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Diamond Dybvig Model 1983


Jim Cramer on subprime. Bill Poole says that it is risky lenders that got what they deserved. Jim Cramer more or less says everyone is in trouble. ... – PowerPoint PPT presentation

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Title: Diamond Dybvig Model 1983

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 placed money (say 1000) in a bank
    (yesterday) before learning when they need the
  • 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 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

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

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
  • 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.

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
  • R1.5 and L.5

Game between patient depositors
Depositor 1
Depositor 2
R1.5, L.5
Our experiment
credit crunch
Normal conditions
What is not captured in the model
  • Uncertainty in depositors preferences.
  • Too many actually need the money today.
  • Riskiness in technology.
  • Perhaps there really isnt enough to meet demand
  • Implication some bank runs will be rational.

Early Solutions to Bank Runs
  • Put money in the windows
  • Slow up payments.

  • Make sure R is not risky.
  • Pay early withdrawers less than 1 or pay late
    withdrawers less than R (and keep more reserves)
  • Problems not best contract.
  • Suspend payments/ Partial Suspension.
  • Problem when number needing money today is
  • Creditor Coordination.
  • Long Term Capital Management ran into trouble in
  • 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 liqudity
  • In 1975,
  • April 14th, Credit Suisse announced lost some
    money in one of its branches. It didnt mention
  • April 25th, The Swiss Central Bank announced it
    was willing to lend money.
  • This had the opposite result cauing share price
    to tumble 20.
  • Deposit Insurance.
  • This works well. Risk-Sharing between banks.

Better Contract
  • Why should the bank pay the depositors
    withdrawing early only 1?
  • The bank can pay them more.
  • This would insure a depositor against needing
    the money early.
  • For R1.5, what would the full insurance contract
    look like. In other words, the payment is the
    same in either period.
  • The amount would solve (2000-X)RX
  • This amounts to a gamble of having either 1000 or
    1500 or 1200 for sure. Risk-averse enough people
    would prefer 1200.
  • Note the best contract (and perhaps fairest) will
    pay depositors withdrawing today somewhere 1000
    and 1200.

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).

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 cant.
  • Do we have a moral hazard problem with deposit

Answer Yes.
  • Marc is the manager of a Springfield SL.
  • 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 wouldnt invest if he
    sees Springfields risky behavior.

Model of Moral Hazard.
  • The bank can choose any investment x, where
  • Any investment costs .95 and is either
    successful and pays of x or unsuccessful and pays
  • The probability of the investment being
    successful is
  • P(X)(3-x)/2.
  • Choosing x1 is safe, choosing x close to 3 is
  • 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 RP(x)1.
  • Without insurance, the bank maximizes
  • P(X)(X-R) where R1/P(x)
  • With insurance, Todd only needs R1. So the bank
  • P(X)(X-R) where R1

Savings and Loans scandal
  • In the 1980s about 1000 SLs went bankrupt.
  • They originally lent money out at fixed rates of
    6 and paid deposits 3.
  • With inflation, they 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
  • In the US, in 2006 Bush signed a law allowing the
    FDIC to charge premiums based upon risk.

Lender of Last Resorts commitment
  • Gambling Jim has a rich uncle.
  • Jims uncle loves him very much.
  • Jim blows his money in a poker game. His rich
    uncle bails him out.
  • His uncle says that is the last time.
  • Jim gambles again and loses. His rich uncle cant
    bear to see Jims legs broken.
  • The problem is that Jim knows his uncle will
    always be there for him.
  • The uncle can either find some way to commit not
    to help Jim afterwards, or sacrifice Jim to stop
    his other nephews from gambling.

Northern Rock and the Subprime crisis.
  • Jim Cramer on subprime.
  • Bill Poole says that it is risky lenders that
    got what they deserved.
  • Jim Cramer more or less says everyone is in
  • Bernanke is thinking about whether to cut rates.

Subprime mortgages
  • Miriam, a divorced mother, was offered a mortgage
    on a 2-28 deal 2 years of a teaser rate of a
    mortgage and the rest floating.
  • Finally, the dream of owning a home is a reality.
  • Miriam did not have to verify income or assets.
    She got a piggyback loan to cover the down
  • She was told that she can refinance after two
    years and with the prices the way they are going
    get some money out as well.
  • She took some extra credit cards and agreed.
  • The bank took her mortgage packaged it up with
    others. The rating agency (paid by the bank)
    rates the package high. It is sold to a hedge
  • The bank now only collects the money.

Sub-prime continued
  • Unfortunately, rates went up and she couldnt
    make the payments.
  • Housing prices didnt go up and she has no
  • The local bank doesnt want to work out a deal so
    forecloses (actually collects extra fees doing
  • These packages drop faster than one would have

Hedge fund
  • Hedge funds are highly leveraged. The price of
    these securities drop more than they should given
    the state of the economy, interest rate, etc.
  • People loaning the hedge funds want to take their
    money out. Forcing the hedge funds to sell more.
    This further suppresses the price.
  • Hedge funds start to go broke.
  • Banks also have these mortgages on their books.
    It isnt clear who owns what.
  • Banks dont want to lend to each other for two
  • Afraid of the financial state of other banks.
  • Want to keep extra reserves in case they cant

Northern Rock
  • Had mortgages not necessarily subprime.
  • To provide funding for these mortgages, it had
    deposits and borrowed from other banks.
  • The other banks were in essence another
  • When the credit dried up, the other banks needed
    the money (became impatient).
  • Northern Rock couldnt continue to borrow.
  • They had to borrow from the lender of last

  • There are a limited number of homes around a
  • The owners of the homes only sometimes go there
    for a few days. They only know if they can go
    last minute.
  • When they dont go, they rent them out. Say that
    they stay there only 1/5 the time and there is 3
    non-owners for every owner during a summer.
  • The owners are indifferent to staying at their
    home or someone elses home.
  • Thus, the owners are not too worried about
    renting out their home since they can always rent
    someone elses home.

Lake Analogy
  • Suddenly, a rumour spreads that it will be hard
    to rent.
  • The owners want to stay very much when they are
    free and take their homes off the market.
  • Since all the owners do so, there is no rental
    market and it is self-fulfilling.

Northern Rock Bank Run
  • Depositors now started to run.
  • Was it rational for shareholders to run as well?
  • Not enough deposit insurance.
  • It also wasnt clear how much lending was to
    Northern Rock.
  • It isnt clear how good their loans are.

What should the Bank of England do?
Should Mervyn King act?
  • Questions
  • Was there a risk of contagion.
  • Was it a solvency problem or a liquidity problem?
  • Would it cost tax-payers?
  • Does this set a bad example?
  • Actions Cut Rate, Lend, Organize a bailout
  • Future
  • Rewrite the deposit insurance?

Other applications
  • Farepak.
  • People saved during the year and got coupons at
    end worth their savings.
  • Company used next years money to pay for this
    years coupons.
  • Defined-Benefit Pension schemes/Social Security.
  • Young pay for old.
  • Usually mandatory to stop runs.

What we learned
  • Theoretical Model of Bank Runs.
  • That these may actually happen (experiment).
  • Possible solutions to the problem.
  • The Moral Hazard problem.
  • A bit about the current crisis.

  • Take the DD model with L.5 and R2. Let us say
    that deposits are insured up to fraction f. For
    what values of f is there only one equilibrium
    and what values are there two equilibria? (Early
    withdrawers are guaranteed to get 1f and late
    get 2f.)
  • How would you modify our classroom experiment to
    test different deposit insurance schemes? Under
    what parameters do you think we will get a bank
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