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Practice Questions
Money and Banking
Summer 2022
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 =
MÌ„ ). 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) Why is velocity increasing in the nominal interest rate?
(b) Suppose households have adaptive inflation expectations of the following
form: Et [πt+1 ] = πt−1 Write inflation today, 1 + πt = Pt /Pt−1 as a function of
past inflation.
(c) 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 < Ȳ of real output. Will money creation today (time t) have any affect on inflation expectations? Therefore, will money creation today change velocity today? Will it have an effect on inflation today? (c) Let M̄ = 100, Ȳ = 100, r = 0, and Yg = 50. How much will the government have to print in order to raise Yg of real output? HINT: solve for the new price level, Pnew as a function of M̄ , Ȳ , Yg , and velocity, vt . What is velocity given that past inflation has been 0? 2. Consider a 3-period economy with a household with the following optimality conditions for t = 1,2, and 3: Lt = (c−σ t c−σ = t Wt γ1 ) Pt Pt βt+1 (1 + it )c−σ t+1 Pt+1 1 (a) Suppose σ = γ, Yt = ct and Yt = Lt . Solve for the level of consumption today (c1 ) as a function of the real wage that is consistent with full employment. Call this cF 1. 1 (b) Suppose you expect that c2 = cF 1 and that P1 = P2 . If β = 1.02 , what is the nominal interest rate consistent with full employment? (c) Suppose β increases to 1.02 but all other variables stay the same. Can the Fed achieve full employment? Why or why not? (d) Suppose the Fed lowers i1 to the zero lower bound. Suppose that P1 = 1 σ and cF 1 = 1. What would c2 P2 have to be to achieve full employment today? In this case, do you expect that there would be an output gap in period 2? How would the Fed achieve this? 3. Short answer questions. (a) What is the Taylor rule? How does it help the monetary authority stabilize prices? (b) Consider the following 2 scenarios. (1) Country B used to export goods to country A, but country A has imposed a trade barrier preventing country B’s exports. (2) Country A’s citizens find out that cheese from country B causes obesity. How would these events impact the current exchange rate E = currency B/currency A? (c) Define systemic risk? Is all risk inefficient? 2 Unit 1: Inflation Wendy Morrison May, 24 2022 Wendy Morrison Unit 1: Inflation May, 24 2022 1 / 58 Introduction What is inflation? Inflation is defined as the growth rate of the overall price level. Typically calculated over a geographic region (e.g. within a country). What do we mean by “overall price level”? Is that a straightforward concept? Why or why not? In this section, we’ll abstract away from multiple goods/prices and present a (very simplified!) model with a single good (GDP) and a single price (P). Why start with inflation? “Inflation is always and everywhere a monetary phenomenon” -Milton Friedman Wendy Morrison Unit 1: Inflation May, 24 2022 2 / 58 Outline 1 What causes ‘hyper-inflation’ ? 2 The New Keynesian Model 3 Why was inflation so low from 1990s-2020? 4 Why is inflation so high now? Wendy Morrison Unit 1: Inflation May, 24 2022 3 / 58 What causes ‘hyper-inflation’ ? Wendy Morrison Unit 1: Inflation May, 24 2022 4 / 58 What do we mean by ‘hyper-inflation’ ? Hyper-inflations are brief periods of extremely high inflation. Defined by Cagan (1956) as 50% monthly inflation or higher. In the first half of today’s class, we’ll be using a simplified model of money demand to examine 2 possible explanations for hyper-inflations: 1 Out of control money creation 2 Out of control inflation expectations We’ll end the analysis by considering why these two forces might be endogenous and self-reinforcing. What do we mean by endogenous? Wendy Morrison Unit 1: Inflation May, 24 2022 5 / 58 Historical Examples Hungary in 1946: Daily inflation of over 200% (prices doubling every 15 hours!) after being ordered to pay reparations to the Soviets following WWII. Zimbabwe in 2007-8: Daily inflation of almost 100% (prices doubling every 25 hours) following Socialist land reforms, which led to a decline in production of 50% and exploding government debt which the government attempted to ‘monetize’. Weimer Germany in 1922: Daily inflation of around 20% with prices doubling every 3 or so days. We’ll look at this case a bit more closely. Wendy Morrison Unit 1: Inflation May, 24 2022 6 / 58 Money Demand We’ll start out with a model of ‘money demand’ and solve for the price level via equilibrium in the money market. P = price level Y = real GDP M = Nominal money supply v = velocity = PY/M Velocity refers to the number of times a unit of currency moves through the economy in a transaction. The basic idea is that nominal GDP (P x Y) = M x v. Why must this be true? Remember GDP is a flow variable that measures transactions that occur within a geographic unit within a given period of time. Wendy Morrison Unit 1: Inflation May, 24 2022 7 / 58 Money Demand We’ll start by assuming monetary neutrality. That is, real variables (e.g. real GDP) is unaffected by the money supply. In fact, we’ll assume that Y is exogenous and constant. Why is this an OK assumption when studying a hyper-inflation? Money supply, M, is also exogenous and controlled directly/perfectly by the monetary authority. Is this realistic? We won’t assume anything about P...that’s what we’re trying to explain (changes in P = inflation!) ... but we still need to model velocity, v. How we decide to model v is the main way in which different models/explanations of inflation differ. Wendy Morrison Unit 1: Inflation May, 24 2022 8 / 58 Inflation in our model We get inflation (growth in P) using the money market equilibrium condition: πt+1 = Pt+1 Mt+1 vt+1 = Pt M t vt So inflation in the money demand model can either come from increases in the money supply or increases in velocity. The Quantity Theory of Money assumes that velocity is constant, so changes in M feed directly into changes in P and therefore money growth is the only explanation for growing prices. Changes in velocity will be the way inflation expectations enter this model. Wendy Morrison Unit 1: Inflation May, 24 2022 9 / 58 Where are the firms? Wait...but who actually changes prices in the real economy? What’s actually happening here? This will become much more clear when we study the New-Keynesian model. For now, you can think of a doubling in M or velocity as consumers coming to the firm with double the purchasing power (say, within a single day!) and because the firm can’t meet this new demand, it has no choice but to double it’s prices. Wendy Morrison Unit 1: Inflation May, 24 2022 10 / 58 Nominal interest rates and money demand Velocity is likely not perfectly constant, even in the short run. How might nominal interest rates affect velocity? When nominal interest rates increase, the opportunity cost of holding liquid assets (money) increases. Why? When the opportunity cost of holding money balances goes up, this incentivizes consumers to hold smaller money balances, meaning each unit of money they do hold must work harder (circulate more). So velocity increases. So we can write, vt (it ) Wendy Morrison Unit 1: Inflation May, 24 2022 11 / 58 Recap: nominal interest rate and inflation What is the relationship between the nominal interest rate and inflation expectations? If a lender charges a nominal rate of 4% and inflation ends up being 2%, what real rate are they actually receiving? But lenders don’t know what inflation will be beforehand! So if a lender wants to receive a real rate r, and they expect inflation to be π, what nominal rate should they demand? it+1 = rt+1 + Et [πt+1 ] Therefore, velocity is increasing in Et [πt+1 ] → vt+1 (Et [πt+1 ]) Wendy Morrison Unit 1: Inflation May, 24 2022 12 / 58 Money supply vs. inflation expectations Now we’re ready to consider the two competing explanations for hyper-inflations. 1 + πt+1 = Mt+1 vt+1 (Et+1 [πt+2 ]) Mt vt (Et [πt+1 ]) But how do we model expectations about inflation? Two methods: 1 Adaptive expectations (backward looking, agents use previous periods’ data) 2 Rational expectations (agents use all available information) Wendy Morrison Unit 1: Inflation May, 24 2022 13 / 58 Adaptive expectations Adaptive expectations are relatively easy to understand: Et [πt+1 ] = αt−1 πt−1 + αt−2 πt−2 + ... Where P αt = 1 (i.e. a weighted average of previous periods’ inflation rates) Intuition: People in the economy look to the recent past to form their expectations about inflation. Usually, we think that αt → 0 as t → ∞ Wendy Morrison Unit 1: Inflation May, 24 2022 14 / 58 Rational Expectations Rational Expectations means that your expectations are model consistent (not systematically wrong) in the sense that you take all available information. This does not necessarily imply perfect foresight: i.e. Et [xt+1 ] ̸= xt+1 in every period. Sometimes we think people are genuinely ‘shocked’ or surprised. However, modeling randomness/shocks is difficult. How can we capture the “idea” of a shock without worrying about modeling probability distributions over events? A simple tool we can use is called an ‘MIT shock’ - we write down a ‘deterministic’ or ‘perfect foresight’ model where the (ex ante) probability of a shock is essentially 0...but then a shock occurs! Therefore it makes sense for agents to act as if the shock won’t happen, and only change their behavior once it does. Wendy Morrison Unit 1: Inflation May, 24 2022 15 / 58 Rational vs. Adaptive What does RE get us? Bottom line: It allows us to capture the idea that news about the future can form expectations, not just past experience (adaptive expectations) To see the difference between the two types of expectations, let’s see how they operate in the model of inflation outlined above: Let Mt+1 /Mt = 1 + µt+1 ... the growth in the money supply Suppose the government has been increasing the money supply at a steady (low) rate, µ forever (or, if you like, as long as anyone can remember). Before period t (so for periods, ... t-3, t-2, t-1), the probability of this changing was extremely low (we’ll just say it’s essentially 0). All of a sudden, a (super low probability) change in the money supply occurs! They start printing money faster (µ̃ > µ)
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Rational vs. Adaptive
Because money growth has been steady forever, it makes sense that (in both
models) inflation expectations – and therefore inflation – has just been determined
by money growth for t-1, t-2, t-3 etc… so Ï€t−1 = Ï€t−2 = Ï€t−3 … = µ
Why does this make sense?
1 + πt−1 =
Mt−1 vt−1 (Et−1 [πt ])
=1+µ
Mt−2 vt−2 (Et−2 [πt−1 ])
At time t, the government announces that Mt+1 = (1 + µ̃)Mt , and money will
grow at µ̃ from then on.
Question: What does each model of expectations predict about the path of
inflation?
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Adaptive Expectations
1 + πt =
Mt vt (Et [Ï€t+1 ])
=1+µ
Mt−1 vt−1 (Et−1 [πt ])
To make it easy, let’s do a simple case where αt−1 = 1 and αt−j = 0 for all j.
So Et [πt+1 ] = πt−1
So what are Et−1 [πt ] and Et [πt+1 ]? Just µ!
Therefore, what is 1 + πt ? πt = µ because the increase in M has been announced
but hasn’t occurred yet!
What about 1 + πt+1 ?
