money and monetary policy - kids in prison program · money and monetary policy an introduction....

Money and Monetary Policy

An Introduction

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.

Money: Definition

Money is the stock of assets that can be readily used to make

transactions.

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

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

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.

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.

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

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.

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

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

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.

13 of 32

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

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

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.

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.

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.

SCENARIO 1:

No banks

With no banks, D = 0 and M = C = $1,000.

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.”

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.

SECONDBANK’S

balance sheet

Assets Liabilities

reserves $800

loans $0

reserves $160

loans $640

SCENARIO 3:


• Secondbank will loan 80% of this deposit.

deposits $800

Suppose the borrower deposits the $800 in

Secondbank.

Initially, Secondbank’s balance sheet is:

SCENARIO 3:


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

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

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.

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


• Leverage: the use of borrowed money to supplement existing funds for purposes of investment

• Leverage ratio = assets/capital

= $(200+500+300)/$50 = 20


Owners’ Equity


Loans 500 Debt 200


50


• 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


Owners’ Equity


Loans 500 Debt 200


50


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.

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

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

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

NOW YOU TRY


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

SOLUTION


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.

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

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

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

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%.

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.

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.

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

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

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…

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

Velocity, cont.

• This suggests the following definition:T

VM

where

V = velocity

T = value of all transactions

M = money supply

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)

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.

The Quantity Theory of Money

• starts with quantity equation

• assumes V is constant & exogenous:

Then, quantity equation becomes:

V V

M V P Y

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


• 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


(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 :


• 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


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.

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?

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

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

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.

Inflation and interest rates

• Nominal interest rate, inot adjusted for inflation

• Real interest rate, radjusted for inflation:

r = i

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.

-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

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

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

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

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

Equilibrium

( , ) M

L r YP

E

The supply of real

money balances Real money

demand

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

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

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.

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

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

money and monetary policy - kids in prison program · money and monetary policy an introduction....

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