The Diamond-Dybvig Model Is Sometimes Described as a “Bubble” or “Sunspot” Theory of Bank Runs

If bank runs were always confined to banks that were already (pre-run) insolvent [when liabilities are greater than its assets], then runs would not be a problem, but, instead, largely salutary. In other industries, an insolvent firm’s creditors whose debts are overdue, and who wish to cut their losses, can legally force the firm into liquidation through an involuntary bankruptcy proceeding. A run on an insolvent bank serves the same function as an involuntary bankruptcy proceeding: it is an action by the bank’s creditors, namely its depositors (or note-holders, but for simplicity we will speak only of depositors), that forces the bank into liquidation. Unlike the rule in a bankruptcy, the assets do not go pro rata to all creditors of equal standing, but instead go preferentially to those who are first in line to redeem their claims (a possibly problematic feature of deposit contracts that will concern us later). The run is salutary in that it closes the insolvent bank immediately, before the bank squanders even more depositor wealth, and goes even further into the red. The run cuts the depositors’ potential losses in the aggregate. The threat of a run, like the threat of bankruptcy in other industries, provides useful discipline. It forces banks to invest smartly, and to work vigorously to avoid insolvency or even the appearance of insolvency.

A problem arises, however, if depositors with imperfect information sometimes run on banks that are not (pre-run) insolvent. In an influential article, Douglas Diamond and Philip Dybvig (1983) emphasized that a run itself can cause a bank to default that would not otherwise have defaulted. A bank forced to liquidate assets hastily may have to accept less for them than they would otherwise be worth, an event known as suffering “fire-sale” losses. A bank run can thereby be a self-reinforcing equilibrium: if enough other depositors are running, the bank will incur large fire-sale losses, default becomes likely, and it becomes each depositor’s own best strategy to run.³ There is a “me-first” scramble as each depositor tries to redeem his claim ahead of others, before the bank’s funds are exhausted. In Diamond and Dybvig’s model, discussed in more detail below, the bank attempting to meet redemption demands by more than a certain proportion of its depositors will incur fire-sale losses so large that its default is a certainty. Any event that makes people anticipate a run, therefore, makes them anticipate insolvency, and so does, in fact, trigger a run. As in a rational speculative “bubble,” the induced outcome validates the anticipation, even if the anticipation is triggered by an intrinsically irrelevant event like the appearance of sunspots. The Diamond-Dybvig model is accordingly sometimes described as a “bubble” or “sunspot” theory of bank runs.

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³ In game-theoretic terms, the bank run is a Nash equilibrium. 

—Lawrence H. White, “Should Government Play a Role in Banking?” in The Theory of Monetary Institutions (Malden, MA: Blackwell Publishers, 1999), 121-122.