A bank run is a loss of confidence in a particular bank; as deposits are payable on demand on a first-in, first-served rule, depositors rush to withdraw their funds whenever they fear the bank may fail. The run itself may cause the bank’s failure because it may be unable to provide cash when too many depositors demand it.
The bank may be solvent - it has more assets than liabilities - but at the same time may be illiquid as normally banks use most of the money they collect from depositors to make loans. They keep minimum reserves in cash to meet any occasional excess demand for withdrawals.
In the case where a bank fails this may create an atmosphere in which depositors lose confidence in other banks; this may cause other banks to fail. If depositors withdraw indiscriminately from both solvent and insolvent banks - due to asymmetric information depositors are usually unable to distinguish which banks fall in each category - the situation can develop into a bank panic in which the loss of confidence hits the country’s whole financial system.
To prevent this happening, after the 1930 crisis in most countries the safety of deposits is guaranteed. In the US the FDIC insures deposits in financial institutions up to a limit of $250,000 per covered account.
During the optimistic years of the Great Moderation the study of economic and financial disruptions have been practically expelled from the economic theory' arena and confined to the economic history field. They were just considered an antiquity to be housed at the museum of economic archeology. Kin-dleberger’s seminal book on the subject was blatantly ignored or looked at with a mixture of contempt and condescension. Minsky’s model simply did not exist for most of the economics profession. In the words of Mankiw’s popular textbook, “today, bank runs are not a major problem for the US banking system or the Fed. The federal government now guarantees the safety of deposits at most banks, primarily through the Federal Deposit Insurance Corporation (FDIC)” Mankiw (2016: 621). The problem is that, as mentioned above, during the Great Moderation years the shadow banking system grew exponentially to such an extent that its gross liabilities represented nearly $22 trillion in June 2007, while traditional banking liabilities were only around $14 trillion in 2007 (Pozsar et al., 2012: 9). And the shadow banks lacked something equivalent to deposit insurance, which made them certainly vulnerable if they suffered a run on their liabilities. This means that the risk of runs did not disappear; it mainly moved away from traditional banking to shadow banking. The 2007/2009 crisis was, in essence, a crisis of the shadow banking system.