money and monetary policy - kids in prison program · money and monetary policy an introduction....
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Money and Monetary Policy
An Introduction
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Lecture Outline
• Money – Definition and Functions
• Determinants of Money Demand
• Money Supply
– Role of the Central Bank
– Role of commercial banks
– Money Multiplier
• Long-run relationship between money and prices
• LM curve - short-run relationship between output and the interest rate equilibrating money demand and supply.
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Money: Definition
Money is the stock of assets that can be readily used to make
transactions.
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Money: Functions
• medium of exchangewe use it to buy stuff
• store of valuetransfers purchasing power from the present to the future
• unit of accountthe common unit by which everyone measures prices and values
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Money: Types
1. Fiat money
– has no intrinsic value
– example: the paper currency we use
2. Commodity money
– has intrinsic value
– examples: gold coins, cigarettes in P.O.W. camps
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Money Demand
• Why do we want to hold money?– To Purchase goods and services.
• regular expenses
• Unexpected expenses
• What would we expect our demand for money to depend on?
• Income or output
• Prices
• That is, our demand for dollars depends on Nominal GDP
• We can also express this as demand for real money balances M/P depending on real GDP, Y.
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Cost of holding money
• Why might we not want to hold our wealth in the form of money? To keep things simple, let us assume we can either hold our financial assets as money, which pays no interest, or bonds which pay a nominal interest rate of i.– By holding money we are forgoing the possibility
of earning interest that we could earn if we held bonds instead.
– Thus the nominal interest rate represents the opportunity cost of holding money.
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The money demand function
(M/P)d = real money demand, depends
– negatively on i
i is the opp. cost of holding money
– positively on Y
higher Y more spending
so, need more money
(“L” is used for the money demand function because money is the most liquid asset.)
( ) ( , )dM P L i Y
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The money supply and monetary policy definitions
• The money supply is the quantity of money available in the economy.
• Monetary policy is the control over the money supply.
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The central bank and monetary control• Monetary policy is conducted by a country’s central
bank.
• The U.S.’ central bank is called the Federal Reserve(“the Fed”).
• To control the money supply, the Fed primarily uses open market operations, the purchase and sale of government bonds.
The Federal Reserve Building
Washington, DC
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11 of 32
iP
P
B
B
$100 $
$ $
$100P
iB 1
The Determination of the Interest Rate
Treasury bills, or T-bills are issued by the U.S. government
promising payment in a year or less. If you buy the bond
today and hold it for a year, the rate of return (or interest) on
holding a $100 bond for a year is ($100 - $PB)/$PB.
If we are given the interest rate, we can figure out the price
of the bond using the same formula.
How do Open Market Operations affect the interest rate?
Bond Prices and Bond Yields
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Open Market Operations and the Interest Rate
Open market operations in which the central bank increases the money supply by buying bonds lead to an increase in the price of bonds by increasing the demand and therefore to a decrease in the interest rate.
Open market operations in which the central bank decreases the money supply by selling bonds lead to a decrease in the price of bonds by increasing the supply relative to demand, and therefore to an increase in the interest rate.
Therefore, by changing the supply of money, the central bank can affect the interest rate.
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The Determination of the Interest RateMoney Demand, Money Supply, and the Equilibrium
Interest Rate
An increase in the supply of
money leads to a decrease in
the interest rate.
The Effects of an
Increase in the Money
Supply on the Interest
Rate
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Money supply measures, December 2012
10,402
M1 + small time deposits,
savings deposits,
money market mutual funds,
money market deposit accounts
M2
2,440
C + demand deposits,
travelers’ checks,
other checkable deposits
M1
1,159CurrencyC
amount
($ billions)assets includedsymbol
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Banks’ role in the monetary system
• The money supply equals currency plus demand (checking account) deposits:
M = C + D
• Since the money supply includes demand deposits, the banking system plays an important role.
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A few preliminaries
• Reserves (R): the portion of deposits that banks have not lent.
• A bank’s liabilities include deposits;
assets include reserves and outstanding loans.
• 100-percent-reserve banking: a system in which banks hold all deposits as reserves.
• Fractional-reserve banking: a system in which banks hold a fraction of their deposits as reserves.
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Banks’ role in the monetary system
• To understand the role of banks, we will consider three scenarios:1. No banks
2. 100-percent-reserve banking(banks hold all deposits as reserves)
3. Fractional-reserve banking(banks hold a fraction of deposits as reserves, use the rest to make loans)
• In each scenario, we assume C = $1,000.
