Bank depositors do have some information about attempted withdrawals by other depositors. The formation of a line outside the bank can persuade others to join the line. The classic bank runs models do not allow for this "herding" behavior, because the withdrawal decision is assumed to be simultaneous in these models. I construct a model of fundamental-based runs, in which depositors receive noisy private signals about returns on the bank's portfolio and they observe the withdrawals by other depositors. I show that given a demand-deposit contract, there exists a perfect Bayesian equilibrium in which the depositors withdraw if their beliefs are below the threshold, and wait otherwise. Bank runs occur when all depositors withdraw because their beliefs are below the threshold. If the prior belief is favorable enough, the private signal that an informed depositor gets is not decisive, and the informed depositor always waits unless she needs to consume immediately. When the belief is in the middle range, the depositors who have not been informed watch the informed depositors' decisions closely. The informed depositors follow their private signals, and their decisions reveal the information obtained. Computed examples show that in some economies a run-admitting contract is optimal because it not only provides more liquidity to the depositors to insure against the liquidity shocks, but also it encourages depositors to reveal the signals they receive. In other economies, the run-proof contract is optimal. Even though it provides less liquidity to the depositors, it prevents the economy from costly bank runs.

Asymmetric Information and Bank Runs, mimeo, May 2006. - PDF  

It is known that sunspots can trigger panic-based bank runs and that the optimal banking contract can tolerate panic-based runs. The existing literature assumes that these sunspots are based on a publicly observed extrinsic randomizing device. In this paper, I extend the analysis of panic-based runs to include an asymmetric-information, extrinsic randomizing device. Depositors observe different, but correlated, signals on the stability of the bank. A depositor does not know for sure whether other depositors will run on the bank or not. She infers the decisions of others from the signal that she receives, which in general is neither purely public nor purely private. I find that if the signals that depositors obtain are highly correlated, there exists a correlated equilibrium for some demand deposit contracts. In this equilibrium, either a full bank run, or a partial bank run, or no bank run occurs depending on the realization of the signals. The number of contracts allowing for such an equilibrium diminishes as the signals become more noisy. Computed examples indicate that in some economies, if the probabilities of full bank runs and partial bank runs are small, a demand-deposit contract that tolerates bank runs and partial bank runs is better than the run proof contract; while in some other economies a run-proof contract is optimal. The results hold in a broad class of mechanisms, which includes partial suspension of convertibility.