Abstract This article highlights a novel channel through which the level of deposits matters for bank fragility and efficiency. We augment a global-game model of bank runs with a consumption-saving choice that determines deposit size in the initial period. We derive two key results. First, depositors’ incentives to run increase with the amount of savings held as bank deposits. Second, a saving externality emerges because individual depositors fail to internalize the impact of their deposit decisions on the likelihood of a bank run. This leads to depositors’ over-saving and inefficient bank liquidity provision, as well as excessive bank fragility. Finally, we characterize the optimal policy to implement the efficient allocation.