Bank Runs and Investment Decisions Revisited

Abstract

We examine how the possibility of a bank run affects the deposit contract offered and the investment decisions made by a competitive bank. Cooper and Ross (1998) have shown that when the probability of a run is small, the bank will offer a contract that admits a bank-run equilibrium. We show that, in this case, the bank will chose to hold an amount of liquid reserves exactly equal to what withdrawal demand will be if a run does not occur. In other words, precautionary or "excess" liquidity will not be held. This result allows us to determine how the possibility of a bank run affects the level of illiquid investment chosen by a bank. We show that when the cost of liquidating investment early is high, the level of investment is decreasing in the probability of a run. However, when liquidation costs are moderate, the level of investment is actually increasing in the probability of a run.

Optimal Bank Regulation in the Presence of Credit and Run Risk

“…Finally, the 28 See Van den Heuvel (2008) and Hanson, Kashyap and Stein (2011) for estimates of the liquidity premium for bank deposits. 29 In a model where the bank is funded only with deposits, Ennis and Keister (2006) show that shifting the asset mix towards more illiquid loans would result in a lower probability of being repaid given that a run occurs, which counterbalances the increase in credit extension when the probability of a run decreases. This does not need to be true in our model, because the increase in the credit extension is funded by more capital.…”

“…A fair amount of literature has focused on run-proof equilibria, which naturally restrict credit intermediation (see Cooper and Ross, 1998, Ennis and Keister, 2006, Diamond and Kashyap. 2016).…”

Bank panics and scale economies

“…9 A large value for n means that the aggregate demand for early withdrawals is high. In this case, it makes sense to devote less per capita resources to investment, reducing the e¤ective return for late withdrawals, spreading the additional early resources more thinly among the more numerous impatient depositors.…”

“…Costly liquidation is prominently featured in the models of Cooper and Ross (1998) and Ennis and Keister (2006). In their environments, liquidating capital at date 1 reduces capital by more than one unit.…”

“…In the models of Cooper and Ross (1998) and Ennis and Keister (2006), if a patient depositor believes that all other depositors are contacting the bank at date 1, he may not have an incentive to follow the crowd. 22 If the patient depositor does in fact contact the bank at date 1, then an additional amount of capital k is liquidated, but only a fraction 0 < < 1 of this liquidated capital, k, is available for consumption.…”