Saving externality: when depositing too much breaks the bank.

This article investigates how the size of bank deposits influences bank fragility and the efficiency of financial intermediation by integrating depositors' consumption-saving decisions into a global-game model of bank runs. It finds that the probability of bank runs increases with the amount of deposits, and individual depositors do not internalize how their saving choices affect the likelihood of runs, creating a "saving externality" that leads to over-saving, excessive bank fragility, and inefficient liquidity provision. The study characterizes the constrained efficient allocation, showing that a social planner would choose lower deposit levels to reduce fragility, and proposes a deposit tax as an optimal policy tool to correct the saving externality and restore efficiency. Extensions of the model confirm the robustness of these results even when accounting for deposit rate dependence, bank portfolio choices, and depositors' portfolio allocation.