Savings, efficiency and the nature of bank runs

Does the level of deposits matter for bank fragility and efficiency? In a banking model with endogenous bank runs and a consumption-saving decision, we show that the level of deposits has opposite effects on bank fragility depending on the nature of bank runs. In an economy with panic-driven runs, higher deposits make banks less fragile, while the opposite is true when runs are only driven by fundamentals. The effect of deposits is not internalized by depositors. A saving externality arises, leading to excessive fragility and insufficient liquidity provision. The economy features under-saving when runs are panic driven, and over-saving when fundamental driven.