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SCENARIO 1:
No banks
With no banks, D = 0 and M = C = $1,000.
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SCENARIO 2:
100-percent-reserve banking
• After the deposit: C = $0, D = $1,000, M = $1,000
• LESSON:100%-reserve banking has no impact on size of money supply.
FIRSTBANK’S
balance sheet
Assets Liabilities
reserves $1,000 deposits $1,000
Initially C = $1000, D = $0, M = $1,000.
Now suppose households deposit the $1,000 at
“Firstbank.”
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FIRSTBANK’S
balance sheet
Assets Liabilities
reserves $1,000reserves $200
loans $800
SCENARIO 3:
Fractional-reserve banking
The money supply now equals $1,800:
–Depositor has $1,000 in demand deposits.
–Borrower holds $800 in currency.
deposits $1,000
Suppose banks hold 20% of deposits in reserve,
making loans with the rest.
Firstbank will make $800 in loans.
LESSON: in a fractional-reserve
banking system, banks create money.
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SECONDBANK’S
balance sheet
Assets Liabilities
reserves $800
loans $0
reserves $160
loans $640
SCENARIO 3:
Fractional-reserve banking
• Secondbank will loan 80% of this deposit.
deposits $800
Suppose the borrower deposits the $800 in
Secondbank.
Initially, Secondbank’s balance sheet is:
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SCENARIO 3:
Fractional-reserve banking
THIRDBANK’S
balance sheet
Assets Liabilities
deposits $640
If this $640 is eventually deposited in Thirdbank,
then Thirdbank will keep 20% of it in reserve
and loan the rest out:
reserves $640
loans $0
reserves $128
loans $512
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Finding the total amount of money:
Original deposit = $1000
+ Firstbank lending = $ 800
+ Secondbank lending = $ 640
+ Thirdbank lending = $ 512
+ other lending…
Total money supply = (1/rr ) $1,000
where rr = ratio of reserves to deposits
In our example, rr = 0.2, so M = $5,000
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Money creation in the banking system
A fractional-reserve banking system creates
money, but it doesn’t create wealth:
Bank loans give borrowers some new money
and an equal amount of new debt.
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Bank capital, leverage, and capital requirements
• Bank capital: the resources a bank’s owners have put into the bank
• A more realistic balance sheet:
AssetsLiabilities and
Owners’ Equity
Reserves $200 Deposits $750
Loans 500 Debt 200
Securities 300Capital (owners’ equity)
50
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Bank capital, leverage, and capital requirements
• Leverage: the use of borrowed money to supplement existing funds for purposes of investment
• Leverage ratio = assets/capital
= $(200+500+300)/$50 = 20
AssetsLiabilities and
Owners’ Equity
Reserves $200 Deposits $750
Loans 500 Debt 200
Securities 300Capital (owners’ equity)
50
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Bank capital, leverage, and capital requirements
• Being highly leveraged makes banks vulnerable.
• Example: Suppose a recession causes our bank’s assets to fall by 5%, to $950.
• Then, capital = assets – liabilities = 950 – 950 = 0
AssetsLiabilities and
Owners’ Equity
Reserves $200 Deposits $750
Loans 500 Debt 200
Securities 300Capital (owners’ equity)
50
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Bank capital, leverage, and capital requirements
Capital requirement:
– minimum amount of capital mandated by regulators
– intended to ensure banks will be able to pay off depositors
– higher for banks that hold more risky assets
2008-2009 financial crisis:
– Losses on mortgages shrank bank capital, slowed lending, exacerbated the recession.
– Govt injected $ billions of capital into banks to ease the crisis and encourage more lending.
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A model of the money supply
• Monetary base, B = C + R
controlled by the central bank
• Reserve-deposit ratio, rr = R/D
depends on regulations & bank policies
• Currency-deposit ratio, cr = C/D
depends on households’ preferences
exogenous variables
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Solving for the money supply:
M C D C D
BB
m B
C D
C R
1cr
cr rr
C Dm
B
where
C D D D
C D R D
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The money multiplier
• If rr < 1, then m > 1
• If monetary base changes by B, then M = m B
• m is the money multiplier, the increase in the money supply resulting from a one-dollar increase in the monetary base.
1crm
cr rr
where,M m B
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NOW YOU TRY
The money multiplier
32
Suppose households decide to hold more of their money as currency and less in the form of demand deposits.
1. Determine impact on money supply.
2. Explain the intuition for your result.
1crm
cr rr
where,M m B
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SOLUTION
The money multiplier
33
Impact of an increase in the currency-deposit ratio cr > 0.