1 + πt+1 = (1 + µ̃)
Wendy Morrison
vt+1 (Et+1 [Ï€t+2 ])
= 1 + µ̃
vt (Et [Ï€t+1 ])
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Rational Expectations
Solving the RE version is a bit more complicated …
Et−1 [πt ] = µ just as in the AE case. Why?
But what about Et [Ï€t+1 ]?
Remember that, starting in t+1, there will be no more shocks, so
Et+1 [πt+1 ] = πt+2 (it’s a perfect foresight model after t+1)
To solve this, we’ll use a ‘guess and verify’ method.
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Guess and Verify
We’ll guess that πt+j = µ̃ for j ≥ 1
Then Et+j [πt+j+1 ] = µ̃
1 + πt+j = (1 + µ̃)
vt+j (Et+j [Ï€t+j+1 ])
= 1 + µ̃
vt+j−1 (Et+j−1 [πt+j ])
Success!
So now we have everything we need to solve for πt
1 + πt = (1 + µ)
Wendy Morrison
vt (Et [Ï€t+1 ])
vt+1 (µ̃)
= (1 + µ)
>1+µ
vt−1 (Et−1 [πt ])
vt (µ)
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What’s the intuition?
In the AE case, no one at time t anticipates the effect of the increase in the money
supply at t+1. Their expectations are firmly routed in the past, meaning there is
no increase in inflation until t+1 when the monetary increase actually occurs.
However, in the RE case, agents take into account news about future money
growth before the growth actually happens.
In this way, inflation can actually precede money growth and become a
‘self-fulfilling prophecy’.
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Weimer Germany
Source: Uribe, Martin. Lecture: Hyper-inflations and Their Ends. (2017)
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Seignoirage
Why do governments do this?! What does it mean to ‘monetize’ government
spending?
Suppose an economy is only capable of producing YÌ„ .
If the government wants to re-apportion some of that output (Y’) – they could
just tax their population: T=Y’. Why might this be difficult?
Suppose instead that the government prints M units of money and uses this new
money to buy Y ′ instead.
How much will they have to print? Because the new money will increase the price
level, they’ll have to print more than Y’ in order to siphon off Y’ in real output.
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Seignoirage Revenue
How to solve for M’, the amount of new money they’ll have to print to get Y’ ?
Note that the following must be true:
M0 + M ′
1
= YÌ„
Pnew
v
M′
1
= Y′
Pnew
v
We have 2 equations and 2 unknowns (M’ and Pnew )
0
So PMnew0 = (Ȳ − Y ′ ) v1 → (ȲvM
= Pnew
−Y ′ )
Finally, M ′ = Y ′ v1 ∗ Pnew
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So what causes hyper-inflation?
Is money printing solely responsible? What would need to be true for this to be
true?
Could expectations begin hyper-inflation before the money supply changed?
Is it right in that case to say expectations are solely responsible?
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The New Keynesian Model
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Why this model?
The New Keynesian Model is the building block of much of the cutting edge
research in macro.
We’ll study a simplified 2-period version of the model
Why this model?
‘Micro-founded’ so more intuitive
Actually model firm behavior who are the ones changing prices!
Can show why monetary policy may have a (short run!) effect on real
outcomes
Can show how supply shocks (e.g. oil shocks, Covid) affect inflation
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Basic Model Details
1
We’ll consider only two periods, t ∈ (1, 2)
2
There’s a bunch of firms who all have market power.
3
Households have utility over consumption and labor (ct , Lt ) in both periods:
1−σ
1+γ
t
t
− L1+γ
u(ct , Lt ) = c1−σ
4
To simplify things, firms produce output with only labor, yjt = Ljt (no
capital)
5
The government has complete control over the nominal interest rate, it .
We’ll talk a lot more about this in the next unit.
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Firms
Inflation is fundamentally many many firms in the economy increasing their prices
all at the same time. So we need to carefully study firms, and figure out why they
would be incentivized to increase their prices all at the same time.
Question 1: What price do firms want to charge? Let’s review from intermediate
micro:
We assume firms aim to maximize profit. Firm profit (Πt ) is given by:
Πt = p(y ) ∗ y − Cost(y )
Two Questions:
1
Why is their price, p a function of y? What do we call this relationship?
2
How do we find the profit maximizing price/quantitiy?
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Profit maximization
p(y) is our inverse demand function! I.e. if we wanted to charge p, only y
customers would be willing to buy at that price.
To maximize profit, we take the derivative with respect to y and set it equal to 0
(assuming p(y) and Cost(y) are concave functions).
′
t
0 = dΠ
dy = p (y )y + p(y ) − MC (where MC = Cost’(y)) →
p(y ) + p ′ (y )y = MC (marginal revenue = marginal cost) →

′
p(y ) (1 + p (y )y /p(y ) = MC p’(y)y/p(y) = 1/ϵ (the price elasticity of
demand)
So p ∗ = (ϵ/(1 + ϵ))MC
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Inflation and Market Power
We derived the following expression for the price firms *want* to charge their
customers:

ϵ
∗ MC
p∗ =
1+ϵ
Where 1/ϵ is the price elasticity of demand (how much demand goes down when
prices go up). What happens to p ∗ when ϵ increases? Intuition?
What would make this elasticity go down (ϵ go up)? Consumer preferences shift
or changes in market structure (e.g. fewer firms).
In March, Sen. Warren tweeted: “Everyone is talking about inflation giant
corporations have figured out that’s an opportunity to not only pass along their
own costs, but also do some price gouging to pad their profits,” Is this a good
explanation for inflation?
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Other explanations for inflation?
Suppose we set aside rising ϵ as an explanation. Why else might firms want to
raise their prices?
Explanations of inflation have to explain increases in marginal costs.
In order to do that, we’ll model the behavior of households who are standing in
for the rest of the economy in this model.
If the firms use only labor for production, yt = Lt , what is the firm’s marginal
cost (additional cost for an additional unit of output)? Just the wage they have
to pay that worker, Wt !
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Households
Households’ utility over work and consumption during the two periods is given by:
1−σ

c11−σ
L1+γ
c2
L1+γ
1
2
−
+β
−
1−σ 1+γ
1−σ 1+γ
They receive a wage Wt for every hour they work
They can invest in a bond, b with interest rate i
Their budget constraint in period 1 is: P1 c1 + b = W1 L1
Their budget constrain in period 2 is: P2 c2 = W2 L2 + (1 + i)b
Sub (1) into (2) using b to get their full budget constraint:
P1 c1 (1 + i) + P2 c2 = W1 L1 (1 + i) + W2 L2
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Household’s Solution
Set up the household’s ‘Lagrangian’ and take the derivative with respect to c1 ,
c2 , W1 , W2 and set them equal to zero:
c1−σ = (1 + i)P1 λ
βc2−σ = P2 λ
1
Lγ1 = (1 + i) W
P1 λ
2
βLγ2 = λ W
P2
Which leads to the inter-temporal (Euler) condition (1) and 2 intra-temporal
(Labor supply) conditions (2) and (3):
c1−σ =
P1
β(1 + i)c2−σ
P2
W1
c1−σ
= Lγ1
P1
W2
c2−σ
= Lγ2
P2
(1)
(2)
(3)
Intuition?
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Labor supply and wages
Remember, there is no capital/investment in this model, so Y1 = c1 and Y2 = c2
Y1−σ = β(1 + i)Y2−σ
W1
Y1−σ
= Lγ1
P1
W2
Y2−σ
= Lγ2
P2
(4)
(5)
(6)
Equations (2) and (3) give us a clue as to why marginal costs may be
increasing in output.
So we can write the wage, Wt = Pt Ytσ Lγt = Pt Ytσ+γ . Why?
σ+γ−1
t
What is ∂W
> 0. What’s the intuition for this?
∂Yt ? Pt (σ + γ)Yt
With a finite labor supply, getting more workers to work for you means
offering higher wages.
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Monetary Policy
Remember, we said that the monetary authority has complete control over the
nominal interest rate, i.
Holding prices today constant, what happens to aggregate demand today when
interests rates are cut? What equation do we need to use?
c1 ↑−σ =
P1
β(1 + i ↓)c2−σ
P2
However, the assumption that prices don’t change (or only adjust slightly) is key
here.
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Flexible prices and monetary neutrality
If firms can fully adjust their prices, then a decline in i will be fully ‘neutralized’
by an increase in P1 .
Lower i → higher c1 = Y1 → more labor needed → higher wages (MC) → higher
P1 → lower c1
Relation to Quantity Theory:
P ∗Y =M ∗v
A decline in i is equivalent to an increase in M (we’ll see how next unit), as both
are a monetary expansion.
In both models, increases in money feed directly into increases in prices. The
new money creates demand for more goods than the economy is capable
of producing.
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Sticky price model
If we believed that this was the end of the story (monetary stimulus creates
inflation and doesn’t affect output), then the central bank would have no role in
combating recessions.
However, in the real world, prices don’t adjust immediately. Firms take a while to
realize that conditions have changed and that they can/should increase their
prices.
We’ll model sticky prices as firms having to choose their prices before they figure
out what their true marginal costs are. This will buy us:
1
Monetary non-neutrality (at least in the short run)
2
A role for expectations in inflation
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Timing of prices
Suppose firms have to set their price they’ll charge for t=1, before they figure out
what their true marginal costs are. Why is this realistic?
In particular, our new pricing equation becomes:

ϵ
pt∗ =
Et−1 [Wt ]
1+ϵ
Suppose expectations are adaptive, E0 [W1 ] = W0
Therefore, P1 is stuck at P0 until expectations adjust. When P1 is stuck, a
decrease in i can actually increase demand.
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The Phillips Curve
In reality, prices aren’t completely sticky. Imagine in our model that a fraction α
of the firms know the true state of the world, whereas the remaining (1-α) are
working with old information.
Suppose demand today increases (c1 = Y1 goes up). We’ve shown that this
means the marginal costs of all the firms go up as they’ll have to pay out higher
wages to attract the workers necessary to make all the new stuff that’s been
demanded.
For simplicity, let’s normalize the previous price level, P0 = 1.

ϵ
ϵ
So inflation, 1 + π1 = P1 /P0 = P1 = α 1−ϵ
MC1 + (1 − α) 1−ϵ
E [MC1 ]
Inflation is therefore determined by a real term and an expectations term.
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The Phillips Curve
Intuition: In the short run, (holding market structure constant) firms set prices
based on a combination of their actual and expected marginal costs.
Though we haven’t considered them yet, factors other than increased demand
pulling up wages can affect a firm’s costs.
So called ‘cost-push shocks, s (e.g. the cost of an important input like oil
suddenly increasing) can also push costs and therefore prices up.
