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Chapter11
Inflation, Money Growth,
and Interest Rates
Macroeconomics
Chapter 11
1
Cross-Country Data on Inflation and
Money Growth
Ms = P· L(Y, i)

Key equation:

Two possible reasons of inflation:

Decrease of real demand for money

Increase of money supply
Macroeconomics
Chapter 11
2
Cross-Country Data on Inflation and
Money Growth


Inflation rates and money growth
rates for 82 countries from 1960 to
2000.
We measure the price level, P, by
the consumer price index (CPI). We
use the CPI, rather than the GDP
deflator, because of data availability.
Macroeconomics
Chapter 11
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Macroeconomics
Chapter 11
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Macroeconomics
Chapter 11
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Macroeconomics
Chapter 11
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Cross-Country Data on Inflation and
Money Growth

Highlights



The inflation rate was greater than 0
for all countries from 1960 to 2000
The growth rate of nominal currency
was greater than 0 for all countries
from 1960 to 2000.
There is a broad cross-sectional range
for the inflation rates and the growth
rates of money.
Macroeconomics
Chapter 11
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Cross-Country Data on Inflation and
Money Growth

Highlights


The median inflation rate from 1960 to
2000 was 8.3% per year, with 30
countries exceeding 10%.
For the growth rate of nominal currency,
the median was 11.6% per year, with
50 above 10%
Macroeconomics
Chapter 11
8
Cross-Country Data on Inflation and
Money Growth

Highlights



In most countries, the growth rate of
nominal currency, M, exceeded the
growth rate of prices.
For a country that has a high inflation
rate in one period to have a high
inflation rate in another period.
Strong positive association between the
inflation rate and the growth rate of
nominal currency.
Macroeconomics
Chapter 11
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Cross-Country Data on Inflation and
Money Growth
Macroeconomics
Chapter 11
10
Cross-Country Data on Inflation and
Money Growth

One lesson from the cross-country data is
that, to understand inflation, we have to
include money growth as a central part of
the analysis.

Milton Friedman’s famous dictum:
“Inflation is always and
everywhere a monetary
phenomenon.”
Macroeconomics
Chapter 11
11
Inflation and Interest Rates

Actual and Expected Inflation



Let π be the inflation rate. The inflation
rate from year 1 to year 2, π1, is the
ratio of the change in the price level to
the initial price level.
π1 = ( P2 − P1)/ P1
π1 = ∆P1/ P1
Macroeconomics
Chapter 11
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Inflation and Interest Rates

Actual and Expected Inflation

π1 = ( P2 − P1)/ P1
π1 = ∆P1/ P1
π1 · P1 = P2 − P1

P2 = ( 1 +π1) · P1


Macroeconomics
Chapter 11
13
Inflation and Interest Rates

Actual and Expected Inflation



Since the future is unknown,
households have to form forecasts or
expectations of inflation.
Denote by πe1 the expectation of the
inflation rate π1.
The actual inflation rate, π1, will usually
deviate from its expectation, πe1, and
the forecast error—or unexpected
inflation—will be nonzero.
Macroeconomics
Chapter 11
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Inflation and Interest Rates

Actual and Expected Inflation


Households try to keep the errors as
small as possible. Therefore, they use
available information on past inflation
and other variables to avoid systematic
mistakes.
Expectations formed this way are called
rational expectations.
Macroeconomics
Chapter 11
15
Inflation and Interest Rates

Real and Nominal Interest Rates

The dollar value of assets held as
bonds rises over the year by the factor
1 + i1. The interest rate i1 is the dollar
or nominal interest rate because i1
determines the change over time in the
nominal value of assets held as bonds.
Macroeconomics
Chapter 11
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Inflation and Interest Rates
Macroeconomics
Chapter 11
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Inflation and Interest Rates

Real and Nominal Interest Rates



The Real interest rate to be the rate
at which the real value of assets held
as bonds changes over time.
dollar assets in year2 =
( dollar assets in year1)·(1+ i1)
P2 = P1 · ( 1 + π1)
Macroeconomics
Chapter 11
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Inflation and Interest Rates

