# New York University Money and Banking Worksheet

Description

Problem Set 1
Due June 2nd, 2022 at 11.59 pm on Gradescope
1. Suppose an economy has maintained a constant zero-rate of money
growth, µL = 0 as long as anyone can remember (…Mt−3 = Mt−2 = Mt−1 =
M̄ ). As a result, they have never experienced inflation. Assume that the current
price level, Pt−1 = 1, output is fixed at Ȳ every period, the real interest rate is
fixed at r̄, and velocity is a function of the nominal interest rate:
vt = 1 + it
(a) Suppose households have adaptive inflation expectations of the following
form: Et [πt+1 ] = 12 πt−1 + 12 πt−2 . Write inflation today, 1 + πt = Pt /Pt−1 as a
function of past inflation.
1
1
t
Solution: M
Pt = Ȳ 1+it = 1+r̄+Et [πt+1 ]
t 1+r̄+Et [πt+1 ]
t
= MMt−1
Therefore, we can write, 1 + πt = PPt−1
1+r̄+Et−1 [πt ]
r̄+ 1 π
+1π
2 t−1
2 t−2
t
Therefore, 1 + πt = MMt−1
r̄+ 1 π
+1π
2
t−2
t−3
2
(b) All of a sudden, the government finds itself unable to pay its debts or
raise taxes. It decides to print new money to obtain Yg

L1+γ
L1+γ
log(c1 ) − ψ 1
+ β log(c2 ) − ψ 2
1+γ
1+γ
The household’s lifetime budget constraint is:
P1 c1 (1 + i) + P2 c2 = W1 L1 (1 + i) + W2 L2
(a) Set up the household’s Lagrangian and find their inter-temporal (Euler)
equations and their intra-temporal (labor supply) conditions.
Solutions: The Lagrangian is given by:

L1+γ
L1+γ
+ β log(c2 ) − ψ 2
+
L = log(c1 ) − ψ 1
1+γ
1+γ

λ W1 L1 (1 + i) + W2 L2 − P1 c1 (1 + i) − P2 c2
The Euler equation is:
1 P1
1
=
β(1 + i)
c1
c2 P2
The intra-temporal condition is:
ψLγt =
2
1 Wt
ct Pt
(b) There is no net-exports (the economy is closed), no government spending,
and no capital. Therefore what is Yt equal to? Use this an the fact that
Yt = F (Lt ) = Lt to solve for wages as a function of output, Yt .
Solution: ct = Yt and therefore Wt = ψYt1+γ
t
(c) Use (b) to solve for ∂W
∂Yt and give intuition for your expression.
γ
t
Solution: ∂W
∂Yt = ψγYt
(d) As γ gets very close to zero, do wages become more responsive or less
responsive to output? HINT: Plug γ = 0 into the expression from (c).
Solution: Wages become much less sensitive.
(e) Recall that the Phillips Curve is given by:
πt = β1 (Yt − Ȳ ) + β2 (E[πt+1 ]) + et
Suppose γ was very close to zero. Would we expect β1 to be large or small?
Explain intuitively.
Solution: Inflation occurs when the output gap increases because
firms have to pay higher wages to their employees in order to satisfy
the new higher demand and they pass these higher costs onto their
customers. If the amount they had to increase wages by less, β1 would
decrease.
3. This question is about alternate theories of the so called ‘flattening’ of the
Phillips curve. To answer this question, use the following form of the Phillips
Curve: πt = β1 (ut − ū) + β2 Et [πt+1 ] + vt
Where ut is unemployment in the United States. A flattening refers to the
coefficient β1 getting smaller.
(a) What theory did Jorgensen and Lansing (2019) offer for the flattening of
the Phillips of the curve (pretend you’re explaining it to a journalist)?
Solution:
(b) Suppose firms are employing more and more workers from abroad. Therefore, their marginal costs are made up of both domestic wages and international
wages. How might this fact provide an alternative/complementary explanation
for the flattening of the Phillips curve?
3
Problem Set 2
Due June 9th, 2022 at 11.59 pm on Gradescope
(a) Why can we think of open market operations as money creation?
(b) What is the difference between borrowed and non-borrowed reserves?
(c) Suppose a crisis in the banking sector shook consumer confidence in banks.
How might that affect the money multiplier? Would this affect the ability of
the Fed to change the total money supply? Explain.
2. Consider the market for inter-bank reserves. Suppose the supply curve of
non-borrowed reserves is 100. The supply of borrowed reserves = 50*(FF-DR).
Let DR = .5. The demand for borrowed reserves is 150-100*FF.
(a) Draw the supply and demand curves for inter-bank reserves. What is the
equilibrium federal funds rate?
(b) Explain the upward sloping relationship between the federal funds ratediscount rate spread (FF-DR) and borrowed reserves.
(c) If the Fed wants to raise the federal funds rate, how should it change the
supply of non-borrowed reserves. Demonstrate on a graph.
(d) If people suddenly stopped using paper currency (cash) in transactions, how
would that affect the demand curve?
