Having it Both Ways: A Theory of the Banking Firm with Time-Consistent and Time-Inconsistent Depositors

Our equilibrium model determines the liquidity premium offered by a monopolistic bank to a pool of depositors made up of time-consistent and time-inconsistent agents. Time-consistent depositors demand compensation for illiquidity, whereas time-inconsistent ones are willing to forgo interest on illiquid savings accounts to discipline their future selves. We show that formal financial markets can reward time-inconsistent clients for illiquidity, even though these agents would agree to pay for it. The explanation combines two factors: the existence of reserve requirements making the bank keen to reward illiquid accounts more than liquid ones, and the presence of time-consistent agents who view illiquidity as a burden and therefore demand compensation for holding illiquid accounts.