π = β1 (∆Y ) + β2 E [∆MC ] + s
Can also write the PC as:
π = β1 (∆u) + β2 E [π] + s
The coefficient β1 captures: increased demand → lower unemployment → higher
wages → higher prices
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Why was inflation so low from 1990s-2020?
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The Great Moderation
Figure: Source: St. Louis Fed
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Missing inflation and deflation
In fact, inflation wasn’t just low and steady, it was less responsive to GDP than
expected.
Remember our model: when Yt goes up, marginal costs go up, and prices
(eventually) should go up. The inverse is true when Yt goes down.
However, there was much less deflation during the Great Recession than
expected. There was also much lower inflation during the recovery than expected.
This led some economists to argue that “the Phillips Curve is Dead”!
Why might this have happened? To answer this question, we’ll need to be a little
more thoughtful about how we model expectations.
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Expectations learned over time
The following is adapted from Jorgensen and Lansing (2019)
Suppose instead of taking only last period’s inflation to form their expectations of
inflation, firms use information about many past periods of inflation:
Et [Ï€t ] = λ(Ï€t + (1 − λ)Ï€t−1 + (1 − λ)2 Ï€t−2 + …)
The basic idea is that λ is not fixed or arbitrary but chosen optimally by firms in
response to their environment.
When λ = 1 what information about past inflation is the firm prioritizing? Last
period’s!
As λ → 0, the relative weight of historical inflation grows and grows in
importance.
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Choosing λ
They show that a firm optimally learning over time (trying to minimize their
forecast errors) will set λ according to:
p
−ϕ + ϕ2 + 4ϕ
λ=
2
Where ϕ is the ‘perceived signal-to-noise’ ratio from the point of view of firms
observing a bit of new inflation data. Deriving the value of λ from their paper is
beyond the scope of this class, but let’s think intuitively about it.
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Expectations learned over time
ϕ = 0: firms think any new hint of inflation is just ‘noise’, not worth taking
into account
ϕ = ∞: firms think new hints of inflation are all ‘signal’ and really mean
something
λ=
−ϕ +
p
Ï•2 + 4Ï•
2
As ϕ → 0, then λ → 0 and firms never adjust their expectations.
As ϕ → ∞, then λ → 1 and firms immediately adjust their expectations
(Et [πt+1 ] = πt )
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Can Monetary Policy influence Ï•?
Suppose the Monetary authority follows a very strong/proactive Taylor Rule:
it = ϕY (Yt − Ȳ ) + ϕπ (π − π̄)
That is, when the CB see’s output climb above it’s estimates of long-run output
(YÌ„ ) or when it observes rising inflation, it immediately hikes rates a lot trying to
maintain a constant inflation target.
Then if a firm observes a bit of new inflation, is this a good ‘signal’ of inflation to
come? Or is it mostly ‘noise’ ?
Intuition: Jorgensen and Lansing’s argue that by following such a strict/credible
Taylor rule since the 1990s, the CB has led firms to believe that any new inflation
is just temporary noise that will be dealt with promptly. Therefore, firms can
ignore new inflation when forming expectations (expectations are anchored).
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Why is inflation so high now?
Wendy Morrison
Unit 1: Inflation
May, 24 2022
49 / 58
Inflation right now
Wendy Morrison
Unit 1: Inflation
May, 24 2022
50 / 58
Sources of current inflation
Let’s analyze the recent rise in inflation through the lens of our Phillips Curve:
π = β1 (∆Y ) + β2 E [∆MC ] + s
1
What forces could have generated an increase in aggregate demand (∆Y )?
2
A cost-push shock?
3
Could inflation expectations have become un-anchored?
Wendy Morrison
Unit 1: Inflation
May, 24 2022
51 / 58
Increases in aggregate demand
1
The $2.2 Trillion CARES Act
2
$900 Billion in additional relief
3
$1.9 Trillion American Rescue Plan (ARP)
This spending (the direct stimulus checks in particular) led to an increase in
aggregate demand beyond what the economy could produce. To meet this new
demand, firms would need more workers leading to a ‘tight’ labor market and
higher wages.
Barnichon, Olivier, and Shapiro (2021) at the San Francisco Fed estimate the
effect of the ARP on inflation in 2 steps:
Estimate the effect of labor market ‘slack’ on wages and therefore on prices
Estimate the effect of the ARP on labor market slack
Wendy Morrison
Unit 1: Inflation
May, 24 2022
52 / 58
Labor market slack
They measure ‘slack’ as the vacancy-to-unemployment ratio.
Vacancies measure the number of firms looking for a worker, while unemployment
measures the number of workers searching for a job.
If there are far more employers looking for workers than workers looking for a job,
there is little/no ‘slack’ and the labor market is very ‘tight’. Lower slack means
higher wages. Why?
πt = β1 (Wt (slack) + β2 E [πt ] + s
Their first step is basically to estimate the historical relationship between slack,
wages, and prices.
Wendy Morrison
Unit 1: Inflation
May, 24 2022
53 / 58
Effect of the ARP on slack
The second step is to estimate the effect of the ARP on slack. This step is much
less straightforward (and unfortunately, much less reliable).
Why can’t they just directly measure the change in slack after the ARP was
passed? What was happening in the economy that might complicate this
picture?1
Crises and fiscal stimulus are endogenous. Therefore they turn to the macro
literature which has come up with several ‘exogenous’ fiscal ‘shocks’.
These are special historical examples of fiscal spending that researches believe
came ‘out of nowhere’ (e.g. spending during a war).
If $100 Billion of war spending decreased slack by X, then they estimate the $1
Trillion ARP package decreased slack by 10X.
1
Why can’t we simply regress the crime rate on the number of police to learn their
effect? Or the effect of wearing masks on hospitalization?
Wendy Morrison
Unit 1: Inflation
May, 24 2022
54 / 58
Why might this be an under-estimate?
Non-linearity: If the ARP was 10 times the size of the fiscal shock they use, that
implies the government bought 10 times the output (potentially needed 10 times
the extra labor).
Hiring 10 times the labor might requiring increasing wages by more than 10 times.
Different type of spending: If the $10 billion war time spending involved
importing steel from Canada to build ships.
Suppose Americans used their stimulus checks to go out to eat when restaurants
opened back up.
Which of these might cause slack in the United States to fall by more?
Wendy Morrison
Unit 1: Inflation
May, 24 2022
55 / 58
Expectations
Could expectations have come un-anchored?
Howard Schneider and Dan Burns. Inflation views tilt the Fed’s way, a bit. Reuters.
Wendy Morrison
Unit 1: Inflation
May, 24 2022
56 / 58
Cost push shocks
What are examples of cost-push shocks firms may have faced over the last year?
1
Oil disruptions due to war in Ukraine
2
Worker shortages due to the pandemic
3
Price of imported goods increasing due to supply chain disruptions
Wendy Morrison
Unit 1: Inflation
May, 24 2022
57 / 58
Revisiting Milton Friedman
So is inflation always and everywhere a monetary phenomenon?
Wendy Morrison
Unit 1: Inflation
May, 24 2022
58 / 58
Unit 2: Monetary Policy
Wendy Morrison
May, 31 2022
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
1 / 59
Outline
1
Banks and money creation
2
Interest rate targeting
3
Optimal Monetary Policy
4
Zero Lower Bound and Forward Guidance
5
Final thoughts and Future Research
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
2 / 59
Banks and money creation
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
3 / 59
Real world monetary policy
Controlling the money supply isn’t as simple as dropping cash from a helicopter.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
4 / 59
Real world monetary policy
Controlling the money supply isn’t as simple as dropping cash from a helicopter.
The reason is that the Central Bank only controls the monetary base, while the
total money supply depends on banks (and consumer’s faith in banks)
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
4 / 59
The Federal Reserve System
The Federal Reserve System (”the Fed”) was created with the 1913 Federal
Reserve Act in response to yet another financial panic, and its structure reflects
the politics of the age.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
5 / 59
The Federal Reserve System
The Federal Reserve System (”the Fed”) was created with the 1913 Federal
Reserve Act in response to yet another financial panic, and its structure reflects
the politics of the age.
12 autonomous regional banks, each sending their president to the FOMC
(New York and DC interests shouldn’t dominate!)
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
5 / 59
The Federal Reserve System
The Federal Reserve System (”the Fed”) was created with the 1913 Federal
Reserve Act in response to yet another financial panic, and its structure reflects
the politics of the age.
12 autonomous regional banks, each sending their president to the FOMC
(New York and DC interests shouldn’t dominate!)
Board of governors appointed by the president and confirmed by Senate
(Direct control by government, not just bankers!)
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
5 / 59
The Federal Reserve System
The Federal Reserve System (”the Fed”) was created with the 1913 Federal
Reserve Act in response to yet another financial panic, and its structure reflects
the politics of the age.
12 autonomous regional banks, each sending their president to the FOMC
(New York and DC interests shouldn’t dominate!)
Board of governors appointed by the president and confirmed by Senate
(Direct control by government, not just bankers!)
The Fed plays many important roles in the economy. We’ll discuss at the end of
next class what it sees as its main focus/objectives.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
5 / 59
The Federal Reserve System
The Federal Reserve System (”the Fed”) was created with the 1913 Federal
Reserve Act in response to yet another financial panic, and its structure reflects
the politics of the age.
12 autonomous regional banks, each sending their president to the FOMC
(New York and DC interests shouldn’t dominate!)
Board of governors appointed by the president and confirmed by Senate
(Direct control by government, not just bankers!)
The Fed plays many important roles in the economy. We’ll discuss at the end of
next class what it sees as its main focus/objectives.
One useful conceptual distinction is the “normal” conduct of the Fed that aims to
control the money supply and “emergency” actions taken during crises to calm
financial markets.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
5 / 59
The Federal Reserve System
The Federal Reserve System (”the Fed”) was created with the 1913 Federal
Reserve Act in response to yet another financial panic, and its structure reflects
the politics of the age.
12 autonomous regional banks, each sending their president to the FOMC
(New York and DC interests shouldn’t dominate!)
Board of governors appointed by the president and confirmed by Senate
(Direct control by government, not just bankers!)
The Fed plays many important roles in the economy. We’ll discuss at the end of
next class what it sees as its main focus/objectives.
One useful conceptual distinction is the “normal” conduct of the Fed that aims to
control the money supply and “emergency” actions taken during crises to calm
financial markets. We’ll use this unit to deal with the former.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
5 / 59
Money supply vs interest rates
Today we’ll start with a very simple (likely familiar) model of the money
multiplier (how banks contribute to money creation)
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
6 / 59
Money supply vs interest rates
Today we’ll start with a very simple (likely familiar) model of the money
multiplier (how banks contribute to money creation)
The central bank in this model will control the monetary base in order to
indirectly influence the total money supply.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
6 / 59
Money supply vs interest rates
Today we’ll start with a very simple (likely familiar) model of the money
multiplier (how banks contribute to money creation)
The central bank in this model will control the monetary base in order to
indirectly influence the total money supply.
