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.

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.

It’s 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 can’t 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.

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.

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.

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 L<1 today.

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 R*£1000.

Bank’s 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 5*1000, and 5*R*1000. The bank has 5000 and R*5000 tomorrow. Thus, a bank makes zero profit.

Danger! The bank can not always remain solvent. If too many depositors try to withdraw today, it won’t 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?

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. R=1.5 and L=.5

Game between patient depositors Depositor 1 Depositor 2 Today Tomorrow 3/2 R=1.5, L= /4