(e) If there was better information processing so banks could predict their deposit needs better, what would that do to the demand curve? Demonstrate on
(f) Can the Fed set any interest rate it wants now? How might paying interest
on reserves help? Demonstrate on your graph.
3. Suppose per-period utility over consumption and labor is given by:
u(ct , Lt ) =
c1−σ
L1+γ
t
− t
1−σ 1+γ
However, now there are three periods instead of two. Assume the household’s
labor income = Lt Wt and that they have access to a bond, b that pays i every
period. Note that β2 does not necessarily equal β3 .
1
(a) What is the household’s new lifetime budget constraint?
(b) Solve the household’s problem to get their 2 inter-temporal (Euler) conditions and 3 intra-temporal (labor supply) conditions.
1
W1
(c) Let L∗1 = (c∗σ
= Y1∗ = c∗1 be the initial level of labor, output, and
1 P1 )
consumption. Suppose β2 increases. If nominal wages are downwardly rigid
(they can’t fall), what happens to P1 ? Why? Holding P2 , c2 , and i constant,
what happens to c1 ? Call the new level of consumption, c′1 . Is c′1 less than,
equal to, or greater than c∗1 ?
(d) Given c′1 and the same W1 , do workers want to work less? How much would
they be willing to work? That is, what is L′1 as a function of c′1 and W1 ? Is it
greater or less than L∗1 ?
(e) What is the definition of potential output? Is output above or below potential output now? Explain.
(f) If the Federal Reserve is following a Taylor rule, how should they respond
to this shock?
2
Problem Set 2
Due June 13th, 2022 at 11.59 pm on Gradescope
(a) Why can we think of open market operations as money creation?
Solution: The Fed must create new electronic money in order to
buy assets. Open market operations is the way in which this new
money enters the economy.
(b) What is the difference between borrowed and non-borrowed reserves?
Solution: Borrowed reserves are borrowed from the Fed at the
Discount Window whereas non-borrowed reserves got their via open
market operations.
(c) Suppose a crisis in the banking sector shook consumer confidence in banks.
How might that affect the money multiplier? Would this affect the ability of
the Fed to change the total money supply? Explain.
Solution: This might increase the amount of cash households want
to hold, increasing c/d. This would decrease the money multiplier but
leave the ability of the Fed to control the money supply unchanged.
2. Consider the market for inter-bank reserves. Suppose the supply curve of
non-borrowed reserves is 100. The supply of borrowed reserves = 50*(FF-DR).
Let DR = .5. The demand for borrowed reserves is 150-100*FF.
(a) Draw the supply and demand curves for inter-bank reserves. What is the
equilibrium federal funds rate?
1
Total supply = 100 + 50(FF-.5). Demand = 150-100*FF. Setting
total reserve supply = total reserve demand gives a FF rate of .5.
(b) Explain the upward sloping relationship between the federal funds ratediscount rate spread (FF-DR) and borrowed reserves.
Solution: The stigma surrounding the discount window means that
banks require a spread over the discount rate to induce them to perform this arbitrage and borrow from the Fed to lend out reserves to
other banks.
(c) If the Fed wants to raise the federal funds rate, how should it change the
supply of non-borrowed reserves. Demonstrate on a graph.
(d) If people suddenly stopped using paper currency (cash) in transactions, how
would that affect the demand curve?
It would have no effect on the demand curve.
(e) If there was better information processing so banks could predict their deposit needs better, what would that do to the demand curve? Demonstrate on
(see below)
(f) Can the Fed set any interest rate it wants now? How might paying interest
on reserves help? Demonstrate on your graph.
The Fed will find it difficult to set any interest rate it wants because the demand curve has become so interest-rate inelastic. Paying
2
interest on reserves will set an interest floor on the supply curve, below which banks will have no incentive to lend.
3. Suppose per-period utility over consumption and labor is given by:
u(ct , Lt ) =
c1−σ
L1+γ
t
− t
1−σ 1+γ
However, now there are three periods instead of two. Assume the household’s
labor income = Lt Wt and that they have access to a bond, b that pays i every
period. Note that β2 does not necessarily equal β3 .
(a) What is the household’s new lifetime budget constraint?
Solution: The lifetime budget constraint is given by:
P1 c 1 +
P2 c 2
P3 c3
L 2 W2
L3 W3
+
= L 1 W1 +
+
1 + i2
(1 + i2 )(1 + i3 )
1 + i2
(1 + i2 )(1 + i3 )
(b) Solve the household’s problem to get their 2 inter-temporal (Euler) conditions and 3 intra-temporal (labor supply) conditions.
