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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.
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
Tomorrow
Today
0
3/4
Today
3/4
1
Depositor 2
1
3/2
Tomorrow
0
3/2
R=1.5, L=.5
Experiment
• We then went to the lab and had 3
treatments with 9 patient and 9 impatient.
• Credit Crunch: R=1.1, L=.11
• Normal Conditions: R=2, L=.7
• Credit Crunch with 90% deposit insurance.
• How many other patient depositors need
to withdraw today for you to want to
withdraw today?
Normal Conditions
Credit crunch
Credit crunch
w/ 90%
deposit ins.
Hidden assumption
• Depositors withdraw sequentially: a bank
cannot count the number of people
wanting to withdraw today and then decide
how much to pay them.
• Otherwise, they can just pay them 5000/N
where N is the number withdrawing early
(for the 10 depositor case). This would
make suspension less painful.
What is not captured in the model
• Uncertainty in depositor’s preferences.
– Too many actually need the money today.
• Riskiness in technology.
– Riskiness in R: Perhaps there really isn’t enough to
meet demand tomorrow.
• Implication: it will be worthwhile to withdraw money
independent of what others do. Sometimes a bank run will be
the unique equilibrium.
– Riskiness in L: Perhaps one can’t really get L.
Particularly if it is a systemic risk.
• With LTCM, prices went down on any asset that LTCM
owned! Dual listed stocks arbitraged by LTCM diverged
Early Solutions to Bank Runs
• Put money in the windows
• Slow up payments.
Solutions.
• Make sure R & L are not risky. Difficult & doesn’t stop multi. Equilibria.
• Pay early withdrawers less than 1 or pay late withdrawers less than
R (and keep more reserves/Narrow Banking)
– Problems: not best contract.
• Suspend payments/ Partial Suspension.
– Problem when number needing money today is uncertain.
• Creditor Coordination.
– Long Term Capital Management ran into trouble in 1998.
– The NY FED organized a bailout with creditors.
• Lender of last resorts.
– Central bank will stop in and loan the bank money to replace deposits.
– This should work with depositors in the case of a problem with liquidity
– In 1975,
• April 14th, Credit Suisse announced lost some money in one of its branches.
It didn’t mention details.
• April 25th, The Swiss Central Bank announced it was willing to lend money.
• This had the opposite result causing share price to tumble 20%.
• Combination Bailout.
– 1907 Banking panic (JP Morgan and US treasury).
• Deposit Insurance.
– This works well. Risk-Sharing between banks.
Insurance Problem: Moral hazard
• Todd buys theft insurance for his laptop.
• Because he buys the insurance, he is
more likely to leave the laptop in his car.
• Ideally, he would like to commit to not
leaving the computer in his car.
• Sometimes, we can contract on it.
• Other times, we can’t.
• Do we have a moral hazard problem with
deposit insurance?
Answer: Yes.
• Marc is the manager of a Springfield S&L.
• Marc pays higher interest than a bigger and safer bank
claiming his small size helps him cut costs.
• Springfield has deposit insurance (100%).
• Todd puts money in Springfield.
• Springfield lends money to a dodgy lecturer at
Springfield State University at a higher rate.
• When there is no default, everyone wins.
• When there is a default, Todd still gets paid.
• Without insurance, Todd wouldn’t invest if he sees
Springfield’s risky behavior.
Model of Moral Hazard.
• The bank can choose any investment x, where 3>x=>1.
• Any investment costs £.95 and is either successful and pays of x or
unsuccessful and pays £0.
• The probability of the investment being successful is
P(X)=(3-x)/2.
• Choosing x=1 is safe, choosing x close to 3 is unsafe.
• Todd is close to risk neutral and wants to earn at least as much as
£1 (in expectation) which the other banks are offering as a risk free
investment. He wants R where R*P(x)=1.
• Without insurance, the bank maximizes
– P(X)*(X-R) where R=1/P(x)
• With insurance, Todd only needs R=1. So the bank maximizes
– P(X)*(X-R) where R=1
Savings and Loans scandal
• In the 1980s about 1000 S&L’s went bankrupt.
• They originally lent money out at fixed rates of
6% and paid deposits 3%.
• With inflation, they had to pay deposits 14% and
lost money.
• Took gambles to catch up, went to Vegas.
• They were able to take high risk due to the
deposit insurance.
• This cost US taxpayers $120 billion.
Solution to Moral Hazard
• One solution is for insurance to not be
100% (co-pay as in the UK).
• However, this requires the depositors to
be savvy and this still keeps the multiple
equilibrium problem.
• In the US, in 2006 Bush signed a law
allowing the FDIC to charge premiums
based upon risk.