You might wonder why the CB in this model uses the money supply as their tool,
whereas the CB from last unit tried to control the nominal interest rate.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
6 / 59
Money supply vs interest rates
Today we’ll start with a very simple (likely familiar) model of the money
multiplier (how banks contribute to money creation)
The central bank in this model will control the monetary base in order to
indirectly influence the total money supply.
You might wonder why the CB in this model uses the money supply as their tool,
whereas the CB from last unit tried to control the nominal interest rate.
We’ll look in depth at what the Fed’s primary goals are and explore why targeting
the monetary base may no longer be the best tool for achieving these goals.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
6 / 59
The Monetary Base
The monetary base or “high powered money” consists of (1) currency (e.g.
paper dollars, coins) and (2) reserves held by banks at the Federal Reserve.
Monetary Base (MB) = C + R
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
7 / 59
The Monetary Base
The monetary base or “high powered money” consists of (1) currency (e.g.
paper dollars, coins) and (2) reserves held by banks at the Federal Reserve.
Monetary Base (MB) = C + R
In order to increase the MB, the Fed (the Open Market Committee in
particular) engages in open market operations meaning the buying or selling of
assets (generally treasury bonds).
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
7 / 59
The Monetary Base
The monetary base or “high powered money” consists of (1) currency (e.g.
paper dollars, coins) and (2) reserves held by banks at the Federal Reserve.
Monetary Base (MB) = C + R
In order to increase the MB, the Fed (the Open Market Committee in
particular) engages in open market operations meaning the buying or selling of
assets (generally treasury bonds).
How is this money creation?
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
7 / 59
The Monetary Base
The monetary base or “high powered money” consists of (1) currency (e.g.
paper dollars, coins) and (2) reserves held by banks at the Federal Reserve.
Monetary Base (MB) = C + R
In order to increase the MB, the Fed (the Open Market Committee in
particular) engages in open market operations meaning the buying or selling of
assets (generally treasury bonds).
How is this money creation? When the Fed decides to buy something, it simply
credits the reserve accounts of the bank. This ‘creates money’ out of thin air.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
7 / 59
The Monetary Base
The monetary base or “high powered money” consists of (1) currency (e.g.
paper dollars, coins) and (2) reserves held by banks at the Federal Reserve.
Monetary Base (MB) = C + R
In order to increase the MB, the Fed (the Open Market Committee in
particular) engages in open market operations meaning the buying or selling of
assets (generally treasury bonds).
How is this money creation? When the Fed decides to buy something, it simply
credits the reserve accounts of the bank. This ‘creates money’ out of thin air.
Buying the assets is the way the new money gets injected into the economy.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
7 / 59
The Monetary Base
The monetary base or “high powered money” consists of (1) currency (e.g.
paper dollars, coins) and (2) reserves held by banks at the Federal Reserve.
Monetary Base (MB) = C + R
In order to increase the MB, the Fed (the Open Market Committee in
particular) engages in open market operations meaning the buying or selling of
assets (generally treasury bonds).
How is this money creation? When the Fed decides to buy something, it simply
credits the reserve accounts of the bank. This ‘creates money’ out of thin air.
Buying the assets is the way the new money gets injected into the economy.
When the Fed sells assets, it takes the money it receives from the sale and
removes it from circulation.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
7 / 59
Open Market Operations
The FOMC is made up of the Board of Governors, the NY Fed president, and a
rotating group of regional Fed presidents, and meets 8 times a year to decide on
policy.
The actual buying a selling occurs via the open markets desk at the NY Fed.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
8 / 59
Open Market Operations
The FOMC is made up of the Board of Governors, the NY Fed president, and a
rotating group of regional Fed presidents, and meets 8 times a year to decide on
policy.
The actual buying a selling occurs via the open markets desk at the NY Fed.
Mechanically, what’s happens when the Fed buys a bond from a bank is shown in
the balance sheets below:
Federal Reserve
A
L
Treasury Bonds
+$100 Reserves
+$100
Banking System
A
Treasury Bonds
-$100
Reserves at Fed
+$100
L
These are referred to as non-borrowed reserves.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
8 / 59
Discount Loans
When the Fed creates reserves out of thin air, in addition to buying securities, it
can also simply loan these funds to banks.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
9 / 59
Discount Loans
When the Fed creates reserves out of thin air, in addition to buying securities, it
can also simply loan these funds to banks.
This temporarily increases the money supply (until the bank repays the loan).
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
9 / 59
Discount Loans
When the Fed creates reserves out of thin air, in addition to buying securities, it
can also simply loan these funds to banks.
This temporarily increases the money supply (until the bank repays the loan).
Federal Reserve
A
Discount Loans
L
+$100
Reserves
+$100
Banking System
A
Reserves at Fed
Wendy Morrison
+$100
L
Discount Loan
Unit 2: Monetary Policy
+$100
May, 31 2022
9 / 59
Discount Loans
When the Fed creates reserves out of thin air, in addition to buying securities, it
can also simply loan these funds to banks.
This temporarily increases the money supply (until the bank repays the loan).
Federal Reserve
A
Discount Loans
L
+$100
Reserves
+$100
Banking System
A
Reserves at Fed
+$100
L
Discount Loan
+$100
These are referred to as borrowed reserves.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
9 / 59
Primary Dealers
Which banks does the Fed buy from and sell to?
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
10 / 59
Primary Dealers
Which banks does the Fed buy from and sell to?
The counter-parties of OMO are called Primary Dealers: banks or other
financial institutions (JP Morgan Chase, Citigroup, Wells Fargo) that have been
granted special status.
They’re able to bid on newly-issued government debt (rather than buying in the
secondary market), but also must meet certain regulatory requirements
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
10 / 59
Banks and money creation
When you think of money, you probably think of your deposits at the bank.
In fact, the deposits that the bank issues are another form of money. These
deposits along with currency make up M1 or the total money supply.
M =C +D
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
11 / 59
Banks and money creation
When you think of money, you probably think of your deposits at the bank.
In fact, the deposits that the bank issues are another form of money. These
deposits along with currency make up M1 or the total money supply.
M =C +D
Imagine you deposit $100 in cash in your checking account. If banks had to keep
100% of deposits in cash/reserves, then nothing would happen to the money
supply by the creation of these deposits.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
11 / 59
Banks and money creation
When you think of money, you probably think of your deposits at the bank.
In fact, the deposits that the bank issues are another form of money. These
deposits along with currency make up M1 or the total money supply.
M =C +D
Imagine you deposit $100 in cash in your checking account. If banks had to keep
100% of deposits in cash/reserves, then nothing would happen to the money
supply by the creation of these deposits.
Because we have a fractional reserve banking system (meaning banks only
have to keep a fraction of their deposits as reserves and can lend out the rest)
banks are able to multiply any increases in the monetary base.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
11 / 59
Deposit creation: Step 1
Suppose banks are able to lend out 90% of all deposits they receive.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
12 / 59
Deposit creation: Step 1
Suppose banks are able to lend out 90% of all deposits they receive.Why does this
make some people (e.g. Mervin King, the former head of the Bank of England)
nervous? What’s the difference between a bank/demand deposit and a loan?
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
12 / 59
Deposit creation: Step 1
Suppose banks are able to lend out 90% of all deposits they receive.Why does this
make some people (e.g. Mervin King, the former head of the Bank of England)
nervous? What’s the difference between a bank/demand deposit and a loan?
Suppose Bank A sells some treasuries to the Fed and $100 of reserves are credited
to its account. Because its deposits haven’t changed, how much of these reserves
can it lend out?
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
12 / 59
Deposit creation: Step 1
Suppose banks are able to lend out 90% of all deposits they receive.Why does this
make some people (e.g. Mervin King, the former head of the Bank of England)
nervous? What’s the difference between a bank/demand deposit and a loan?
Suppose Bank A sells some treasuries to the Fed and $100 of reserves are credited
to its account. Because its deposits haven’t changed, how much of these reserves
can it lend out? All of them!
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
12 / 59
Deposit creation: Step 1
Suppose banks are able to lend out 90% of all deposits they receive.Why does this
make some people (e.g. Mervin King, the former head of the Bank of England)
nervous? What’s the difference between a bank/demand deposit and a loan?
Suppose Bank A sells some treasuries to the Fed and $100 of reserves are credited
to its account. Because its deposits haven’t changed, how much of these reserves
can it lend out? All of them!
These new funds become $100 of new deposits for the loan recipient.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
12 / 59
Deposit creation: Step 1
Suppose banks are able to lend out 90% of all deposits they receive.Why does this
make some people (e.g. Mervin King, the former head of the Bank of England)
nervous? What’s the difference between a bank/demand deposit and a loan?
Suppose Bank A sells some treasuries to the Fed and $100 of reserves are credited
to its account. Because its deposits haven’t changed, how much of these reserves
can it lend out? All of them!
These new funds become $100 of new deposits for the loan recipient.
Bank A
A
L
Securities -$100 Deposits +$100
Reserves +$100
Loans +$100
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
12 / 59
Deposit creation: Step 2
But the loan recipient doesn’t just keep the money in the bank/their pocket they go out and spend it! Suppose the recipient is a firm who uses the loan to
pay wages. The deposits are transferred from their bank to Bank B.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
13 / 59
Deposit creation: Step 2
But the loan recipient doesn’t just keep the money in the bank/their pocket they go out and spend it! Suppose the recipient is a firm who uses the loan to
pay wages. The deposits are transferred from their bank to Bank B.
With a 10% reserve requirement, how much can bank B lend out?
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
13 / 59
Deposit creation: Step 2
But the loan recipient doesn’t just keep the money in the bank/their pocket they go out and spend it! Suppose the recipient is a firm who uses the loan to
pay wages. The deposits are transferred from their bank to Bank B.
With a 10% reserve requirement, how much can bank B lend out?
Bank B
A
L
Reserves +$10 Deposits +$100
Loans +$90
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
13 / 59
Deposit creation: Step 2
But the loan recipient doesn’t just keep the money in the bank/their pocket they go out and spend it! Suppose the recipient is a firm who uses the loan to
pay wages. The deposits are transferred from their bank to Bank B.
With a 10% reserve requirement, how much can bank B lend out?
