We study ex post efficient policy responses to a run on the banking system and the ex ante incentives these responses create. We show that the efficient response to a run is typically not to freeze all remaining deposits, since doing so imposes heavy costs on some individuals. Instead, once a run is underway, (benevolent) government institutions would allow additional deposit withdrawals, placing further strain on the banking system. When depositors anticipate these extra withdrawals, their incentive to participate in the run increases. In fact, ex post efficient interventions can generate the conditions necessary for a self-fulfilling run to occur. (JEL G21, G8)

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We examine the growth implications of bank runs. To do so, we construct an endogenous growth model in which bank runs occur with positive probability in equilibrium. In this setting, a bank run has a permanent effect on the capital stock and on the level of output. In addition, the possibility of a bank run changes the portfolio choice of banks and thereby affects the long-run growth rate. We consider two different equilibrium selection rules. In the first, a run is triggered by sunspots and occurs with a fixed probability. A higher probability of a run in this case leads banks to hold a more liquid portfolio, which decreases total investment and thereby reduces capital formation. Hence the economy grows slower, even when a run does not occur. Under the second selection rule, the probability of a run is influenced by the bank's portfolio choice. This leads banks to place more resources in long-term investment, and the economy both grows faster and experiences fewer runs.

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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.