Money and Inflation
Money Demand
Price Indices: Pt
• Two most commonly used price indices
are GDP Deflator and Consumer Price
Index (CPI)
• The CPI is the price of a representative
market basket of goods relative to the
price of that same basket during a
benchmark/base year (multiplied by 100).
• The GDP deflator is the ratio of nominal
GDP to Real GDP (multiplied by 100).
Nominal GDP GDP
P  GDP Deflator 

Real GDP
Y
Hong Kong CPI vs. GDP Deflator
120
100
80
60
40
20
19
75
19
77
19
79
19
81
19
83
19
85
19
87
19
89
19
91
19
93
19
95
19
97
19
99
20
01
20
03
0
CPI
GDP Deflator
CPI vs. GDP Deflator
• CPI is calculated monthly, GDP deflator is
calculated quarterly.
• CPI measures the price of consumer goods.
GDP deflator measures the price of all goods
produced including investment or government
goods.
• CPI measures the change in price of a constant
market basket. Market basket of GDP deflator
changes as goods produced changes.
The Data
• Data on money supply is inevitably
measured by the central bank and usually
the data is available for free.
Example: Hong Kong Monetary Authority
• Data on
Listing of Central Bank Websites.
What is a central bank?
• Central banks have two main roles:
– Banker to the government
• Manage many financial assets of the government.
• Monopoly on the issue of banknotes/currency (true
almost everywhere, but not HK)
• Arm of government policymaking
– Banker to commercial banks.
• Operate the Payment System
• Regulate Banking System
• Lender of Last Resort during a crisis
• Central Bank:
A special
governmental
organization or
quasigovernmental
institution within
the financial
system that
controls the
medium of
exchange.
Economy
Central Bank
HK
Hong Kong
Monetary Authority
USA
Federal Reserve
EU
European
Central Bank
People’s Bank of
China
Bank of ….
PRC
UK,
Canada,
Japan,
Korea
Readings
• Money Demand
– Branson, Chapter 14, especially p.335-339
– Sachs Chapter 8
• Inflation
Money
• Financial Asset Used in
Transactions
• Legal Tender: Government
accepts money as payment for
taxes and a transfer of money as a
settlement for a contract.
Characteristics of Money
1. Medium of Exchange – Token that can be offered
as a payment for goods.
2. Unit of Account – All goods will have a value in
money and, thus, can be used to measure all
goods
3. Store of Value – If money is to be accepted for
goods today it must have durable value. (Money is
an Asset).
Two categories of money
1. Definitive Money (sometimes known as
monetary base): Money that can be used
immediately for transactions without
conversion to more basic forms of money.
– Currency+ Reserve accounts
2. Broad Money: A set of assets, typically
some form of bank deposit, which can be
easily converted to definitive money.
– Checking Accounts, Savings Accounts, Liquid
Time Deposits and CD’s
Categories
of Broad
Money
M1
M2
M3
M1 Currency
+ Checking Acct.
M2 +Savings Acct.
+ “More Liquid”
Time Deposit
M3 + “Less Liquid”
Time Deposit
China
0.3
0.25
0.2
0.15
0.1
0.05
0
1999
2000
2001
2002
2003
2004
2005
-0.05
Inflation
Money
2006
2007
2008
2009
2010
Velocity
0.85
0.8
0.75
0.7
0.65
0.6
0.55
0.5
0.45
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
Mpney Types in HK
M3
M1
M2
Incremental M3 is trivial in HK
HK$ Money Categories
Source: HKMA http://www.info.gov.hk
Legal
tender notes
and coins
in hands
of public
Demand
deposits
with
licensed
banks
M1
145,852
207,444
353,297
Savings
deposits
with
licensed
banks
Time
deposits
with
licensed
banks
NCDs
issued by
licensed
banks
and held
by public
M2
788,211
1,288,193
76,342
2,506,043
Broad Money vs. Narrow Money
• Broad money has grown much faster than
narrow money.
• Narrow money is money directly controlled
by the government.
• Broad money includes money printed by the
government plus deposits at banks.
• Money multiplier is ratio of broad money to
narrow money.
Categories
• M0 = Reserves + Cash
• M2 = Cash + Demand Deposits + Savings
Deposits
CDS
MM 