Real and Nominal Interest Rates


(dollar assets in year2/P2 )=
(dollar assets in year1/P1) ·
(1+i1)/(1+π1)
real assets in year2 =
(real assets in year1) · (1+i1)/(1+π1)
Macroeconomics
Chapter 11
19
Inflation and Interest Rates

Real and Nominal Interest Rates


Since the real interest rate, denoted by
r1, is the rate at which assets held as
bonds change in real value:
(1+r1) = (1+i1)/(1+π1)
Macroeconomics
Chapter 11
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Inflation and Interest Rates

Real and Nominal Interest Rates

r1 = i1 − π1 − r1·π1


the cross term, r1 · π1, which tends to be
small;
real interest rate= nominal interest
rate− inflation rate

r1 = i1 − π1
Macroeconomics
Chapter 11
21
Inflation and Interest Rates

Fisher Equation
i

= r +π
Fisher Effect
Macroeconomics
i
Chapter 11
π
22
Inflation and Interest Rates

The Real Interest Rate and
Intertemporal Substitution

When the inflation rate, π, is not zero,
it is the real interest rate, r, rather than
the nominal rate, i, that matters for
intertemporal substitution.
Macroeconomics
Chapter 11
23
Inflation and Interest Rates

Actual and Expected Real Interest
Rates



The expected inflation rate determines
the expected real interest rate, ret
r e t = it − π e t
expected real interest rate= nominal interest rate
− expected inflation rate
Macroeconomics
Chapter 11
24
Inflation and Interest Rates

Measuring expected inflation



Ask a sample of people about their expectations.
Use the hypothesis of rational expectations,
which says that expectations correspond to
optimal forecasts, given the available information.
Then use statistical techniques to gauge these
optimal forecasts.
Use market data to infer expectations of inflation
Macroeconomics
Chapter 11
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Inflation and Interest Rates

Measuring expected inflation


Livingston Survey
Ask a sample of people（50 economists）
about their expectations.
Macroeconomics
Chapter 11
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Inflation and Interest Rates
Macroeconomics
Chapter 11
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Inflation and Interest Rates
Macroeconomics
Chapter 11
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Inflation and Interest Rates

Measuring expected inflation


Indexed bonds, real interest rates, and
expected inflation rates
Indexed government bonds, which adjust
nominal payouts of interest and principal
for changes in consumer-price indexes.
These bonds guarantee the real interest
rate over the maturity of each issue.
Macroeconomics
Chapter 11
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Inflation and Interest Rates
Macroeconomics
Chapter 11
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Inflation and Interest Rates
Macroeconomics
Chapter 11
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Inflation and Interest Rates

Interest Rates on Money

real interest rate on money=
nominal interest rate on money − πt

real interest rate on money = −πt
Macroeconomics
Chapter 11
32
Inflation in the Equilibrium BusinessCycle Model

Goals


To see how inflation affects our
conclusions about the determination of
real variables, including real GDP,
consumption and investment,
quantities of labor and capital services,
the real wage rate, and the real rental
price.
To understand the causes of inflation.
Macroeconomics
Chapter 11
33
Inflation in the Equilibrium BusinessCycle Model


Assume fully anticipated inflation,
so that the inflation rate, πt, equals
the expected rate, πet .
Extend the equilibrium businesscycle model to allow for money
growth.
Macroeconomics
Chapter 11
34
Inflation in the Equilibrium BusinessCycle Model

Assume the government prints new
currency and gives it to people.


They receive a transfer payment
from the government.
The payments are lump-sum
transfers, meaning that the amount
received is independent of how much
the household consumes and works,
how much money the household holds,
and so on.
Macroeconomics
Chapter 11
35
Inflation in the Equilibrium BusinessCycle Model

Intertemporal-Substitution Effects


The expected real interest rate, ret ,
has intertemporal-substitution effects
on consumption and labor supply.
Therefore, for given it, a change in πt
will have these intertemporalsubstitution effects.
Macroeconomics
Chapter 11
36
Inflation in the Equilibrium BusinessCycle Model

Bonds and Capital



i = (R/P)·κ − δ(κ)
Replace the nominal interest rate on
bonds, i, by the real rate, r,
r = (R/P)·κ − δ(κ)
Macroeconomics
Chapter 11
37
Inflation in the Equilibrium BusinessCycle Model

