Editing Bank run (section)

==Theory==
{{main|Diamond–Dybvig model}}
[[File:War of wealth bank run poster.jpg|thumb|A poster for the 1896 Broadway [[melodrama]] ''The War of Wealth'' depicts a 19th-century bank run in the U.S.]]

Under [[fractional-reserve banking]], the type of banking currently used in most [[developed country|developed countries]],  banks retain only a fraction of their [[demand deposit]]s as cash. The remainder is invested in securities and [[loan]]s, whose terms are typically longer than the demand deposits, resulting in an [[asset–liability mismatch]]. No bank has enough [[Bank reserves|reserves]] on hand to cope with all deposits being taken out at once.<ref name=bag>{{Cite book |last=Bagehot |first=Walter |year=1897 |title=Lombard Street: A Description of the Money Market   |publisher= Charles Scribner's Sons |publication-date=1897 |publication-place=New York  |url=https://archive.org/details/lombardstreetdes00bagerich |access-date=21 July 2014 }} via Archive.org</ref>{{bettersource|date=November 2023}}

Diamond and Dybvig developed an influential model to explain why bank runs occur and why banks issue deposits that are more [[Market liquidity|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.<ref name=Diamond2007/><ref name=Diamond-Dybvig-1983>{{cite journal |journal= J Political Econ |year=1983 |volume=91 |issue=3 |pages=401–19 |title= Bank runs, deposit insurance, and liquidity |last1=Diamond |first1=D. W. |last2=Dybvig |first2=P. H. |url=http://minneapolisfed.org/research/QR/QR2412.pdf |doi= 10.1086/261155|citeseerx=10.1.1.434.6020 |s2cid=14214187 }} Reprinted (2000)<!--month?--> in ''Federal Reserve Bank of Minneapolis Quarterly Review'' '''24''' (1), 14–23.</ref> The Diamond–Dybvig model provides an example of an economic [[Game theory|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.<ref name=Diamond2007/>

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 (finance)|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 [[House|housing]] or [[automobile]]s. 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 account]]s, 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.<ref name=Diamond2007/> Banks can charge much higher interest on their long-term loans than they pay out on demand deposits, allowing them to earn a profit.

[[File:Bundesarchiv Bild 102-12023, Berlin, Bankenkrach, Andrang bei der Sparkasse.jpg|thumb|Depositors clamor to withdraw their savings from a bank in Berlin, 13 July 1931]]
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 [[correlation|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.<ref name=Diamond2007/>

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.<ref name=Diamond2007>{{cite journal |journal=Federal Reserve Bank of Richmond Economic Quarterly |year=2007 |volume=93 |issue=2 |pages=189–200 |title=Banks and liquidity creation: a simple exposition of the Diamond-Dybvig model |last=Diamond |first=D. W. |url=http://www.rich.frb.org/publications/research/economic_quarterly/2007/spring/pdf/diamond.pdf |access-date=2008-10-17 |archive-date=2012-05-13 |archive-url=https://web.archive.org/web/20120513200015/http://www.rich.frb.org/publications/research/economic_quarterly/2007/spring/pdf/diamond.pdf |url-status=dead }}</ref> 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]].<ref name=Diamond2007/> 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]]''.<ref>{{cite book |title= Social Theory and Social Structure |last= Merton |first=R. K. |edition= enlarged |year=1968 |publisher= Free Press |location= New York |isbn=978-0-02-921130-4 |oclc=253949 |page=[https://archive.org/details/socialtheorysoci00mert/page/477 477] |orig-year=1949|title-link= Social Theory and Social Structure |author-link= Robert K. Merton }}</ref> [[Mervyn King, Baron King of Lothbury|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.<ref>{{cite web |url=http://www.ft.com/cms/s/2/5d7ff324-a0e6-11e1-9fbd-00144feabdc0.html |archive-url=https://web.archive.org/web/20120524023501/http://www.ft.com/cms/s/2/5d7ff324-a0e6-11e1-9fbd-00144feabdc0.html#axzz1wFPfjHwz |archive-date=2012-05-24 |url-access=subscription |url-status=bot: unknown |title=The only way to stop a eurozone bank run |work=Financial Times |date=2012-05-20 |access-date=2012-05-29 }}</ref>