Behavioral Banking: A Theory of the Banking Firm with Time-Inconsistent Depositors

Abstract

Time-consistent savers require compensation for holding savings accounts that are illiquid rather than liquid. In equilibrium, banks subject to reserve requirements for liquidity management are keen to offer that compensation. Yet the presence of time-inconsistent agents, who value illiquidity as a commitment device to discipline their future selves, reshuffles the deck. Our model determines the equilibrium liquidity premium––the interest spread between illiquid and liquid deposits––offered by a bank to a pool comprising known proportions of time-consistent and time-inconsistent savers, under the assumption that individual time consistency or inconsistency is private information. We characterize pooling and separating equilibria, and uncover two asymmetric externalities: time-inconsistent agents obtain a higher premium than they would request ex ante for holding illiquid accounts, while time-inconsistent agents make it harder for their time-consistent counterparts to get illiquid accounts. We also deliver insights on reserve requirements for banking regulation.

Keywords: Behavioral economics, banking, savings account, liquidity premium, time inconsistency, commitment, quasi-hyperbolic discounting

JEL Classification: G21, E21, D53, D91, G28