Interest Rates and the Demand for Money

The tradeoff between earning assets and
holding money is


( i − π) − (−π) = i
Therefore, the nominal interest rate, i, still
determines the cost of holding money rather
than earning assets. We can therefore still
describe real money demand by the function
Md / P = L( Y, i )
Macroeconomics
Chapter 11
38
Inflation in the Equilibrium BusinessCycle Model

Interest Rates and the Demand for
Money


It is the real interest rate, r, that has
intertemporal-substitution effects on
consumption and labor supply.
It is the nominal interest, i, that
influences the real demand for money,
Md/P.
Macroeconomics
Chapter 11
39
Inflation in the Equilibrium BusinessCycle Model
Macroeconomics
Chapter 11
40
Inflation in the Equilibrium BusinessCycle Model
Macroeconomics
Chapter 11
41
Inflation in the Equilibrium BusinessCycle Model

Inflation and the Real Economy


A change in the inflation rate, π, does
not shift the demand or supply curve
for capital services. Therefore, ( R/P) *
and (κK) * do not change.
A change in the inflation rate, π, does
not shift the demand or supply curve
for labor. Therefore, ( w/ P) * and L*
do not change.
Macroeconomics
Chapter 11
42
Inflation in the Equilibrium BusinessCycle Model

Inflation and the Real Economy

Real GDP, Y, is determined by the
production function
Y= A· F(κ K, L)

We conclude that a change in π does
not influence real GDP, Y.
Macroeconomics
Chapter 11
43
Inflation in the Equilibrium BusinessCycle Model

Inflation and the Real Economy


The real rental price, R/P, and the capital
utilization rate, κ, determine the real
rate of return from owning capital,
(R/P) · κ − δ(κ), and therefore the real
interest rate, r,
r = ( R/ P) · κ − δ(κ) .
Since R/P and κ are unchanged, we find
that a change in the inflation rate, π,
does not affect the real interest rate, r.
Macroeconomics
Chapter 11
44
Inflation in the Equilibrium BusinessCycle Model

Inflation and the Real Economy


If we continue to ignore income effects
from inflation, π, we know that C does
not change.
Since Y is fixed, we conclude that I
does not change.
Macroeconomics
Chapter 11
45
Inflation in the Equilibrium BusinessCycle Model



We have found that the time paths of
money growth and inflation do not affect a
group of real variables.
This group comprises real GDP, Y; inputs of
labor and capital services, L and κK;
consumption and investment, C and I; the
real wage rate, w/P; the real rental price,
R/P; and the real interest rate, r.
The neutrality of money apply, as an
approximation, to the entire path of money
growth.
Macroeconomics
Chapter 11
46
Inflation in the Equilibrium BusinessCycle Model

Money Growth, Inflation, and the
Nominal Interest Rate


Analyze how the time path of the
nominal quantity of money, Mt,
determines the time path of the price
level, Pt, and, hence, the inflation
rate,πt.
We also assume for now that Yt and rt
are constant over time.
Macroeconomics
Chapter 11
47
Inflation in the Equilibrium BusinessCycle Model

Money Growth, Inflation, and the
Nominal Interest Rate






∆Mt =Mt+1−Mt
µt = ∆Mt/Mt
Mt+1 = (1+µt)·Mt
πt = ∆ Pt/ Pt
πt = (Pt+1−Pt)/Pt
Pt+1 = (1+πt)·Pt
Macroeconomics
Chapter 11
48
Inflation in the Equilibrium BusinessCycle Model

Money Growth, Inflation, and the
Nominal Interest Rate

Show that


When Mt grows steadily at the rate µ, the
price level, Pt, will also grow steadily at
the rate µ.
π=µ
Macroeconomics
Chapter 11
49
Inflation in the Equilibrium BusinessCycle Model

Money Growth, Inflation, and the
Nominal Interest Rate

The real quantity of money demanded,
L(Y, i), does not vary over time.
real GDP, Y, is fixed.
 i = r+ π
 i = r+ µ


Since we assumed that r and µ are fixed, i is
unchanging. Since Y and i are fixed, we have
verified that the real quantity of money
demanded, L(Y, i), is unchanging.
Macroeconomics
Chapter 11
50
Inflation in the Equilibrium BusinessCycle Model

Money Growth, Inflation, and the
Nominal Interest Rate

The level of real money demanded, L(Y,
i), equals the unchanging level of real
money balances, Mt/Pt .

