How Noisy should a Noise Signal be? Optimal Level of Noise for Bank Stability and Depositor Welfare

There is a strand of literature on bank runs, where depositors decide whether or not to withdraw their deposits based on noisy signals about the viability of the bank. The models used in these papers assume that the level of noise is very small and go on to establish a unique equilibrium with a threshold level below which depositors would withdraw. Noise indicates the level of transparency of the bank's future financial state. In reality however, noise need not be very small. The level of transparency of the information that is made available to the depositors can be endogenised so that it is chosen by the banks or the regulators. This paper attempts to determine the optimal level of noise for bank stability and depositor welfare. The objective of the financial regulators and the authorities would be to minimise the probability of bank runs, while the objective of banks operating in a competitive environment would be to maximise the expected utility of depositors. This paper uses a simple theoretical model of bank runs to demonstrate that there should be high level of transparency about the banks' future profitability to both minimise bank runs and maximise the expected utility of depositors.