Solution: The lagrangian is given by:
1−σ

1−σ

c1−σ
L1+γ
c2
L1+γ
c3
L1+γ
1
1
2
3
L=

+ β2

+ β3

1−σ 1+γ
1−σ 1+γ
1−σ 1+γ

L2 W2
L3 W3
P2 c2
P3 c 3
+λ L1 W1 +
+
− P1 c1 −

1 + i2
(1 + i2 )(1 + i3 )
1 + i2
(1 + i2 )(1 + i3 )
3
Taking the derivative with respect to c1 , c2 , C3 , L1 , L2 , L3 and using
λ to combine equations gives:
W1
= Lγ1
P1
W2
cσ2
= Lγ2
P2
W3
cσ3
= Lγ3
P3
cσ1
P1
(1 + i2 )c−σ
2
P2
P2
(1 + i3 )c−σ
c−σ
3
2 = β3
P3
c−σ
1 = β2
(1)
(2)
(3)
(4)
(5)
1
W1 γ
= Y1∗ = c∗1 be the initial level of labor, output, and
(c) Let L∗1 = (c−∗σ
1
P1 )
consumption. Suppose β2 increases. If nominal wages are downwardly rigid
(they can’t fall), what happens to P1 ? Why? Holding P2 , c2 , and i constant,
what happens to c1 ? Call the new level of consumption, c′1 . Is c′1 less than,
equal to, or greater than c∗1 ?
Solution: If W2 can’t fall, then prices can’t fall either, so P1 stays
constant. Therefore, using equation (4) we see that c∗1 > c′1 .
(d) Given c′1 and the same W1 , do workers want to work less? How much would
they be willing to work? That is, what is L′1 as a function of c′1 and W1 ? Is it
greater or less than L∗1 ?
Using equation (1) we can see that when W1 is the same and c′1
goes down then L′1 > L∗1 .
(e) What is the definition of potential output? Is output above or below potential output now? Explain.
Potential output is the level of output that an economy can achieve
without prices rising (inflation). In this model, prices rise because
wages rise, so potential output is the level of output we could achieve
without having to raise wages. We know that at W1 , workers would be
willing to produce Y1∗ = L∗1 > L′1 . Therefore, we could increase output
without raising wages, so we’re below potential output.
(f) If the Federal Reserve is following a Taylor rule, how should they respond
to this shock?
There has been no inflation or deflation, but there has been a decrease in the output gap. Therefore they should decrease the interest
rate.
4
Unit 3: Financial Crises
Wendy Morrison
June, 14 2022
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
1 / 59
Introduction
In Unit 2, we saw how the banking system is key for the transmission of monetary
policy.
In Unit 5, we’ll explore how the financial system solves key information frictions
and helps allocate resources effectively (a bit on that today as well, banks will
perform an insurance function).
History is full of examples of the financial system malfunctioning in serious way,
wreaking havoc on the ‘real’ economy.
In this Unit, we’ll consider both traditional and more modern explanations.
1
In what way are financial crises ‘rational’ economic responses?
2
What if anything can policy makers do?
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
2 / 59
Outline
1
Bank Runs
2
The 2008 Crisis
3
Systemic Risk
4
Policy Options
5
The COVID Crisis
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Unit 3: Financial Crises
June, 14 2022
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Bank Runs
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
4 / 59
Bank Runs: Background
A key feature of the American banking system (and that of many other countries)
that we’ve alluded to is maturity mismatch.
That is, banks take in demand deposits which they allow to be withdrawn at any
time whereas when they loan out these funds, these loans won’t mature for
months or years.
What happens when depositors all of a sudden withdraw their deposits before the
loans have matured? (i.e. a bank run)
In 1983, Diamond and Dybvig (DD) came up with a bank run model that helps
think through why bank runs happen and what policies help prevent them.
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
5 / 59
Diamond and Dybvig (1983)
Model Features:
3 periods: t=0,1,2
Many identical depositors, each of whom receive an endowment of output,
y=1 (not modeling production here) which they put in the bank
The bank can either hold the endowments as reserves (gross return = 1), or
lend it out to a firm. If they lend it out at t=0, they must wait until t=2 to
Loans cut short before t=2 earn a gross return of 1
Heterogeneous liquidity needs that are unknown initially: type B depositors
won’t need their cash until t=2 but type A depositors will get hit with a
shock a need their funds at t=1.
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
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Depositors
Specifically, there will be θ Type A depositors and (1 − θ) Type B depositors.
UA (c1 ) = lnc1 and UB (c1 , c2 ) = ρln(c1 + c2 )
Where 0 1
Depositors (and the bank) don’t know their type until t=1 (think of this as a
consumption shock)
The expected utility of a depositor at time = 0 is given by:
E (U) = θlnc1 + (1 − θ)ρln(c1 + c2 )
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
7 / 59
Why have banks?
One big insight from the DD model is that banks (at least in normal times) are
able to improve the welfare of depositors compared to financial autarchy.
Autarchy: The case where individual households are not able to pool their
resources together to mutually insure against shocks. Each household is just
“going it alone”.
How do we see that? That is, how do we make determinations about welfare in
economics?
Use the ‘social planner’ to figure out the “first best”. That is, how would
someone who had perfect control of all the resources divide them up if she
aimed to maximize the sum of everyone’s expected utility?
Show that autarchy falls short of this ideal, but that banks achieve it!
