Gale, D. and Yorulmazer, T. (2020). Bank capital, fire sales, and the social value of deposits Economic Theory, 69(4):919--963.

We describe a model in which bank deposits yield liquidity services and therefore earn a lower rate of return than bank equity. In this sense, deposits are a cheaper source of funding than equity. The bank{\textquoteright}s equilibrium capital structure is determined by a trade-off between the funding advantages of deposits and the risk of costly default. Default is costly because banks assets are sold in fire sales, which transfer value to the purchasers. This transfer is a private cost for the owners of failed banks, but not a deadweight loss for society. As a result, deposits are under-used and banks{\textquoteright} funding costs receive a subsidy from depositors. This subsidy eventually causes banks to grow too large and accumulate too many assets.