Optimal reserves and short-term interest rates in a model of bank runs

A global game framework of bank runs is used to analyse a bank's choice of its reserve level and short-term interest rate. Higher level of reserves and a lower short-term interest rate would decrease the probability of bank runs. When the bank's reserve policy is transparent, it will hold excess reserves to discourage withdrawals by patient depositors. This inefficiency of excess reserves increases with the proportion of impatient depositors. When the bank has private information about its reserve level, it will follow a more risky strategy of choosing lower reserves and higher early return than what maximizes depositor welfare and increases the probability of bank runs.