Optimal Reserves and Short Term Interest Rates in a Model of Bank Runs

Abstract

Banks can fail because of bad economic fundamentals, and/or general panic withdrawals by depositors who feel the bank does not have sufficient reserves to meet the demand. This paper attempts to find the optimal reserve level and early returns the banks should decide on. If the reserve policy of the bank is transparent, it is found that more reserves have to be put aside over and above the real need, and this inefficiency increases with the proportion of impatient agents. It is also found that the optimal early return is lower than the first-best. The model recommends that when reserve policy is transparent there is no need for regulation. However, if reserve policy is not transparent, the model recommends regulation for both reserves and early returns. This is because of the moral hazard problem, the banks would keep lower reserves and offer higher early returns than what maximises depositor welfare.