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
8 / 59
Autarchy
If households are all ‘going it alone’, what will they each do?
Each will take their endowment and find a firm to lend to in period t=0.
The lucky type B’s will get to wait until t=2 and get their return, R, while the
unlucky type A’s will have to pull out and end up with a gross return of 1.
Will type B’s have any c1 ? Will type A’s have any c2 ?
So what’s the autarchy EU?
EU = θln(1) + (1 − θ)ρln(R)
Is this as good as the social planner could do? I.e. is this the ‘first best’ ?
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
9 / 59
The Social Planner
It’s important to note that the social planner has access to the same resources as
the households and must take their preferences as given.
She isn’t able to prevent type A household’s from experiencing a shock or change
the t=1 return from 1 to R.
However, she can pool the resources of both types and divide them as she sees fit.
In particular, she can invest the entire endowment of both households and take
more than θ out at t=1 to give to the type A’s experiencing a shock.
Ex-post type B’s will be worse off, but ex-ante expected utility may be higher.
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
10 / 59
The Planner’s Solution
Let cA be the consumption offered to type-A households in period 1. This means
the planner has to withdraw θcA from the loans, leaving only R(1 − θcA ) divided
between the remaining 1-θ households.
The planner problem is:
max θln(cA ) + (1 − θ)ρln(R(1 − cA θ)/(1 − θ))
cA
How do we solve? dcdA = cθA − θ(1−θ)ρ
1−θcA = 0 →
cA∗ =
1
>1
θ + (1 − θ)ρ
ρR
How do we find cB∗ ? cB∗ = R(1 − θcA )/(1 − θ) = θ+(1−θ)ρ
0 (R>1).
Suppose the bank in our economy offers a gross return of cA∗ to depositors who
withdraw their funds at t=1 and a gross return of cB∗ at t=2.
Key insight: if everyone tried to withdraw funds early at t=1, the return
promised (cA ) is greater than 1, but the project/loan hasn’t matured yet. I.e. the
bank only has 1 unit of output per each depositor, but owes cA∗ > 1 to each
depositor.
If this happens, someone isn’t getting their money back…
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
14 / 59
‘Rational’ Depositor Behavior
We know that type-A depositors will want to withdraw at t=1 to meet their
liquidity needs.
From the point of view of an individual type-B depositor, what is the “rational”
thing to do at t=1?
The insight of the DD model is that, what’s rational actually depends on the
depositor’s belief about what other depositors are going to do?
In other words, in deciding whether to withdraw your deposits at t=1 or not,
type-B depositors are playing a ‘game’ (in the formal game theory sense) with
other depositors.
We can use the concept of a Nash Equilibrium to figure out each depositor’s
optimal strategy.
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
15 / 59
The Game
Let’s set up this game. Let W stand for ‘withdraw early’ and D stand for ‘don’t
withdraw early’. These are the two ‘strategies’.
Let’s find a type-B household’s payoff [pi stand for ‘payoff] for each strategy
s ∈ (W , D), given the strategy of all the other type B’s: pi (W |Sj̸=i ) and
pi (D|Sj̸=i )
For simplicity, we assume each household is so small, that even if the bank only
keeps cA∗ θ in reserves, paying out to one additional type-B household won’t
matter.
cA∗ θ ≈ cA∗ (θ + ϵ) or
cA∗ θ
≈ cA∗
θ+ϵ
So if they’re the only type-B household to withdraw, they’ll get about cA∗ .
That is, pi (W |Sj̸=i = D) ≈ cA∗
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
16 / 59
The Game
What will I get if only type-A’s withdraw and I just wait? I’ll get cB∗ !
pi (D|Sj̸=i = D) = cB∗
What about if everyone tries to withdraw but I don’t?
The bank must legally honor it’s agreement to try and give out cA∗ to anyone who
tries to withdraw at t=1. To do this, they must liquidate their investments in
order to meet the demand for liquidity, leaving nothing for period 2.
pi (D|Sj̸=i = W ) = 0
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
17 / 59
The Game
If I try to withdraw at t=1 along with everyone else, am I guaranteed to get cA∗ ?
No! Remember, cA∗ > 1 so there isn’t enough to go around. Let γ be the fraction
of households who are early enough to actually get cA∗ . Then cA∗ γ = 1 → γ = c1∗
A
So my expected utility is: γρln(cA∗ ) + (1 − γ)ρln(0) = pi (W |Si̸=j = W )
But I still prefer that to getting nothing with certainty.
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
18 / 59
Symmetric Nash Equilibrium
How do we find the symmetric Nash Equilibrium? If all the household are
identical, we need to find the intersection of best response functions (i.e.
when my best response to X is X)
First let’s write down the ‘best-response’ of the individual depositor given the
strategies of the other depositors:
ui (cB∗ ) > ui (cA∗ ) → the best response to Sj̸=i = D is D (Don’t withdraw)
γρln(cA∗ ) + (1 − γ)ρln(0) > ρln(0) → the best response to Sj = W is W
(Withdraw)
Therefore, none of the type-B’s withdrawing is a NE but so is all of the type-B’s
withdrawing. We call the latter a run on the bank.