Bank B
A
L
Reserves +$10 Deposits +$100
Loans +$90
These loans go to a household, who uses them to buy dinner out on their credit
card. The $90 is deposited in the restaurant’s bank, Bank C.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
13 / 59
Deposit creation: Step 2
But the loan recipient doesn’t just keep the money in the bank/their pocket they go out and spend it! Suppose the recipient is a firm who uses the loan to
pay wages. The deposits are transferred from their bank to Bank B.
With a 10% reserve requirement, how much can bank B lend out?
Bank B
A
L
Reserves +$10 Deposits +$100
Loans +$90
These loans go to a household, who uses them to buy dinner out on their credit
card. The $90 is deposited in the restaurant’s bank, Bank C. How much can
Bank C lend out?
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
13 / 59
Deposit creation: Step 2
But the loan recipient doesn’t just keep the money in the bank/their pocket they go out and spend it! Suppose the recipient is a firm who uses the loan to
pay wages. The deposits are transferred from their bank to Bank B.
With a 10% reserve requirement, how much can bank B lend out?
Bank B
A
L
Reserves +$10 Deposits +$100
Loans +$90
These loans go to a household, who uses them to buy dinner out on their credit
card. The $90 is deposited in the restaurant’s bank, Bank C. How much can
Bank C lend out? $81!
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
13 / 59
Deposit creation: Step 3
Remember, each time new deposits are created, new money is created, as
deposits are a form of money.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
14 / 59
Deposit creation: Step 3
Remember, each time new deposits are created, new money is created, as
deposits are a form of money.
This $100 of new reserves became $100, then $90, then $81, then …
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
14 / 59
Deposit creation: Step 3
Remember, each time new deposits are created, new money is created, as
deposits are a form of money.
This $100 of new reserves became $100, then $90, then $81, then …
Equivalently:
M = 100 ∗ (1 +
Wendy Morrison
9
92
+
+ …
10 10
Unit 2: Monetary Policy
May, 31 2022
14 / 59
Deposit creation: Step 3
Remember, each time new deposits are created, new money is created, as
deposits are a form of money.
This $100 of new reserves became $100, then $90, then $81, then …
Equivalently:
M = 100 ∗ (1 +

M = 100
Wendy Morrison
9
92
+
+ …
10 10
1
9
1 − 10
Unit 2: Monetary Policy

May, 31 2022
14 / 59
The Money Multiplier
Another way to see this is to write:
M
C +D
c/d + 1
=
=
B
C +R
c/d + rr
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
15 / 59
The Money Multiplier
Another way to see this is to write:
M
C +D
c/d + 1
=
=
B
C +R
c/d + rr
It happened to be the case that the preferred c/d ratio was 0 in the above
1
example, so M
B = rr
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
15 / 59
The Money Multiplier
Another way to see this is to write:
M
C +D
c/d + 1
=
=
B
C +R
c/d + rr
It happened to be the case that the preferred c/d ratio was 0 in the above
1
example, so M
B = rr No! It didn’t matter that c/d=0 in the above example.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
15 / 59
The Money Multiplier
Another way to see this is to write:
M
C +D
c/d + 1
=
=
B
C +R
c/d + rr
It happened to be the case that the preferred c/d ratio was 0 in the above
1
example, so M
B = rr No! It didn’t matter that c/d=0 in the above example.
Does a decline in the desire to hold currency affect the central bank’s ability to
control the money supply?
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
15 / 59
The Money Multiplier
Another way to see this is to write:
M
C +D
c/d + 1
=
=
B
C +R
c/d + rr
It happened to be the case that the preferred c/d ratio was 0 in the above
1
example, so M
B = rr No! It didn’t matter that c/d=0 in the above example.
Does a decline in the desire to hold currency affect the central bank’s ability to
control the money supply?
This is a key point to understand. As long as the Fed can create reserves and
these reserves translate into lending and spending (deposit creation) through the
banking system, the demand for cash doesn’t matter!
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
15 / 59
Excess Reserves
Excess Reserves are reserves that banks hold beyond what is required legally.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
16 / 59
Excess Reserves
Excess Reserves are reserves that banks hold beyond what is required legally.
Therefore, the multiplier equation should actually read (where er = E/D):
M
C +D
c/d + 1
=
=
B
C +R
c/d + rr + er
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
16 / 59
Excess Reserves
Excess Reserves are reserves that banks hold beyond what is required legally.
Therefore, the multiplier equation should actually read (where er = E/D):
M
C +D
c/d + 1
=
=
B
C +R
c/d + rr + er
Why might banks hold excess reserves?
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
16 / 59
Excess Reserves
Excess Reserves are reserves that banks hold beyond what is required legally.
Therefore, the multiplier equation should actually read (where er = E/D):
M
C +D
c/d + 1
=
=
B
C +R
c/d + rr + er
Why might banks hold excess reserves? What do we mean when we say “reserves
are insurance against deposit outflows?”
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
16 / 59
Excess Reserves
Excess Reserves are reserves that banks hold beyond what is required legally.
Therefore, the multiplier equation should actually read (where er = E/D):
M
C +D
c/d + 1
=
=
B
C +R
c/d + rr + er
Why might banks hold excess reserves? What do we mean when we say “reserves
are insurance against deposit outflows?”
Remember, deposits are a short term liability – they can be demanded at any
time, whereas a loan payment is made many months (or years) in the future
(maturity mismatch). Therefore, banks may keep excess reserves on hand to
meet unexpected outflows of deposits.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
16 / 59
Excess Reserves
Excess Reserves are reserves that banks hold beyond what is required legally.
Therefore, the multiplier equation should actually read (where er = E/D):
M
C +D
c/d + 1
=
=
B
C +R
c/d + rr + er
Why might banks hold excess reserves? What do we mean when we say “reserves
are insurance against deposit outflows?”
Remember, deposits are a short term liability – they can be demanded at any
time, whereas a loan payment is made many months (or years) in the future
(maturity mismatch). Therefore, banks may keep excess reserves on hand to
meet unexpected outflows of deposits.
Before the 2008 crisis, excess reserves were extremely low. They grew
significantly following a massive round of new reserve creation following the crisis.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
16 / 59
Excess Reserves
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
17 / 59
Interest rate targeting
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
18 / 59
Is this how central bankers think about monetary policy?
By changing the monetary base, the central bank in this simple model is able to
mechanically and directly change the money supply.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
19 / 59
Is this how central bankers think about monetary policy?
By changing the monetary base, the central bank in this simple model is able to
mechanically and directly change the money supply.
But is the money supply itself really what the central bank cares about?
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
19 / 59
Is this how central bankers think about monetary policy?
By changing the monetary base, the central bank in this simple model is able to
mechanically and directly change the money supply.
But is the money supply itself really what the central bank cares about?
The Fed cares about aggregate spending (I+G)
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
19 / 59
Is this how central bankers think about monetary policy?
By changing the monetary base, the central bank in this simple model is able to
mechanically and directly change the money supply.
But is the money supply itself really what the central bank cares about?
The Fed cares about aggregate spending (I+G)
What if the central bank creates a bunch of new reserves, but banks can’t lend
those extra reserves out profitably? The model above assumes that every dollar a
bank takes in automatically gets loaned out, spent, and loaned out again.
But that isn’t necessarily the case.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
19 / 59
Is this how central bankers think about monetary policy?
By changing the monetary base, the central bank in this simple model is able to
mechanically and directly change the money supply.
But is the money supply itself really what the central bank cares about?
The Fed cares about aggregate spending (I+G)
What if the central bank creates a bunch of new reserves, but banks can’t lend
those extra reserves out profitably? The model above assumes that every dollar a
bank takes in automatically gets loaned out, spent, and loaned out again.
But that isn’t necessarily the case.
A new unit of currency only matters if it actually leaves the bank and is spent!
We saw last class that nominal spending (e.g. an increase in c1 in the NK model)
is what effects employment and prices!
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
19 / 59
Interest rate targeting
According to Woodford, many mistakes in monetary policy analysis are based on
the (erroneous), “common assumption that the effects of monetary policy depend
upon a mechanical connection between the monetary base and the volume of
nominal spending”
In fact, no such ‘mechanical connection’ need exist.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
20 / 59
Interest rate targeting
According to Woodford, many mistakes in monetary policy analysis are based on
the (erroneous), “common assumption that the effects of monetary policy depend
upon a mechanical connection between the monetary base and the volume of
nominal spending”
In fact, no such ‘mechanical connection’ need exist.
Instead, “a central bank only needs to be able to control the level of short-term
nominal interest rates to achieve its stabilization goals.”
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
20 / 59
Interest rate targeting
According to Woodford, many mistakes in monetary policy analysis are based on
the (erroneous), “common assumption that the effects of monetary policy depend
upon a mechanical connection between the monetary base and the volume of
nominal spending”
In fact, no such ‘mechanical connection’ need exist.
Instead, “a central bank only needs to be able to control the level of short-term
nominal interest rates to achieve its stabilization goals.”
Intuition?
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
20 / 59
Interest rate targeting
According to Woodford, many mistakes in monetary policy analysis are based on
the (erroneous), “common assumption that the effects of monetary policy depend
upon a mechanical connection between the monetary base and the volume of
nominal spending”
In fact, no such ‘mechanical connection’ need exist.
Instead, “a central bank only needs to be able to control the level of short-term
nominal interest rates to achieve its stabilization goals.”
Intuition? Nominal interest rates directly affect the amount of
borrowing/spending by households (think about the NK model) and by firms.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
20 / 59
Interest rate targeting
In the previous class, we saw how the interest rate directly determines aggregate
spending in the New Keynesian model through the Euler equation.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
21 / 59
Interest rate targeting
In the previous class, we saw how the interest rate directly determines aggregate
spending in the New Keynesian model through the Euler equation.
There is a new body of research (including some of my own work) casting some
doubt as to whether this is the only, or even the primary channel, (we’ll return to
this later), but for now, we’ll assume the New Keynesian model is more-or-less
correct.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
21 / 59
Interest rate targeting
In the previous class, we saw how the interest rate directly determines aggregate
spending in the New Keynesian model through the Euler equation.
There is a new body of research (including some of my own work) casting some
doubt as to whether this is the only, or even the primary channel, (we’ll return to
this later), but for now, we’ll assume the New Keynesian model is more-or-less
correct.
What tools does the central bank have at its disposable to control interest rates?
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
21 / 59
Interest rate targeting
In the previous class, we saw how the interest rate directly determines aggregate
spending in the New Keynesian model through the Euler equation.
There is a new body of research (including some of my own work) casting some
doubt as to whether this is the only, or even the primary channel, (we’ll return to
this later), but for now, we’ll assume the New Keynesian model is more-or-less
correct.
What tools does the central bank have at its disposable to control interest rates?
