Bank runs
Week 8
Allen and Gale Ch3.3-3.10
Intro
What is a bank run
• In the banks e cient solution, c1*≤ c2*
• Bank run- many customers (late consumers) withdraw their money from a bank early (t=1)
◦ At t=1 the bank does not know who is an early consumer
◦ The bank must promise ct* to whoever comes to the bank at t
◦ If the bank defaults at t and distributes all returns to the consumers at t, and there is no bank
at t=1
Modelling
• A bank run is when at t=1, the number of consumers that come for the bank is > λ
◦ This is self ful lling as even if the bank can ful ll their nancial obligations, if customers
withdraw early they then develop a liquidity issue
◦ This is a problem because consumers can choose the timing of terminating their deposit
contracts, but cannot coordinate with other consumers
◦ This means that even if you know that the panic that caused the bank run was unfounded,
your optimal solution is to withdraw funds
Fora singleinfinitesimal Exolateconsumer
ASE
1 allotherlate consumers withdraw at t 1
Xc l f e c y't isimpossible
thebankdefaultsandc tc Y Bankrunequilibrium
2 nobank optimaltowithdraw at t 1 too
CASE Nootherlateconsumer withdraws at t 1
achieved
Act y'tandefficientsolutioncatsc
Allowing premature liquidation
• If the assumption of the long asset giving nothing at t=1, r=0, so premature liquidation —> rx at
t=1 r≤1 , or Rx at t=2, R>1
◦ Insolvency- the bank can meet the demands of its deposits but only by liquidating some of
the long asset
◦ Default- the bank can or meet the demands of its depositors even after liquidating all short
and long assets
Week 8
Allen and Gale Ch3.3-3.10
Intro
What is a bank run
• In the banks e cient solution, c1*≤ c2*
• Bank run- many customers (late consumers) withdraw their money from a bank early (t=1)
◦ At t=1 the bank does not know who is an early consumer
◦ The bank must promise ct* to whoever comes to the bank at t
◦ If the bank defaults at t and distributes all returns to the consumers at t, and there is no bank
at t=1
Modelling
• A bank run is when at t=1, the number of consumers that come for the bank is > λ
◦ This is self ful lling as even if the bank can ful ll their nancial obligations, if customers
withdraw early they then develop a liquidity issue
◦ This is a problem because consumers can choose the timing of terminating their deposit
contracts, but cannot coordinate with other consumers
◦ This means that even if you know that the panic that caused the bank run was unfounded,
your optimal solution is to withdraw funds
Fora singleinfinitesimal Exolateconsumer
ASE
1 allotherlate consumers withdraw at t 1
Xc l f e c y't isimpossible
thebankdefaultsandc tc Y Bankrunequilibrium
2 nobank optimaltowithdraw at t 1 too
CASE Nootherlateconsumer withdraws at t 1
achieved
Act y'tandefficientsolutioncatsc
Allowing premature liquidation
• If the assumption of the long asset giving nothing at t=1, r=0, so premature liquidation —> rx at
t=1 r≤1 , or Rx at t=2, R>1
◦ Insolvency- the bank can meet the demands of its deposits but only by liquidating some of
the long asset
◦ Default- the bank can or meet the demands of its depositors even after liquidating all short
and long assets