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
19 / 59
Limits of the DD Model
The DD model tells us that a bank run can be thought of as economically
rational (a NE).
Question: Does this model successfully explain bank runs? Why or why not?
Yes, in the sense that it explains runs as a rational response to the belief
that everyone else is also running
No, in the sense that it doesn’t say where these beliefs come from or how
likely each NE is.
What might set off the ‘bank panic’ NE?
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
20 / 59
Bank Panic 1930-1
One possibility is that solvency issues in one (important) institution could
generate suspicion of other solvent institutions when information is
imperfect/asymmetric (bank managers know things about bank that depositors
don’t).
Question: What’s the difference between solvency and liquidity?
The value of an insolvent institution’s assets are not high enough to cover
its liabilities
An solvent but illiquid institution’s assets cover its liabilities, but it may not
be able to sell/liquidate these assets in time to meet short-term liabilities
In 1930, the conglomerate Caldwell and Co. became insolvent after losing a
substantial amount of money in the 1929 stock market crash. The banks it owned
failed as a result.
As a depositor in TN and KY at the time, you have no idea how exposed your
bank might be to stock market losses…so you might run even if your bank was
perfectly solvent.
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
21 / 59
Solutions
The 1930-1 bank panic turned nation wide as Newspapers reported on more and
more runs on more and more banks.
In response to this panic (which was a major contributor to the Great
Depression), Congress passed the Glass-Steagall Act in 1933 that among other
things created the Federal Deposit Insurance Corporation (FDIC) which
stated that the Federal Government would insure deposits up to \$2500 for FDIC
member (commercial) banks.
This limit has been raised several times and is currently \$250,000.
How does deposit insurance change the depositor’s best responses?
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
22 / 59
Deposit Insurance
Deposit insurance essentially equalizes the payoffs in the ‘normal’ and ‘run’ cases.
The bank owes you cA∗ if you withdraw at t=1 and cB∗ if you withdraw at t=2. If
it can’t meet these obligations because of a run, the government will step in and
ensure you get the promised pay off.
I.e. now pi (W |Sj̸=i = W ) = cA∗ and pi (D|Sj̸=i = W ) = cB∗
Is waiting and not withdrawing (strategy D) a dominant strategy? How do we
know? It is because it delivers the highest payoff (cB∗ > cA∗ ), no matter what
other depositors do.
Therefore, it will always be rational for type-B depositors to wait until t=2 and
not to run, no matter what!
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
23 / 59
Modern runs
If we have deposit insurance, are we safe? Maybe not.
The FDIC coverage applies only to FDIC member commercial banks. In
particular, it does not apply to any ‘investment product’ including money market
mutual funds.
Money Market Mutual Funds (MMF): a financial vehicle that pools investor
funds and buys very safe, short-term, ‘high-quality’ fixed income assets (e.g.
treasury bonds). They’re often considered a safe, slightly higher return alternative
to bank deposits.
In 2008, one of the most prominent MMF (the Reserve Primary Fund) had
invested in super short term loans to Lehman Brothers.
Even though only a small fraction was loaned to Lehman, investors got nervous.
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
24 / 59
MMF Runs
When Lehman went down (more on that shortly), the Reserve Primary Fund was
probably still solvent, but the news was enough to trigger a bank run Nash
Equilibrium.
Instead of withdrawing deposits, a run on a MMF involves investors ‘redeeming
their shares’ all at once.
Just as in 1931, news of a run on one (albeit very prominent) MMF – in the
context of imperfect/asymmetric information – spooked other MMF investors,
triggering runs throughout the MMF industry.
In 2008 (and again in 2020) the Fed stepped and provided emergency lending to
MMF in response.Is this just implicit insurance?
Do you think there should be ‘official’ insurance for institutions other than
deposit taking banks?
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
25 / 59
The 2008 Crisis
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
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How it started
In the decade and a half leading up to the GFC, there was an explosion in
borrowing, especially home mortgage borrowing.
Possible culprits for increased mortgage borrowing:
1
Monetary easing keeping rates low
2
A glut of savings from wealthy and abroad pushing rates down
3
Financial innovations (ARM, MBS, CDO)
Cheaper mortgages mean it’s easier to borrow to buy a house. What will that do
to house prices? House prices exploded.
Note* these slides in part rely on “The Great Recession and Its Aftermath” by John Weinberg, Federal Reserve Bank of
Richmond
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Unit 3: Financial Crises
June, 14 2022
27 / 59
House Prices
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
28 / 59
Usually, households with poor credit would have a hard time getting a mortgage.
Sub-prime lending was virtually non-existent before 2000 (Bailey et al. 2008)
Adjustable rate mortgages (ARMs) came on the scene with low ‘teaser’ rates.
After several years however, the rates become adjustable, meaning based on
market interest rates (like the Fed Funds rate). If market rates were to increase
(spoiler!), the interest these borrowers owe all goes up at once.