L(Y, i) and Mt/Pt are both fixed over time.
Therefore, if the levels of the two
variables are equal in the current year,
year 1,they will remain equal in every
future year.
Macroeconomics
Chapter 11
51
Inflation in the Equilibrium BusinessCycle Model

Money Growth, Inflation, and the
Nominal Interest Rate

Determination of price level:


P1 = M1 / L( Y, i)
πt, is the constant π = µ.
Macroeconomics
Chapter 11
52
Inflation in the Equilibrium BusinessCycle Model

Money Growth, Inflation, and the
Nominal Interest Rate



The inflation rate, π, equals the
unchanging growth rate of money, µ.
Real money balances, Mt/Pt, are fixed
over time.
The nominal interest rate, i, equals r + µ,
where r is the unchanging real interest
rate.
Macroeconomics
Chapter 11
53
Inflation in the Equilibrium BusinessCycle Model

Money Growth, Inflation, and the
Nominal Interest Rate


The real quantity of money demanded,
L(Y, i), is fixed over time, where Y is
the unchanging real GDP.
P1 = M1 / L( Y, i)
Macroeconomics
Chapter 11
54
Inflation in the Equilibrium BusinessCycle Model

A Trend in the Real Demand for
Money

Assume that L(Y, i) grows steadily at
the constant rate γ .

This growth might reflect long-term
growth of real GDP
Macroeconomics
Chapter 11
55
Inflation in the Equilibrium BusinessCycle Model

A Trend in the Real Demand for
Money


Real money balances, Mt/Pt, increase
because of growth in the numerator, Mt,
at the rate µ, but decrease because of
growth in the denominator, Pt, at the
rate π.
growth rate of Mt/ Pt = µ − π
Macroeconomics
Chapter 11
56
Inflation in the Equilibrium BusinessCycle Model

A Trend in the Real Demand for
Money

If L(Y, i) grows at rate γ , Mt/Pt must
also grow at rate γ.

γ=µ−π

π=µ−γ
Macroeconomics
Chapter 11
57
Inflation in the Equilibrium BusinessCycle Model
Macroeconomics
Chapter 11
58
Inflation in the Equilibrium BusinessCycle Model

A Shift in the Money Growth Rate

Suppose that the monetary authority
raises the money growth rate from µ to
µ’ in year T.
Macroeconomics
Chapter 11
59
Inflation in the Equilibrium BusinessCycle Model
Macroeconomics
Chapter 11
60
Inflation in the Equilibrium BusinessCycle Model

A Shift in the Money Growth Rate




i’− i = µ’ − µ
Mt/Pt is constant before year T.
Mt/Pt is constant after year T.
Mt/Pt after year T is lower than that
before year T (because of the rise in
the nominal interest rate from i to i’).
Macroeconomics
Chapter 11
61
Inflation in the Equilibrium BusinessCycle Model

Government Revenue from Printing
Money


Have assumed, thus far, that the
monetary authority prints new money
(currency) and gives it to households as
transfer payments.
Governments get revenue from
printing money and can use this
revenue to pay for a variety of
expenditures.
Macroeconomics
Chapter 11
62
Inflation in the Equilibrium BusinessCycle Model

Government Revenue from Printing
Money

Nominal revenue from printing money
= Mt+1−Mt = ∆Mt


Real revenue from printing money
= ∆Mt/ Pt+1
Real money growth rate
µt = ∆ Mt/ Mt
Macroeconomics
Chapter 11
63
Inflation in the Equilibrium BusinessCycle Model

Government Revenue from Printing
Money

Real revenue from printing money
= µt·( Mt /Pt+1)
≈ µt·( Mt / Pt )
= (money growth rate) · (level of real
money balances)
Macroeconomics
Chapter 11
64
Macroeconomics
Chapter 11
65