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The Cost of Information and Herd Behavior in Bank Runs

In the classic models of herding (Banerjee (1992), Bikhchandani, Hirshleifer, and Welch (1992, 1998), etc), agents’ private signals are costless. This paper studies how costly private signals affect depositors’ herding behavior in bank runs. I assume that the quality of a depositor’s private signal depends on how much costs the depositor is willing to pay. More expensive signal means more precise information. The depositors are able to observe the predecessors’ actions. However, the cost on a private signal is each depositor’s private information. The model shows if some depositors choose to infer the quality of the bank’s investment by observing the predecessors’ withdrawal decisions rather than buying their own private signals, bank runs occur earlier. The depositors are able to anticipate whether the predecessors’ private signals are informative or not when their predecessors make different decisions. This paper demonstrates that the second patient depositor has the incentive to purchase more expensive information than the first patient depositor if the quality of his private signal is more improved and exceeds a critical level. When the second patient depositor’s private signal is more informative than the first patient depositor’s, the second patient depositor makes a withdrawal decision independent of the first patient depositor’s action. The third patient depositor does not have the incentive to purchase his private signal and a herd begins on the third agent. Therefore, the first two patient depositors’ decisions determine the existence of a bank runs equilibrium.