We’ve already mentioned open market operations – i.e. injecting reserves
into banks
We’ll examine how this is supposed to work
We’ll then consider why technological developments made this less effective,
and what the Fed needed to do to adapt (based on Woodford, 2000)
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
21 / 59
Traditional (US) Interest Rate Control
The next few slides apply to the traditional US approach to managing interest
rates.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
22 / 59
Traditional (US) Interest Rate Control
The next few slides apply to the traditional US approach to managing interest
rates.
Before proceeding, we’ll need to (re)introduce a few extra concepts:
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
22 / 59
Traditional (US) Interest Rate Control
The next few slides apply to the traditional US approach to managing interest
rates.
Before proceeding, we’ll need to (re)introduce a few extra concepts:
1
Borrowed Reserves: Reserves borrowed
at the discount window from the Fed. Not to be confused with reserves
borrowed between banks. This is thought to come with some “implicit
costs” or “stigma”.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
22 / 59
Traditional (US) Interest Rate Control
The next few slides apply to the traditional US approach to managing interest
rates.
Before proceeding, we’ll need to (re)introduce a few extra concepts:
1
Borrowed Reserves: Reserves borrowed
at the discount window from the Fed. Not to be confused with reserves
borrowed between banks. This is thought to come with some “implicit
costs” or “stigma”.
2
The Discount Rate: The rate charged by the Fed to borrow reserves
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
22 / 59
Traditional (US) Interest Rate Control
The next few slides apply to the traditional US approach to managing interest
rates.
Before proceeding, we’ll need to (re)introduce a few extra concepts:
1
Borrowed Reserves: Reserves borrowed
at the discount window from the Fed. Not to be confused with reserves
borrowed between banks. This is thought to come with some “implicit
costs” or “stigma”.
2
The Discount Rate: The rate charged by the Fed to borrow reserves
3
Non-Borrowed Reserves: Reserves sitting in banks’ accounts, put there via
open market operations. They’re ‘non-borrowed’ because they resulted from
a sale of assets to the Fed.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
22 / 59
Traditional (US) Interest Rate Control
The next few slides apply to the traditional US approach to managing interest
rates.
Before proceeding, we’ll need to (re)introduce a few extra concepts:
1
Borrowed Reserves: Reserves borrowed
at the discount window from the Fed. Not to be confused with reserves
borrowed between banks. This is thought to come with some “implicit
costs” or “stigma”.
2
The Discount Rate: The rate charged by the Fed to borrow reserves
3
Non-Borrowed Reserves: Reserves sitting in banks’ accounts, put there via
open market operations. They’re ‘non-borrowed’ because they resulted from
a sale of assets to the Fed.
4
The Federal Funds Rates: The rate at which banks borrow reserves from
each other.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
22 / 59
Interbank reserve market
The Fed Funds rate is the interest rate (the price) banks charge each other to
borrow reserves.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
23 / 59
Interbank reserve market
The Fed Funds rate is the interest rate (the price) banks charge each other to
borrow reserves.
What factors might determine the day-to-day demand for borrowing reserves?
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
23 / 59
Interbank reserve market
The Fed Funds rate is the interest rate (the price) banks charge each other to
borrow reserves.
What factors might determine the day-to-day demand for borrowing reserves?
A bank may not be able to perfectly predict their withdrawal/payments
demands that day. Remember, banks use reserves to ‘settle’ payments made
by their depositors at the Fed
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
23 / 59
Interbank reserve market
The Fed Funds rate is the interest rate (the price) banks charge each other to
borrow reserves.
What factors might determine the day-to-day demand for borrowing reserves?
A bank may not be able to perfectly predict their withdrawal/payments
demands that day. Remember, banks use reserves to ‘settle’ payments made
by their depositors at the Fed
What about the supply of loanable reserves?
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
23 / 59
Interbank reserve market
The Fed Funds rate is the interest rate (the price) banks charge each other to
borrow reserves.
What factors might determine the day-to-day demand for borrowing reserves?
A bank may not be able to perfectly predict their withdrawal/payments
demands that day. Remember, banks use reserves to ‘settle’ payments made
by their depositors at the Fed
What about the supply of loanable reserves? There are two ways banks get
reserves that are able to be supplied out.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
23 / 59
Interbank reserve market
The Fed Funds rate is the interest rate (the price) banks charge each other to
borrow reserves.
What factors might determine the day-to-day demand for borrowing reserves?
A bank may not be able to perfectly predict their withdrawal/payments
demands that day. Remember, banks use reserves to ‘settle’ payments made
by their depositors at the Fed
What about the supply of loanable reserves? There are two ways banks get
reserves that are able to be supplied out.
1
Receive reserves via open market operations (exogenous, set by Fed)
2
Borrow them from the Fed if the interest rate is lower than what they could
charge in the open market!
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
23 / 59
Interbank reserve market
Figure: Focus on D1 for now!
Source: Woodford (2000)
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
24 / 59
Interbank reserve market
Figure: Focus on D1 for now!
Source: Woodford (2000)
(1) Why is the demand for borrowing reserves downward sloping?
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
24 / 59
Interbank reserve market
Figure: Focus on D1 for now!
Source: Woodford (2000)
(1) Why is the demand for borrowing reserves downward sloping? (2) Why is the
supply of reserves lent out constant and then increasing in the ‘spread’
(difference)
between FF and DR?Unit 2: Monetary Policy
Wendy Morrison
May, 31 2022
24 / 59
Supply and demand for reserves
The reason the demand curve is downward sloping is straightforward: the Federal
Funds rate is the interest rate banks charge each other to borrow reserves. When
that goes up, the price of borrowing goes up and banks want fewer reserves lent
to them.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
25 / 59
Supply and demand for reserves
The reason the demand curve is downward sloping is straightforward: the Federal
Funds rate is the interest rate banks charge each other to borrow reserves. When
that goes up, the price of borrowing goes up and banks want fewer reserves lent
to them.
When the FF ≤ DR, banks who want to lend out reserves only have the reserves
currently in their accounts to work with (the NBR).
In theory they could go to the Discount Window and borrow reserves to turn
around and lend them out again, but they’d lose money on every dollar of
reserves they did this with.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
25 / 59
Supply and demand for reserves
The reason the demand curve is downward sloping is straightforward: the Federal
Funds rate is the interest rate banks charge each other to borrow reserves. When
that goes up, the price of borrowing goes up and banks want fewer reserves lent
to them.
When the FF ≤ DR, banks who want to lend out reserves only have the reserves
currently in their accounts to work with (the NBR).
In theory they could go to the Discount Window and borrow reserves to turn
around and lend them out again, but they’d lose money on every dollar of
reserves they did this with.
But that’s not true when DRDR) to borrow from
another bank instead of the Fed.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
26 / 59
Discount Window Stigma
Question: Why might one think that the supply curve should be perfectly
horizontal at FF=DR, with banks willing to lend an infinite amount at this rate,
and the DR serving as a upper limit on FF?
If I’m a bank wanting to borrow reserves, if you charge me 3% but the Fed
charges me 2% at the Discount Window, I’ll just go with them, right?
In reality, there is a well documented ‘stigma’ surrounding borrowing reserves
from the Fed. Banks are willing to pay a premium (FF>DR) to borrow from
another bank instead of the Fed.
And banks that want to perform this ‘arbitrage’ need a bigger and bigger spread
to get them to do it.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
26 / 59
Monetary policy (changing NBR)
How do open market operations change the Federal Funds rate?
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
27 / 59
Monetary policy (changing NBR)
How do open market operations change the Federal Funds rate?
Open market operations change the quantity of reserves already in the accounts
of banks (the NBR):
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
27 / 59
The Fed-Funds rate and other interest rates?
Is the Fed Funds rate the same interest rate we saw in the last unit?
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
28 / 59
The Fed-Funds rate and other interest rates?
Is the Fed Funds rate the same interest rate we saw in the last unit?
Some interest rates (certain loans banks charge firms, flexible rate mortgages)
depend directly on the Fed Funds rate.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
28 / 59
The Fed-Funds rate and other interest rates?
Is the Fed Funds rate the same interest rate we saw in the last unit?
Some interest rates (certain loans banks charge firms, flexible rate mortgages)
depend directly on the Fed Funds rate.
The FFR also represents a cost that banks must pay to operate. Banks – like all
other for-profit institutions – pass a portion of those costs onto their customers
via higher interest rates (including longer term rates).
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
28 / 59
The Fed-Funds rate and other interest rates?
Is the Fed Funds rate the same interest rate we saw in the last unit?
Some interest rates (certain loans banks charge firms, flexible rate mortgages)
depend directly on the Fed Funds rate.
The FFR also represents a cost that banks must pay to operate. Banks – like all
other for-profit institutions – pass a portion of those costs onto their customers
via higher interest rates (including longer term rates).
To see how the federal funds could affect longer term interest rates that actually
affect household and firm spending, we’ll need to understand the yield curve.
Definition: The Yield Curve refers to the relationship between short term interest
rates and long term interest rates
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
28 / 59
The Yield Curve
Suppose banks are borrowing/lending reserves at the FF (an overnight rate)
Let’s say a bank is considering lending the funds out to a consumer for a month
instead. Let iM be the monthly rate they plan to charge.
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
29 / 59
The Yield Curve
Suppose banks are borrowing/lending reserves at the FF (an overnight rate)
Let’s say a bank is considering lending the funds out to a consumer for a month
instead. Let iM be the monthly rate they plan to charge.
If instead they kept lending the reserves out over-night, over and over, 30 times,
they could earn (1 + FF1 )(1 + E [FF2 ])(1 + E [FF3 ])…(1 + E [FF30 ]) = 1 + iFF
Wendy Morrison
Unit 2: Monetary Policy
May, 31 2022
29 / 59
The Yield Curve
Suppose banks are borrowing/lending reserves at the FF (an overnight rate)
Let’s say a bank is considering lending the funds out to a consumer for a month
instead. Let iM be the monthly rate they plan to charge.
