The optimal distribution of insured and uninsured deposits across banks

I study a model of self-fulfilling bank runs where government-provided deposit insurance covers small (retail) deposits but not large (wholesale) deposits. The share of the banking system that may be affected by runs depends on the distribution of retail and wholesale deposits across banks. The magnitude of runs is minimized if banks with both retail and wholesale depositors (reminiscent of commercial banks) coexist with banks that cater only to wholesale depositors (reminiscent of shadow banks). The shadow banking sector should be large enough to absorb enough wholesale deposits from commercial banks to keep them shielded from runs. In a decentralized equilibrium, the magnitude of runs tends to be larger than optimal as a result of wholesale depositors’ incentive to invest in the banks with the highest share of retail depositors.