Bank Run - Theory

Theory

Under fractional-reserve banking, the type of banking currently used in most developed countries, banks retain only a fraction of their demand deposits as cash. The remainder is invested in securities and loans, whose terms are typically longer than the demand deposits, resulting in an asset liability mismatch. No bank has enough reserves on hand to cope with all deposits being taken out at once.

Diamond and Dybvig developed an influential model to explain why bank runs occur and why banks issue deposits that are more liquid than their assets. According to the model, the bank acts as an intermediary between borrowers who prefer long-maturity loans and depositors who prefer liquid accounts. The Diamond-Dybvig model provides an example of an economic game with more than one Nash equilibrium, where it is logical for individual depositors to engage in a bank run once they suspect one might start, even though that run will cause the bank to collapse.

In the model, business investment requires expenditures in the present to obtain returns that take time in coming, for example, spending on machines and buildings now for production in future years. A business or entrepreneur that needs to borrow to finance investment will want to give their investments a long time to generate returns before full repayment, and will prefer long maturity loans, which offer little liquidity to the lender. The same principle applies to individuals and households seeking financing to purchase large-ticket items such as housing or automobiles. The households and firms who have the money to lend to these businesses may have sudden, unpredictable needs for cash, so they are often willing to lend only on the condition of being guaranteed immediate access to their money in the form of liquid demand deposit accounts, that is, accounts with shortest possible maturity. Since borrowers need money and depositors fear to make these loans individually, banks provide a valuable service by aggregating funds from many individual deposits, portioning them into loans for borrowers, and spreading the risks both of default and sudden demands for cash. Banks can charge much higher interest on their long-term loans than they pay out on demand deposits, allowing them to earn a profit.

If only a few depositors withdraw at any given time, this arrangement works well. Barring some major emergency on a scale matching or exceeding the bank's geographical area of operation, depositors' unpredictable needs for cash are unlikely to occur at the same time; that is, by the law of large numbers, banks can expect only a small percentage of accounts withdrawn on any one day because individual expenditure needs are largely uncorrelated. A bank can make loans over a long horizon, while keeping only relatively small amounts of cash on hand to pay any depositors who may demand withdrawals.

However, if many depositors withdraw all at once, the bank itself (as opposed to individual investors) may run short of liquidity, and depositors will rush to withdraw their money, forcing the bank to liquidate many of its assets at a loss, and eventually to fail. If such a bank were to attempt to call in its loans early, businesses might be forced to disrupt their production while individuals might need to sell their homes and/or vehicles, causing further losses to the larger economy. Even so, many if not most debtors would be unable to pay the bank in full on demand and would be forced to declare bankruptcy, possibly affecting other creditors in the process.

A bank run can occur even when started by a false story. Even depositors who know the story is false will have an incentive to withdraw, if they suspect other depositors will believe the story. The story becomes a self-fulfilling prophecy. Indeed, Robert K. Merton, who coined the term self-fulfilling prophecy, mentioned bank runs as a prime example of the concept in his book Social Theory and Social Structure. Mervyn King, governor of the Bank of England, once noted that it may not be rational to start a bank run, but it is rational to participate in one once it had started.