RC
C
S
1
D
D 1
R C

D D
Determinant of the Multiplier.
• The greater is the currency-deposit ratio the
smaller is the multiplier.
• The greater is the savings to demand
deposit ratio the greater is the multiplier.
• The higher is the fraction of deposits kept
on reserve, the smaller is the multiplier.
Money Multiplier in China
14
12
24000
20000
10
16000
8
12000
6
8000
4
4000
0
90 91 92 93 94 95 96 97 98 99 00 01 02 03 04
MULTIPLIER
M2
M0
Monetary Theory
• Two Assets
• Money (M) can be used for transactions but
pays no interest.
• Bonds (B) will pay a nominal interest rate of i
but cannot be used for transactions.
• If you buy a bond with $1, you will get $(1+i)
from the issuer of the bond.
Liquidity Problem
• The household earns an income equal to (PQ)
which they will spend evenly over the course of a
month.
• If they keep their whole income in their backpocket to do shopping they will lose interest
income.
• If they buy interest earning bonds with all of their
income, they will have to make many costly trips
to the bank when they want to buy goods. The
cost of each trip to the bank will be P∙b.
Liquidity Strategy
• Household strategy will be to keep a
share of their income in the form of
money, M*, and put the rest into bonds.
• They will spend that money until it is
gone, return to the bank, and convert
bonds into M* again.
Choose # of trips to the bank.
• The household will have to make P  Y
*
M
trips to the bank.
• The average balances held by the
household will be M *
2
Money holdings over the month
Money
M*
M*
2
time
Bond holdings over the month
Bonds
time
Costs of Strategy
M
• If the household is on average holding 2
they will forego the opportunity to earn
interest equal to M *
i
2
• The total transactions costs of converting
their bonds into cash is
P Y
P b  *
M
*
Minimize Total Costs
• Total liquidity costs of holding M*
P Y
M
P b  *  i 
M
2
*
• Choose the number of trips that would
minimize the total costs (including interest
costs).
Cost Minimization
• Trade-off: The more trips you make, the
more interest you will earn but the less will
be the transactions cost.
– Choosing the number of trips is equivalent to
choosing M*
Optimal Money Demand
• Money demand is an increasing function of the
price level, and output and a decreasing
function of interest rates.
P Y
M
min TC ( M )  P  b  *  i 
M*
M
2
P Y
i
2bY
*
TC '  0  P  b 
 M P
2
2
i
M*
*
*
 
M
 2bY 



P  i 
*
1
2
Money Demand
• Intuition: The greater is P and Y, the greater
are the need for money for transactions. The
greater is i, the greater the interest rate
costs.
• Money Demand is typically represented in
terms of money divided by the price level,
referred to as real balances. M
P
Money Demand Curve
i
Y↑
M
P
Velocity
• Velocity is defined as the speed at which
money circulates or as the number of
transactions that each unit of money is
used in per period.
• Velocity is measured as the ratio of current
dollar GDP to the money supply.
PY
Yt
t t
V

Mt Mt
Pt
BT Theory and Velocity
• According to Baumol-Tobin theory, money
velocity should grow with output.
• Asian experience suggests the opposite.
• Possible reason: If b represents the costs
of goods that could have been produced in
the absence of a trip to the bank, b would
likely grow with productivity.
Long Run
• Demand for real balances a proportional
function of GDP as well as a function of
interest rates.
Mt
Mt
 Yt f (it ) ex.
 v  Yt  1 
it
Pt
Pt

• The higher is the interest rate, the more willing
the household is to incur the costs of not
holding cash.
Empirical Studies of Money
Demand
• The Baumol Tobin model suggests a loglinear form.
Mt
ln
 a0  a1 ln Yt  a2 ln it
Pt
mt  a0  a1 yt  a2 ln i
Empirical Studies of Money
Demand
• The Baumol Tobin model suggests a log-linear
form.
Mt
ln
 a0  a1 ln Yt  a2 ln it
Pt
mt  a0  a1 yt  a2 ln i
• Empirical reality suggests that this does not
capture short-term endogeneity between money,
interest rates, and output.
Inflation
• We are concerned with explaining the rate
of change of the price level or the inflation
rate
Pt  Pt 1
P
t 
Pt 1
  ln Pt 
P
• First difference the log of the money
demand function
 log M t   t   log Yt   log it
g  t  g   g
M
t
Y
t
i
t
Money Growth and the Nominal
Interest Rate
• Define the real interest rate, as the amount
of extra goods that can be gained, if you
give up 1 good today.
1  it 

1
1  rt 
 1  it   Pt  Pt 1
Pt 1
Pt

1  it 
1   t 1 
 rt  it   t 1
Long Run Inflation Rate
• Assume that there is a long run inflation
rate and real variables are unaffected by
inflation in the long run.
Δln i = 0
• Then long run inflation is money growth
minus output growth.
 g g
M
Y
Neo-classical Dichotomy
• Assume given Y and r which is not affected by
money supply or growth rate.
– Money is just paper which should not affect real
outcomes.
• Then, in the long run, we can solve for the
price level as a function of the level of money
and output and their growth rates (in addition
to the real interest rate).
Price Level
• Then, in the long run, we can solve for the
price level as a function of the level of
money and output and their growth rates
(in addition to the real interest rate).