1. An increase in cr increases the denominator
of m proportionally more than the numerator.
So m falls, causing M to fall.
2. If households deposit less of their money,
then banks can’t make as many loans,
so the banking system won’t be able to
create as much money.
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The instruments of monetary policy
The Fed can change the monetary base using– open market operations (the Fed’s preferred
method of monetary control)• To increase the base,
the Fed could buy government bonds, paying with new dollars.
– the discount rate: the interest rate the Fed charges on loans to banks• To increase the base,
the Fed could lower the discount rate, encouraging banks to borrow more reserves
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The instruments of monetary policy
The Fed can change the reserve-deposit ratio using
– reserve requirements: Fed regulations that impose a minimum reserve-deposit ratio• To reduce the reserve-deposit ratio,
the Fed could reduce reserve requirements
– interest on reserves: the Fed pays interest on bank reserves deposited with the Fed• To reduce the reserve-deposit ratio,
the Fed could pay a lower interest rate on reserves
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Why the Fed can’t precisely control M
• Households can change cr, causing m and M to change.
• Banks often hold excess reserves(reserves above the reserve requirement).
If banks change their excess reserves, then rr, m, and M change.
,M m B 1cr
mcr rr
where
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CASE STUDY:
Quantitative Easing
0
500
1,000
1,500
2,000
2,500
3,000
1956 1961 1966 1971 1976 1981 1986 1991 1996 2001 2006
bill
ion
s o
f d
olla
rs
Monetary base
From 8/2008 to 8/2011,
the monetary base tripled,
but M1 grew only about 40%.
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CASE STUDY:
Quantitative Easing• Quantitative easing: the Fed bought long-term govt
bonds instead of T-bills to reduce long-term rates.
• The Fed also bought mortgage-backed securities to help the housing market.
• But after losses on bad loans, banks tightened lending standards and increased excess reserves, causing money multiplier to fall.
• If banks start lending more as economy recovers, rapid money growth may cause inflation. So far, inflation has remained relatively low, and in some countries is even negative.
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The Long-Run Relationship between Money, Prices and Inflation
• Next we want to examine the relationship between money and prices, and money growth and the inflation rate.
• We will also examine the relationship between the inflation rate, the real interest rate and the nominal interest rate.
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0%
2%
4%
6%
8%
10%
12%
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
% c
han
ge fro
m 1
2 m
os. ea
rlie
rU.S. inflation and its trend,
1960–2012
% change in
GDP deflator
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0%
2%
4%
6%
8%
10%
12%
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
% c
han
ge fro
m 1
2 m
os. ea
rlie
rU.S. inflation and its trend,
1960–2012
long-run trend
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The quantity theory of money
• A simple theory linking the inflation rate to the growth rate of the money supply.
• Begins with the concept of velocity…
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Velocity• basic concept:
the rate at which money circulates
• definition: the number of times the average dollar bill changes hands in a given time period
• example: In 2012,
– $500 billion in transactions
– money supply = $100 billion
– The average dollar is used in five transactions in 2012
– So, velocity = 5
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Velocity, cont.
• This suggests the following definition:T
VM
where
V = velocity
T = value of all transactions
M = money supply
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Velocity, cont.
• Use nominal GDP as a proxy for total transactions.
Then, P Y
VM
where
P = price of output (GDP deflator)
Y = quantity of output (real GDP)
P Y = value of output (nominal GDP)
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The quantity equation• The quantity equation
M V = P Yfollows from the preceding definition of velocity.
• It is an identity:it holds by definition of the variables.
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The Quantity Theory of Money
• starts with quantity equation
• assumes V is constant & exogenous:
Then, quantity equation becomes:
V V
M V P Y
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The quantity theory of money, cont.
How the price level is determined:
– Real GDP is determined by the economy’s
supplies of K and L and the production function.
– With V constant, the money supply determines
nominal GDP (P Y ).
– The price level is
P = (nominal GDP)/(real GDP).
M V P Y
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The quantity theory of money, cont.
• Recall from earlier: The growth rate of a product equals the sum of the growth rates.
• The quantity equation in growth rates:
M V P Y
M V P Y
The quantity theory of money assumes
is constant, so = 0.V
VV
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The quantity theory of money, cont.
(Greek letter pi )
denotes the inflation rate:
M P Y
M P Y
P
P
M Y
M Y
The result from the
preceding slide:
Solve this result
for :
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The quantity theory of money, cont.