If instead they kept lending the reserves out over-night, over and over, 30 times,
they could earn (1 + FF1 )(1 + E [FF2 ])(1 + E [FF3 ])…(1 + E [FF30 ]) = 1 + iFF
Suppose the bank was completely risk neutral. Could iM < iFF ? Why or why not? Wendy Morrison Unit 2: Monetary Policy May, 31 2022 29 / 59 The Yield Curve Suppose banks are borrowing/lending reserves at the FF (an overnight rate) Let’s say a bank is considering lending the funds out to a consumer for a month instead. Let iM be the monthly rate they plan to charge. If instead they kept lending the reserves out over-night, over and over, 30 times, they could earn (1 + FF1 )(1 + E [FF2 ])(1 + E [FF3 ])...(1 + E [FF30 ]) = 1 + iFF Suppose the bank was completely risk neutral. Could iM < iFF ? Why or why not? What if the bank was a bit risk averse? Wendy Morrison Unit 2: Monetary Policy May, 31 2022 29 / 59 The Yield Curve Suppose banks are borrowing/lending reserves at the FF (an overnight rate) Let’s say a bank is considering lending the funds out to a consumer for a month instead. Let iM be the monthly rate they plan to charge. If instead they kept lending the reserves out over-night, over and over, 30 times, they could earn (1 + FF1 )(1 + E [FF2 ])(1 + E [FF3 ])...(1 + E [FF30 ]) = 1 + iFF Suppose the bank was completely risk neutral. Could iM < iFF ? Why or why not? What if the bank was a bit risk averse? iFF = iM + δ where δ is a premium for Fed Funds rate risk. Wendy Morrison Unit 2: Monetary Policy May, 31 2022 29 / 59 The Yield Curve Suppose banks are borrowing/lending reserves at the FF (an overnight rate) Let’s say a bank is considering lending the funds out to a consumer for a month instead. Let iM be the monthly rate they plan to charge. If instead they kept lending the reserves out over-night, over and over, 30 times, they could earn (1 + FF1 )(1 + E [FF2 ])(1 + E [FF3 ])...(1 + E [FF30 ]) = 1 + iFF Suppose the bank was completely risk neutral. Could iM < iFF ? Why or why not? What if the bank was a bit risk averse? iFF = iM + δ where δ is a premium for Fed Funds rate risk. Assume δ is constant. If FF1 goes down, what must happen to iM ? Wendy Morrison Unit 2: Monetary Policy May, 31 2022 29 / 59 The Yield Curve Suppose banks are borrowing/lending reserves at the FF (an overnight rate) Let’s say a bank is considering lending the funds out to a consumer for a month instead. Let iM be the monthly rate they plan to charge. If instead they kept lending the reserves out over-night, over and over, 30 times, they could earn (1 + FF1 )(1 + E [FF2 ])(1 + E [FF3 ])...(1 + E [FF30 ]) = 1 + iFF Suppose the bank was completely risk neutral. Could iM < iFF ? Why or why not? What if the bank was a bit risk averse? iFF = iM + δ where δ is a premium for Fed Funds rate risk. Assume δ is constant. If FF1 goes down, what must happen to iM ? It goes down! Wendy Morrison Unit 2: Monetary Policy May, 31 2022 29 / 59 The Yield Curve Suppose banks are borrowing/lending reserves at the FF (an overnight rate) Let’s say a bank is considering lending the funds out to a consumer for a month instead. Let iM be the monthly rate they plan to charge. If instead they kept lending the reserves out over-night, over and over, 30 times, they could earn (1 + FF1 )(1 + E [FF2 ])(1 + E [FF3 ])...(1 + E [FF30 ]) = 1 + iFF Suppose the bank was completely risk neutral. Could iM < iFF ? Why or why not? What if the bank was a bit risk averse? iFF = iM + δ where δ is a premium for Fed Funds rate risk. Assume δ is constant. If FF1 goes down, what must happen to iM ? It goes down! What about if E (FF2 ) goes down? Wendy Morrison Unit 2: Monetary Policy May, 31 2022 29 / 59 What if we all stop using cash? Does it matter that the demand for cash has fallen significantly? Wendy Morrison Unit 2: Monetary Policy May, 31 2022 30 / 59 What if we all stop using cash? Does it matter that the demand for cash has fallen significantly? No! “the complete elimination of the use of currency in minor transactions would only make monetary control under current operating procedures easier, by making it simpler for the central bank to control the supply of bank reserves.” Wendy Morrison Unit 2: Monetary Policy May, 31 2022 30 / 59 What if we all stop using cash? Does it matter that the demand for cash has fallen significantly? No! “the complete elimination of the use of currency in minor transactions would only make monetary control under current operating procedures easier, by making it simpler for the central bank to control the supply of bank reserves.” Before, if consumers wanted to withdraw cash (and their demand for cash changes over time) banks would need to exchange their reserves for currency to meet the demand. Therefore, quantity of NBR changed over time! Without demand for cash, banks will no longer be trading in their reserves for currency. This gives the Fed even tighter control over NBR. Wendy Morrison Unit 2: Monetary Policy May, 31 2022 30 / 59 What if we all stop using cash? Does it matter that the demand for cash has fallen significantly? No! “the complete elimination of the use of currency in minor transactions would only make monetary control under current operating procedures easier, by making it simpler for the central bank to control the supply of bank reserves.” Before, if consumers wanted to withdraw cash (and their demand for cash changes over time) banks would need to exchange their reserves for currency to meet the demand. Therefore, quantity of NBR changed over time! Without demand for cash, banks will no longer be trading in their reserves for currency. This gives the Fed even tighter control over NBR. Think about our money multiplier - did the C/D ratio affect the ability of the CB to control the total money supply? Wendy Morrison Unit 2: Monetary Policy May, 31 2022 30 / 59 What if they demand for reserves changes? Why might the demand for borrowing reserves from other banks change? Remember, banks borrow reserves over-night because they are unable to perfectly predict their payment-withdrawal needs. Wendy Morrison Unit 2: Monetary Policy May, 31 2022 31 / 59 What if they demand for reserves changes? Why might the demand for borrowing reserves from other banks change? Remember, banks borrow reserves over-night because they are unable to perfectly predict their payment-withdrawal needs. What might better information processing do to this demand? Wendy Morrison Unit 2: Monetary Policy May, 31 2022 31 / 59 What if they demand for reserves changes? Why might the demand for borrowing reserves from other banks change? Remember, banks borrow reserves over-night because they are unable to perfectly predict their payment-withdrawal needs. What might better information processing do to this demand? What about if banks no longer need to go through the Fed to clear payments? Would they need reserves at all? Wendy Morrison Unit 2: Monetary Policy May, 31 2022 31 / 59 What if the demand for reserves changes? Is monetary policy still effective? I.e. can the central bank set any interest rate it wants? Wendy Morrison Unit 2: Monetary Policy May, 31 2022 32 / 59 Paying interest on reserves In the previous graph, demand for borrowing reserves has fallen significantly and become less interest rate elastic, requiring a significant contraction in the supply of reserves to control the rate and making controlling the rate more difficult. Wendy Morrison Unit 2: Monetary Policy May, 31 2022 33 / 59 Paying interest on reserves In the previous graph, demand for borrowing reserves has fallen significantly and become less interest rate elastic, requiring a significant contraction in the supply of reserves to control the rate and making controlling the rate more difficult. Paying a (non-zero) interest rate on reserve balances held at the Fed is a potential solution. Countries like New Zealand had been doing this for a while and the US started doing this in 2008 after years of lobbying Congress to gain approval. Wendy Morrison Unit 2: Monetary Policy May, 31 2022 33 / 59 Paying interest on reserves In the previous graph, demand for borrowing reserves has fallen significantly and become less interest rate elastic, requiring a significant contraction in the supply of reserves to control the rate and making controlling the rate more difficult. Paying a (non-zero) interest rate on reserve balances held at the Fed is a potential solution. Countries like New Zealand had been doing this for a while and the US started doing this in 2008 after years of lobbying Congress to gain approval. If the Fed pays interest on reserves, no bank will be willing to lend their reserves out for less than what they could earn at the Fed. In theory, the Fed could change the interest rate they pay on reserves to reflect its interest rate target. Wendy Morrison Unit 2: Monetary Policy May, 31 2022 33 / 59 Interest rate on reserves Wendy Morrison Unit 2: Monetary Policy May, 31 2022 34 / 59 Interest rate on reserves Why does the supply curve look like this now? Does it matter if demand fluctuates from D1 to D2 ? Wendy Morrison Unit 2: Monetary Policy May, 31 2022 34 / 59 Another reason for IOR Following the 2008 crisis, the Fed injected a very large amount of reserves into banks (it’s balance sheet went up by around 700 billion!). What would that look like on our graph of the interbank lending market? Wendy Morrison Unit 2: Monetary Policy May, 31 2022 35 / 59 Another reason for IOR Following the 2008 crisis, the Fed injected a very large amount of reserves into banks (it’s balance sheet went up by around 700 billion!). What would that look like on our graph of the interbank lending market? Wendy Morrison Unit 2: Monetary Policy May, 31 2022 35 / 59 IOR as a solution Wendy Morrison Unit 2: Monetary Policy May, 31 2022 36 / 59 IOR as a solution Wendy Morrison Unit 2: Monetary Policy May, 31 2022 36 / 59 Optimal Monetary Policy Wendy Morrison Unit 2: Monetary Policy May, 31 2022 37 / 59 How does the Fed choose an it ? We’ve discussed (1) how the Fed controls it and (2) how it affects spending and prices. But what does the Fed actually hope to achieve? Wendy Morrison Unit 2: Monetary Policy May, 31 2022 38 / 59 How does the Fed choose an it ? We’ve discussed (1) how the Fed controls it and (2) how it affects spending and prices. But what does the Fed actually hope to achieve? When thinking about what interest rate policy to set, the Fed takes into account its duel mandate: 1 ‘Full’ employment 2 Stable prices (low steady inflation) Wendy Morrison Unit 2: Monetary Policy May, 31 2022 38 / 59 How does the Fed choose an it ? We’ve discussed (1) how the Fed controls it and (2) how it affects spending and prices. But what does the Fed actually hope to achieve? When thinking about what interest rate policy to set, the Fed takes into account its duel mandate: 1 ‘Full’ employment 2 Stable prices (low steady inflation) Let’s go back to our New Keynesian model from the last unit, to see how a shock (i.e. a recession) plays out, and what monetary policy can do about the shock, and how the Fed weighs its two goals. Wendy Morrison Unit 2: Monetary Policy May, 31 2022 38 / 59 The NK model revisited We’ll make two