns are low. Our model generates multiple stationary equilibria as well as chaotic equilibria that can lead to coordination failures, making bank runs, bank defaults, and banking crises more likely. We suggest that banking regulations, including leverage limits, central bank credit policies, as well as restrictions on bank size and deposit rate ceilings can be instituted not only to enhance stable franchise values and sound asset portfolios, but also to eliminate multiple and complex equilibria.