In certain cases, borrowers were told they could refinance before the rates went
up based on the value of their home increasing. But that required house prices to
keep going up…
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Unit 3: Financial Crises
June, 14 2022
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Mortgage Backed Securities (MBS)
Low teaser rates may have been enough to get sub-prime borrowers to take out a
mortgage, but why did anyone lend to these risky borrowers?
Mortgage-Backed Securities (MBS): Bonds that are secured or ‘backed’ by a
pool of mortgages (the mortgage loans themselves are the collateral).
Homeowners make their mortgage payments every month, and a portion of these
payments are passed through as payments to the MBS holder.
What’s the logic here? Why would anyone buy an MBS ‘backed’ by sub-prime
mortgages?
The idea was that even though individual sub-prime borrowers each had a high
probability of default, their risk was uncorrelated (they were unlikely to all default
at the same time), so the pool of mortgages was less risky/more attractive.
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Unit 3: Financial Crises
June, 14 2022
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Collateralized Debt Obligations (CDO)
Collateralized Debt Obligations (CDO): A pool of debt securities including
MBS (so yes, a pool of pools) separated out into ‘tranches’ that simply denote
who gets paid first.
If you buy the best (but also lowest return) tranch, you’re first in line to get paid.
This pushes essentially all the risk down to the lower tranches.
Because of the complexity (and novelty) of both sub-prime backed MBS and
CDO, many argue that the riskiness of these securities was not properly
understood.
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Unit 3: Financial Crises
June, 14 2022
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Who held MBSs and CDOs?
Several prominent, high profile investment banks were particularly exposed to
MBSs and CDOs:
1
Lehman Brothers
2
Bear Stearns
3
Citigroup
What do we mean by ‘exposed to’ a certain asset? Holding a large quantity of
that asset or being directly connected to institutions that do.
1
The insurance company AIG insured many of these heavily exposed
institutions
2
Certain money market mutual funds provided lots of short term lending to
these institutions (asset-backed commercial paper)
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Unit 3: Financial Crises
June, 14 2022
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Beginning of the Crisis
Home prices peaked in early 2007, and began to fall. Ultimately, home prices
would fall by over a fifth!
This created a wave of uncertainty about mortgage related products and the
institutions that held them.
There was a run on the money market mutual funds that provided short-term
lending to these institutions.
Ultimately:
1
Bear Sterns was sold to JP Morgan Chase, facilitated by the Fed
2
Lehman Brothers went bankrupt
3
AIG, Bank of America, and Citigroup all sought government support
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Unit 3: Financial Crises
June, 14 2022
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Fed Reaction (Lender of Last Resort)
In addition to dropping interest rates to essentially 0% and LSAP (large scale
asset purchases), the Fed created several new emergency lending facilities to
support the non-bank financial system.
These included (not limited to!):
1
Asset-Backed Commercial Paper Money Market Mutual Fund Liquidity
Facility (AMLF)
2
Term Securities Lending Facility (TSLF): a loan facility for primary dealers
3
Primary Dealer Credit Facility (PDCF)
What do they all have in common? They support financial institutions.
Despite these efforts, the unemployment rate grew from 5% to 10%, and US
GDP fell by 4.3%
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Unit 3: Financial Crises
June, 14 2022
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Why was the broader economy affected?
This is not a straightforward question. It’s not immediately obvious why banks
that held few mortgage related securities or firms unrelated to the housing sector
would suffer when the price of these securities went down.
Sub-prime mortgages were only a small portion of the total mortgage market and
financial system.
”At this juncture [March 28, 2007], however, the impact on the broader economy
and financial markets of the problems in the subprime market seems likely to be
contained…. Thus far, the weakness in housing and in some parts of
manufacturing does not appear to have spilled over to any significant extent to
other sectors of the economy.” -Ben Bernanke (Fed Chair)
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Unit 3: Financial Crises
June, 14 2022
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Systemic Risk
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Unit 3: Financial Crises
June, 14 2022
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What do we mean by systemic risk?
A system/economy has systemic risk when agents in the economy have
incentives to take on “too-much” risk, meaning the social costs outweigh the
social benefits. The presence of any risk on its own is not enough to be
problematic.
We’ll study 2 broad categories/sources of systemic risk:
1
Externalities: the actions of one agent affecting the outcomes/prices facing
another agent in a way that they don’t take into account when making
decisions

2
1
Fire-sales
Implicit guarantees: agents taking on levels of risk because they believe that
they will be made whole if anything goes wrong. 1
K. B. Athreya: Systemic Risk and the Pursuit of Efficiency
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Unit 3: Financial Crises
June, 14 2022
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Leverage
A financial institution’s leverage ratio refers to it’s total assets relative to bank
capital (equity)
Why is it important to keep a certain leverage ratio? (Why not finance yourself
entirely with debt?)
1
If their assets fall in value, they risk becoming insolvent and defaulting on
debt.
2
Lenders will only lend if leverage ratios are above a certain level.
Example: What would happen if the value of this bank’s assets fell by 60%?