adjustments to the NK presented in the previous unit: Wendy Morrison Unit 2: Monetary Policy May, 31 2022 39 / 59 The NK model revisited We’ll make two adjustments to the NK presented in the previous unit: 1 3 periods instead of 2 (t ∈ (1, 2, 3)) 2 Downwardly rigid wages (nominal wages can never go down) Wendy Morrison Unit 2: Monetary Policy May, 31 2022 39 / 59 The NK model revisited We’ll make two adjustments to the NK presented in the previous unit: 1 3 periods instead of 2 (t ∈ (1, 2, 3)) 2 Downwardly rigid wages (nominal wages can never go down) The first change will allow to add a ‘medium run’ period. Wendy Morrison Unit 2: Monetary Policy May, 31 2022 39 / 59 The NK model revisited We’ll make two adjustments to the NK presented in the previous unit: 1 3 periods instead of 2 (t ∈ (1, 2, 3)) 2 Downwardly rigid wages (nominal wages can never go down) The first change will allow to add a ‘medium run’ period. The second change will give us unemployment (why?) and let us study the concept of potential output. Potential output: the level of output such that all of the economy’s resources (in our case, all workers) are put to full use and there is no inflation. Wendy Morrison Unit 2: Monetary Policy May, 31 2022 39 / 59 Households Remember that households worked for the firm every period, earning wage Wt , and were able to save in a bond, bt . Wendy Morrison Unit 2: Monetary Policy May, 31 2022 40 / 59 Households Remember that households worked for the firm every period, earning wage Wt , and were able to save in a bond, bt . On the homework, you’ll solve the household’s optimization problem in 3 periods and show that they now have: 3 intra-temporal conditions instead of 2 2 Euler equations instead of 1 ct−σ = Wendy Morrison Pt −σ βt+1 (1 + i)ct+1 Pt+1 Unit 2: Monetary Policy May, 31 2022 40 / 59 Households Remember that households worked for the firm every period, earning wage Wt , and were able to save in a bond, bt . On the homework, you’ll solve the household’s optimization problem in 3 periods and show that they now have: 3 intra-temporal conditions instead of 2 2 Euler equations instead of 1 ct−σ = Pt −σ βt+1 (1 + i)ct+1 Pt+1 Note that the β terms now have a time subscript. This means they can change over time. Wendy Morrison Unit 2: Monetary Policy May, 31 2022 40 / 59 Households Remember that households worked for the firm every period, earning wage Wt , and were able to save in a bond, bt . On the homework, you’ll solve the household’s optimization problem in 3 periods and show that they now have: 3 intra-temporal conditions instead of 2 2 Euler equations instead of 1 ct−σ = Pt −σ βt+1 (1 + i)ct+1 Pt+1 Note that the β terms now have a time subscript. This means they can change over time. If there are only 3 periods, how much will the household save in the last period? Wendy Morrison Unit 2: Monetary Policy May, 31 2022 40 / 59 Households Remember that households worked for the firm every period, earning wage Wt , and were able to save in a bond, bt . On the homework, you’ll solve the household’s optimization problem in 3 periods and show that they now have: 3 intra-temporal conditions instead of 2 2 Euler equations instead of 1 ct−σ = Pt −σ βt+1 (1 + i)ct+1 Pt+1 Note that the β terms now have a time subscript. This means they can change over time. If there are only 3 periods, how much will the household save in the last period? Then what will they consume? Wendy Morrison Unit 2: Monetary Policy May, 31 2022 40 / 59 Households Remember that households worked for the firm every period, earning wage Wt , and were able to save in a bond, bt . On the homework, you’ll solve the household’s optimization problem in 3 periods and show that they now have: 3 intra-temporal conditions instead of 2 2 Euler equations instead of 1 ct−σ = Pt −σ βt+1 (1 + i)ct+1 Pt+1 Note that the β terms now have a time subscript. This means they can change over time. If there are only 3 periods, how much will the household save in the last period? Then what will they consume? c3 P3 = W3 Wendy Morrison Unit 2: Monetary Policy May, 31 2022 40 / 59 Firms Remember that ytj = Ljt and that firms set their prices according to the following equation: ϵ ϵ Pt = E [MCt ] = E [Wt ] 1−ϵ 1−ϵ Wendy Morrison Unit 2: Monetary Policy May, 31 2022 41 / 59 Firms Remember that ytj = Ljt and that firms set their prices according to the following equation: ϵ ϵ Pt = E [MCt ] = E [Wt ] 1−ϵ 1−ϵ A fraction α of the firms know the true marginal cost so E [MCt ] = Wt , while (1 − α) have to base their price off of their backward looking expectations, E [MCt ] = Wt−1 . Wendy Morrison Unit 2: Monetary Policy May, 31 2022 41 / 59 Firms Remember that ytj = Ljt and that firms set their prices according to the following equation: ϵ ϵ Pt = E [MCt ] = E [Wt ] 1−ϵ 1−ϵ A fraction α of the firms know the true marginal cost so E [MCt ] = Wt , while (1 − α) have to base their price off of their backward looking expectations, E [MCt ] = Wt−1 . Question: If nominal wages (Wt ) never go down, will there ever be deflation in this model? Wendy Morrison Unit 2: Monetary Policy May, 31 2022 41 / 59 Firms Remember that ytj = Ljt and that firms set their prices according to the following equation: ϵ ϵ Pt = E [MCt ] = E [Wt ] 1−ϵ 1−ϵ A fraction α of the firms know the true marginal cost so E [MCt ] = Wt , while (1 − α) have to base their price off of their backward looking expectations, E [MCt ] = Wt−1 . Question: If nominal wages (Wt ) never go down, will there ever be deflation in this model? Finally, remember that when we derived this relationship, we used the fact that demand for the output of each firm, ytj was a negative function of their price, p (law of demand). Wendy Morrison Unit 2: Monetary Policy May, 31 2022 41 / 59 Central Bank Finally, remember that we had a central bank that can set the nominal interest rate, it . Wendy Morrison Unit 2: Monetary Policy May, 31 2022 42 / 59 Central Bank Finally, remember that we had a central bank that can set the nominal interest rate, it . We’ll show that the Central Bank can achieve its policy goals by following a Taylor Rule of the form (ϕy and ϕπ are both positive): it = i¯ + ϕy (Yt − Ȳ ) + ϕπ (πt ) Where Ȳ is ‘potential output’ and Y − Ȳ is the ‘output gap’. Wendy Morrison Unit 2: Monetary Policy May, 31 2022 42 / 59 A shock to β Suppose their is a positive shock to β2 (intuition?). Holding all else equal, what happens to c1 ? c1−σ = Wendy Morrison P1 β2 (1 + i1 )c2−σ P2 Unit 2: Monetary Policy May, 31 2022 43 / 59 A shock to β Suppose their is a positive shock to β2 (intuition?). Holding all else equal, what happens to c1 ? c1−σ = P1 β2 (1 + i1 )c2−σ P2 Consumers demand less stuff today at current prices. Wendy Morrison Unit 2: Monetary Policy May, 31 2022 43 / 59 A shock to β Suppose their is a positive shock to β2 (intuition?). Holding all else equal, what happens to c1 ? c1−σ = P1 β2 (1 + i1 )c2−σ P2 Consumers demand less stuff today at current prices. Can firms lower their prices? Wendy Morrison Unit 2: Monetary Policy May, 31 2022 43 / 59 A shock to β Suppose their is a positive shock to β2 (intuition?). Holding all else equal, what happens to c1 ? c1−σ = P1 β2 (1 + i1 )c2−σ P2 Consumers demand less stuff today at current prices. Can firms lower their prices? No! Wages can’t fall, so firms keep prices constant, P1 = P0 and just produce less, Y1 = c1 . Wendy Morrison Unit 2: Monetary Policy May, 31 2022 43 / 59 A shock to β Suppose their is a positive shock to β2 (intuition?). Holding all else equal, what happens to c1 ? c1−σ = P1 β2 (1 + i1 )c2−σ P2 Consumers demand less stuff today at current prices. Can firms lower their prices? No! Wages can’t fall, so firms keep prices constant, P1 = P0 and just produce less, Y1 = c1 . How much labor do they demand then? Wendy Morrison Unit 2: Monetary Policy May, 31 2022 43 / 59 A shock to β Suppose their is a positive shock to β2 (intuition?). Holding all else equal, what happens to c1 ? c1−σ = P1 β2 (1 + i1 )c2−σ P2 Consumers demand less stuff today at current prices. Can firms lower their prices? No! Wages can’t fall, so firms keep prices constant, P1 = P0 and just produce less, Y1 = c1 . How much labor do they demand then? LD 1 = Y1 = c1 Wendy Morrison Unit 2: Monetary Policy May, 31 2022 43 / 59 A shock to β Suppose their is a positive shock to β2 (intuition?). Holding all else equal, what happens to c1 ? c1−σ = P1 β2 (1 + i1 )c2−σ P2 Consumers demand less stuff today at current prices. Can firms lower their prices? No! Wages can’t fall, so firms keep prices constant, P1 = P0 and just produce less, Y1 = c1 . How much labor do they demand then? LD 1 = Y1 = c1 Do workers want to work less? Recall that the first-period intra-temporal (labor supply) condition is: c1−σ W1 = Lγ1 Wendy Morrison Unit 2: Monetary Policy May, 31 2022 43 / 59 A shock to β Suppose their is a positive shock to β2 (intuition?). Holding all else equal, what happens to c1 ? c1−σ = P1 β2 (1 + i1 )c2−σ P2 Consumers demand less stuff today at current prices. Can firms lower their prices? No! Wages can’t fall, so firms keep prices constant, P1 = P0 and just produce less, Y1 = c1 . How much labor do they demand then? LD 1 = Y1 = c1 Do workers want to work less? Recall that the first-period intra-temporal (labor supply) condition is: c1−σ W1 = Lγ1 1 No! If anything they want to work more. LS1 = (W1 /c1σ ) γ Wendy Morrison Unit 2: Monetary Policy May, 31 2022 43 / 59 Potential output and the ‘output gap’ We just saw that when a β shock causes demand to fall, downwardly rigid nominal wages means that the amount of labor demanded is less than the amount that workers are willing to supply at that wage. Therefore we do not have full employment. Wendy Morrison Unit 2: Monetary Policy May, 31 2022 44 / 59 Potential output and the ‘output gap’ We just saw that when a β shock causes demand to fall, downwardly rigid nominal wages means that the amount of labor demanded is less than the amount that workers are willing to supply at that wage. Therefore we do not have full employment. Question: could firms employ more labor and therefore produce more without raising prices? Wendy Morrison Unit 2: Monetary Policy May, 31 2022 44 / 59 Potential output and the ‘output gap’ We just saw that when a β shock causes demand to fall, downwardly rigid nominal wages means that the amount of labor demanded is less than the amount that workers are willing to supply at that wage. Therefore we do not have full employment. Question: could firms employ more labor and therefore produce more without raising prices? Yes! How do we know this? Wendy Morrison Unit 2: Monetary Policy May, 31 2022 44 / 59 Potential output and the ‘output gap’ We just saw that when a β shock causes demand to fall, downwardly rigid nominal wages means that the amount of labor demanded is less than the amount that workers are willing to supply at that wage. Therefore we do not have full employment. Question: could firms employ more labor and therefore produce more without raising prices? Yes! How do we know this? Right now, LS (W1 ) − LD (W1 ) > 0, so firms could easily induce more workers to
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