Banking and Bank Runs

1
Banking and Bank Runs

• We are going to learn a bit about what a bank
  does and why it leads to the possibility of bank
  runs.
• We will start out today with a couple of movie
  clips.
• Then discuss a theoretical model of a bank.
• Next week, we will talk specifically about the
  current crisis.

2
Mary Poppins

• Two things to notice.
• Bank Run was caused by panic w/o financial
  reasons. The bank was fully solvent.
• The bank closed its doors stopped payment.

3
Its a Wonderful Life

• It was a systemic panic.
• There may have been a justification for the bank
  run.
• A bank takes money and invests it in long-term
  assets (mortgages).
• The bank cant easily liquidate these assets.
• The bank did not fully suspend payments. Doing so
  would hurt depositors.
• There was a degree of negotiation on who gets
  what.

4
Diamond Dybvig Model (1983)

• Captures elements of what a bank does.
• Shows that there is a basic problem of bank runs.
• The model consists of two parties.
• Depositors
• Banks
• The model has three time periods yesterday,
  today and tomorrow.

5
Depositors

• Depositors placed money (say 1000) in a bank
  (yesterday) before learning when they need the
  money.
• Depositors either need their money today
  (impatient) or tomorrow (patient). There is a 50
  chance of being either type.
• The ones that need their money tomorrow can
  always take the money today and hold onto it.
• The ones that need money today get relatively
  very little utility for the money tomorrow.

6
Banks

• Banks have both a short term and a long term
  investment opportunity for the money.
• The short term investment (reserves) is locking
  the money in the vault. This investment returns
  the exact amount invested.
• The long term investment returns an amount R
  tomorrow. It is illiquid and returns only Llt1
  today.

7
Deposit Contract

• The depositors invested 1000 yesterday have a
  contract with the bank.
• The depositors can withdraw their money today and
  receive 1000 or wait until tomorrow and receive
  R1000.

8
Banks decision

• How can the bank meet this contract?
• The bank can divide into two parts.
• Take half and keep it as reserves.
• Take the other half and put it in the long term
  investment.
• Say there are 10 depositors 5 patient and 5
  impatient. The bank puts 5000 in the vault and
  invests 5000.
• Demands today are 51000, and 5R1000. The bank
  has 5000 and R5000 tomorrow.
• Thus, a bank makes zero profit.

9
Danger!

• The bank can not always remain solvent.
• If too many depositors try to withdraw today, it
  wont be able to meet the contract tomorrow.
• For instance if 7 depositors withdraw today, then
  the bank can pay 5000 out of reserves. It then
  must sell its illiquid asset to meet the rest of
  the needs, 2000.
• How much must it sell to meet the needs? How much
  is left?
• How much does those withdrawing tomorrow receive?
• On average, how much does those withdrawing today
  receive?
• At what value of L does is the bank unable to
  meet demands today for those 7 depositors?

10
Multiple equilibria

• This leads to multiple (Nash) equilibria.
• It is inherent in banking.
• Here is an example with 2 patient depositors (and
  2 impatient depositors).
• This forms a 2x2 game between the patient
  depositors.
• R1.5 and L.5

11
Game between patient depositors
Depositor 1
Tomorrow
Today
0
3/4
Today
3/4
1
Depositor 2
1
3/2
Tomorrow
0
3/2
R1.5, L.5