• Normal economic growth requires a certain amount of money supply growth to facilitate the growth in transactions.
• Money growth in excess of this amount leads to inflation.
M Y
M Y
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The quantity theory of money, cont.
Y/Y depends on growth in the factors of
production and on technological progress
(all of which we take as given, for now).
M Y
M Y
Hence, the quantity theory predicts
a one-for-one relation between
changes in the money growth rate and
changes in the inflation rate.
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Confronting the quantity theory with data
The quantity theory of money implies:
1. Countries with higher money growth rates
should have higher inflation rates.
2. The long-run trend in a country’s inflation rate
should be similar to the long-run trend in the
country’s money growth rate.
Are the data consistent with these implications?
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International data on inflation and money growth
Infl
atio
n r
ate
(per
cen
t)
Money supply growth(percent)
-5
0
5
10
15
20
25
30
35
40
-10 0 10 20 30 40 50
China
IraqTurkey
Belarus
Zambia
U.S.
Mexico
Malta
Cyprus
Serbia
Suriname
Russia
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0%
2%
4%
6%
8%
10%
12%
14%
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
% c
han
ge fro
m 1
2 m
os. ea
rlie
rU.S. inflation and money growth,
1960–2012
M2 growth rate
inflation rate
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0%
2%
4%
6%
8%
10%
12%
14%
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
% c
han
ge fro
m 1
2 m
os. ea
rlie
rU.S. inflation and money growth,
1960–2012Inflation and money growth
have the same long-run trends,
as the quantity theory predicts.
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Inflation and interest rates
• Nominal interest rate, inot adjusted for inflation
• Real interest rate, radjusted for inflation:
r = i
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The Fisher effect
• The Fisher equation: i = r +
• S = I determines r.
• Hence, an increase in causes an equal increase in i.
• This one-for-one relationship is called the Fisher effect.
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-2%
2%
6%
10%
14%
18%
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
U.S. inflation and nominal interest rates, 1960–2012
inflation rate
nominal
interest rate
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Inflation and nominal interest rates in 96 countries
Nominal
interest rate(percent)
Inflation rate(percent)
0
5
10
15
20
25
30
35
40
-5 0 5 10 15 20 25
MalawiGeorgia
Turkey
Ghana
Iraq
U.S.
Poland
Japan
Brazil
Kazakhstan
Mexico
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NOW YOU TRY
Applying the theory
Suppose V is constant, M is growing 5% per year, Y is growing 2% per year, and r = 4.
a. Solve for i.
b. If the Fed increases the money growth rate by 2 percentage points per year, find i.
c. Suppose the growth rate of Y falls to 1% per year.
• What will happen to ?
• What must the Fed do if it wishes to keep constant?
61
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Two real interest rates
Notation:
• = actual inflation rate (not known until after it has occurred)
• E = expected inflation rate
• Two real interest rates:
• i – E = ex ante real interest rate: the real interest rate people expect at the time they buy a bond or take out a loan
• i – = ex post real interest rate:the real interest rate actually realized
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The money demand function
When people are deciding whether to hold money or bonds, they don’t know what inflation will turn out to be.
Hence, the nominal interest rate relevant for money demand is r + E.
( ) ( , )dM P L i Y
( , ) rL YE
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Equilibrium
( , ) M
L r YP
E
The supply of real
money balances Real money
demand
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The LM curve
The LM curve is a graph of all combinations of r and
Y that equate the supply and demand for real
money balances.
Thus the equation for the LM curve is the
equilibrium condition:
Or rewritten as Y = f(r) or r = g(Y)
( , ) M
L r YP
E
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Deriving the LM curve
M/P
r
1M
P
L (r ,Y1 )
r1
r2
r
YY1
r1L (r ,Y2 )
r2
Y2
LM
(a) The market for
real money balances(b) The LM curve
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Why the LM curve is upward sloping
• An increase in income raises money demand.
• Since the supply of real balances is fixed, there is now excess demand in the money market at the initial interest rate.
• The interest rate must rise to restore equilibrium in the money market.
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How M shifts the LM curve
M/P
r
1M
P
L (r ,Y1 )r1
r2
r
YY1
r1
r2
LM1
(a) The market for
real money balances(b) The LM curve
2M
P
LM2
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The short-run equilibrium
The short-run equilibrium is the
combination of r and Y that
simultaneously satisfies the
equilibrium conditions in the
goods & money markets:
( ) ( )Y C Y T I r G
Y
r
( , )M P L r Y
IS
LM
Equilibrium
interest
rate
Equilibrium
level of
income