Assets
100
Wendy Morrison
Liabilities
Debt: 50
Equity: 50
Unit 3: Financial Crises
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Bank Leverage Before the Crisis
Source: Tobias Adrian, Michael J. Fleming, and Or Shachar. Market Liquidity after the Financial Crisis. 2017.
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Leverage Ratios: An Example
Suppose there are two big banks in the economy, as well as a bunch of other
non-bank financial actors who buy and sell assets. Assume banks prefer a 2-1
leverage ratio (in reality it’s much higher!)
Suppose Bank 1 only holds Asset A (our ‘safe’ asset). Bank 2 holds some Asset A
as well as some Asset B (MBS).
Bank 1
Assets
Asset A: 10 x \$10
Liabilities
Debt: 50
Equity: 50
Bank 2
Assets
Asset A: 6 x \$10
Asset B (MBS): 4 x \$10
Liabilities
Debt: 50
Equity: 50
How do we see that their leverage ratio is 2/1?
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Unit 3: Financial Crises
June, 14 2022
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Shock to Bank 2
Now suppose that the price of MBS falls to \$0. Is Bank 2’s leverage ratio still
2/1? What is it?
Bank 2
Assets
Asset A: 6 x \$10
Asset B (MBS): 4 x \$0
Liabilities
Debt: 50
Equity: 10
What does bank 2 have to do to maintain it’s leverage ratio? Sell some assets in
order to restore the required leverage ratio. How do we figure out how much
they’ll have to sell?
Asset Anew = 60-X*10 and Debtnew = 50-X*10 and Equitynew = Asset Anew Debtnew = 10 … so if they sell 4 units of Asset A, the new total assets would be
20, debt would be 10 and equity would be 10, restoring their preferred 2/1 ratio!
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Unit 3: Financial Crises
June, 14 2022
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Fire Sales or Loss Spirals
Suppose Bank 2 is not unique and is among several very large institutions forced
to sell off assets. What happens to the price of Asset A if many institutions are
forced to sell their Asset A holdings?
If the supply of Asset A increases, this will push down the price. Suppose the
price of Asset A falls by \$1. What does this do to Bank 1’s balance sheet? What
is their new leverage ratio?
Bank 1
Assets
Asset A: 10 x \$9
Liabilities
Debt: 50
Equity: 40
9/4 > 2 … so they’ll have to do what? And the cycle continues …
This phenomenon is known as a fire sale or a loss spiral (Brunnermeier, 2009).
You simply have to own some similar assets as failing institutions for their failure
to spill over onto your balance sheet.
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Unit 3: Financial Crises
June, 14 2022
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Margin Spirals
An additional pressure from lenders exacerbates this spiral: when lenders to Bank
2 realize that many of the assets they’re holding are worthless, they’ll demand a
smaller leverage ratio in order to keep lending. Brunnermeier (2009) called this a
margin spiral.
If Bank 2’s MBS fell to \$0 and it’s debt holders demanded a leverage ratio of 1.5,
how much would they have to sell off?
Bank 2
Assets
Asset A: 6 x \$10
Asset B (MBS): 4 x \$0
Liabilities
Debt: 50
Equity: 10
Asset Anew = 60-X*10 = 1.5*Equity = 15, so they’d have to sell off 4.5 units of
Asset A. This would put even more pressure on the price of Asset A.
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Unit 3: Financial Crises
June, 14 2022
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In the years leading up to the financial crisis, many non-financial corporations
turned to money market mutual funds for short term financing, issuing
commercial paper to carry out their operations.
Corporations found that selling commercial paper to MMF was cheaper and easier
than bank loans (Schmidt et al. 2016).
Even though the commercial paper of financial institutions that were heavily
exposed to mortgage-related securities made up only a tiny fraction of the overall
assets held by major MMF like the Reserve Primary Fund, the mortgage crisis
was enough to set off a run on the fund.
This meant that any corporation that simply shared the same method of
short-term financing as a mortgage-exposed institution (like Lehman Brothers)
was indirectly exposed.
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Unit 3: Financial Crises
June, 14 2022
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Externalities
Remember we defined systemic risk as the presence of incentives to take on an
inefficient amount of risk, meaning expected social costs > expected social
benefits.
So far, we’ve shown how the phenomenon of fire sales (loss spirals and margin
spirals) and in-direct linkages mean that the choices of one financial institution
spill over into consequences for other financial institutions.
That is, the expected social costs are greater than just the expected private
costs to the failing financial institutions.
However, a bank takes on a risk (makes a risky loan, buys a risky asset) if it
believes the expected private benefit > expected private costs (i.e. expected
gains outweigh opportunity cost and expected losses).
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Unit 3: Financial Crises
June, 14 2022
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Implicit Guarantees
If a bank takes on any risk, is that sufficient to say there is systemic risk?
No! If they (their employees, shareholders, etc) benefit from all the profits, BUT
have to suffer the consequences if something goes wrong, and still thinking taking
on a risk is ‘worth it’, then expected private costs = expected social costs =
expected social benefits.