1M
M
Y
P
 rg g
v Y


Socially Optimal Inflation Rate
• Friedman Rule: Socially optimal inflation rate
sets the interest rate equal to zero.
• If the interest rate were zero, workers in
Baumol and Tobin model would keep all of
their pay in cash and not have to make any
costly trips to the bank.
• Set money growth gM = r - gY
Zero Lower Bound
• Friedman rule interest rate is also theoretical
lower bound on the interest rate.
• Nominal interest rates on bonds cannot go
below 0 because there is a freely available asset
that always pays an interest rate at least equal to
zero.
• Main objection to Friedman rule is that if we have
a long run zero interest rate, the central bank will
never be in a position to reduce interest rates.
ZIRP: Japan
JP: Call Rate: Uncollaterized: Overnight
% pa
10
9
8
7
6
5
4
3
2
1
0
Jul-1985
Jul-1988
Jul-1991
Jul-1994
Jul-1997
Jul-2000
Jul-2003
Jul-2006
Why inflation?
• If zero or negative inflation is socially
optimal, why is it so pervasive.
• Possible reason (especially in developing
world): It is a source of government
revenue (called seignorage).
• When the government prints new currency,
it can use the money to pay off its old debts
or buy new goods.
Real Seignorage
• Amount of goods purchased by the printing
of money
M t  M t 1 M t  M t 1 M t 1 M t
gM M


Pt
M t 1
M t Pt 1  g M P
• The higher is the money growth rate, the
higher is the fraction of real balances that
can be collected through seignorage.
Substitution Effect
• Higher money growth reduces demand for
real balances. Higher inflation will mean
higher interest rates, which will mean that
people will spend money more quickly which
drives up prices at a given output level.
• Assume r = gY, i=gM
g


g
M
g
M 

g
Y 
Y
M
M
M
1 g P 1 g
1 g
M
M
M 1 
Inflation Tax
% of Y
gM
How does declining money demand
reduce the seignorage revenue?
• Consumers facing high inflation and thus
high interest rates, want to hold relatively low
money balances and are willing to make
more trips to the bank.
• With a given amount of money chasing a
given amount of output more quickly, prices
will be higher and the amount that any newly
printed dollar will buy will be reduced.
Hyper Inflation
• Hyperinflation occurs when inflation increases at
a rate of 50% or more per month.
• In the long run, this rate of inflation is counterproductive to the government in terms of raising
seignorage.
• Usually, a sign of a government trying to
maximize short-term revenue by accelerating
money growth faster than inflationary
expectations.
– Prices in China rose 250000% in Chungking from
1937-1945.
Current Chinese Inflation Rates
• Between 1984 and 1996, China frequently
had very high inflation rates, reaching to
levels of 20% or more per year.
• Since then inflation has been steady or
decreasing.
Chinese CPI and Broad Money
25000
20000
15000
10000
400
5000
350
0
300
250
200
150
90 91 92 93 94 95 96 97 98 99 00 01 02 03 04
CPICHINA
M2
Velocity in China
5
4.5
4
3.5
3
M1 Velocity
2.5
M2 Velocity
2
1.5
1
0.5
20
01
20
03
19
99
19
95
19
97
19
91
19
93
19
89
19
85
19
87
19
81
19
83
19
79
0
Deposits are major channel for
saving in PRC
Bank Deposits as Share of GDP
200.0%
180.0%
160.0%
140.0%
120.0%
100.0%
80.0%
60.0%
40.0%
20.0%
0.0%
China
USA
Money & Inflation: 1975-1994
Inflation & Money OECD Countries
0.2
0.18
Average Inflation Rate
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0
0.02
0.04
0.06
0.08
0.1
0.12
Average Money Growth
0.14
0.16
0.18
Causes of Extremely Rapid Inflation
• Government generates revenues by printing
new money (referred to as seignorage).
• Government facing borrowing constraints
may be forced to rely on inflation tax for
deficit financing.
19
70
19
71
19
72
19
73
19
74
19
75
19
76
19
77
19
78
19
79
19
80
19
81
19
82
19
83
19
84
19
85
19
86
19
87
19
88
19
89
19
90
Israel 1970-1990
Inflation
400
350
300
250
200
150
100
50
0
Israel 1970-1990
Surplus (% of GDP)
5.00%
-5.00%
-10.00%
-15.00%
-20.00%
-25.00%
-30.00%
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
1977
1976
1975
1974
1973
1972
1971
1970
0.00%
Hyperinflation
Mid-term Exam III
• Monday, December 13th 4:30-7:30PM
• Lecture Theater A
• Semi-open Book (Bring 1 A4 size paper
with handwritten notes)) also calculator
and writing instruments.
• Coverage. Lecture notes including this
one.
• Lecture Theater A, 4:30-7:30