How does this formula change if they believe they’ll be ‘bailed out’ in the event of
losses?
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Unit 3: Financial Crises
June, 14 2022
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Policy Options
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
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Basel
The Basel Committee is an international regulatory body established in 1988
tasked with setting standards for each member country’s financial institutions.
Following the financial crisis, the committee passed its third Accord – called Basel
III, which was meant to deal with specific concerns related to systemic risk.
In particular, Basel III instituted 3 ‘pillars’ of additional regulation:
1
Supervision (e.g. stress testing)
2
3
Capital requirements (we’ll focus on two)

Minimum Leverage Ratios
Risk-weighted capital requirements
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Unit 3: Financial Crises
June, 14 2022
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Leverage Ratios
Remember that a leverage ratio measures the amount of leverage relative to an
institution’s total assets.
Basel III forces financial institutions to hold no less than 3% of their assets as
‘Tier-1’ capital (still seems pretty low!)
How might lower leverage help mitigate some systemic risk?
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Unit 3: Financial Crises
June, 14 2022
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Effect of leverage ratios
What would have happened in our example if Bank 2 had been forced to hold less
leverage (debt) and more equity?
Bank 2
Assets
Asset A: 6 x \$10
Asset B (MBS): 4 x \$10
Liabilities
Debt: 30
Equity: 70
Remember that before the leverage ratio was 2. What is it now? 100/70≈1.42.
If the price of MBS fell to 0, what would their equity be? 70 – 30 = 40. Are they
respecting the leverage ratio of 1.42?
What will they have to do maintain their legal leverage ratio?
(60 – X = new assets) / (60-X-(30-X) = equity) 8%
Risk-weighted assets
In our example, this would mean that Bank 1 (who held no MBS) would be
allowed to have more leverage than Bank 2.
The exact formula used to determine riskiness is too ‘in the weeds’ for this class.
However, can anyone think of a problem with determining capital requirements
based on (even a very sophisticated measure of) risk?
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June, 14 2022
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Dodd-Frank Act
Implicit guarantees arise because of ambiguity about what will happen if a
large/important institution runs into trouble.
The 2010 Dodd-Frank Act requires large banks (over \$250 billion in assets) to
submit a resolution plan (a.k.a. a living will, outlining how the bank will be
resolved should they become insolvent.
How does this help address the problem of implicit guarantees?
Does it work? Cetorelli and Traina (2018) offer evidence that banks’ funding costs
go up once the living wills are in place. They argue that this is evidence that the
implicit guarantees have been eliminated (private costs are now higher). Banks’
funders no longer offer low funding costs that implicitly counted on a bailout.
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Unit 3: Financial Crises
June, 14 2022
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The COVID Crisis
Wendy Morrison
Unit 3: Financial Crises
June, 14 2022
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What did the Fed do following the Covid-19 outbreak?
Rough timeline:
2/28: Stock market reports biggest 1 week decline since GR
3/3: Fed lowers target rate by 50 basis points and lowers the (primary) discount
rate to 1.75 percent. What’s the difference?
3/17: Fed sets up several lending ‘facilities’
Commercial paper funding facility (CPFF)
Primary Dealer Credit Facility (PDCF)
Money Market Mutual Fund Liquidity Facility (MMLF on 3/18)
These facilities were largely revived 2008 facilities.
Source: St. Louis Federal Reserve
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June, 14 2022
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CPFF
Coronavirus related panic caused demand for CP to plummet, and many firms
reported having to pay huge premiums and offer extremely short maturities.
Fed is essentially agreeing to act as a lender of last resort. It promises to buy CP
from firms (with certain terms and conditions about the amount, the rates, and
credit standards).
This allows firms to keep issuing/rolling over CP, but also makes buying CP more
attractive to investors.
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Unit 3: Financial Crises
June, 14 2022
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PDCF
Primary dealers are the NY Fed’s primary trading partners/counter-parties.
They’re the banks/financial institutions the Fed enacts monetary policy through.
This facility essentially offers overnight loans to primary dealers in exchange for
collateral. It was created during the 2008 financial crisis.
It’s similar to the discount window, except the DW applies to all depository
institutions, not just primary dealers.
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MMLF
Money market funds invest in very short term debt (like commercial paper!), but
the crisis caused a mass withdrawal from MMFs as investors needed cash.
This facility loans to certain eligible institutions for the express purpose of
investing in these funds.
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What did the Fed do?
Timeline continued:
3/23: Fed announces a new round of measures
Pledges to make asset purchases in whatever quantity needed
Established additional lending facilities to ‘large employers’ and announces
plan to increase credit to small businesses (PPP loans and Main Street
Lending Facility). That is, the Fed lent to non-financial businesses.
They also created direct lending facilities to state and local municipalities
Expanded existing facilities
4/29: FOMC Statement
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June, 14 2022
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Differences between 2008 and 2020
In what ways did the Fed’s response differ this time around?
Did not rely on financial system to pass-through support to non-financial
businesses and local governments. Lent directly themselves.
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