PowerPoint Slides
to accompany
Prepared by Apostolos Serletis
University of Calgary
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1
Chapter11
Inflation, Money Growth,
and Interest Rates
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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.
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Cross-Country Data on Inflation and Money
Growth
• Highlights
– The inflation rate was greater than zero for all
countries from 1960 to 2000
– The growth rate of nominal currency was greater than
zero for all countries from 1960 to 2000.
– There is a broad cross-sectional range for the inflation
rates and the growth rates of money.
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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%
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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.
– There is a tendency for a country that has a high
inflation rate in one period to have a high inflation rate
in another period.
– There is strong positive association between the
inflation rate and the growth rate of nominal currency.
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Cross-Country Data on Inflation and Money
Growth
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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.”
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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
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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
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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.
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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.
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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.
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Inflation and Interest Rates
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Inflation and Interest Rates
• Real and Nominal Interest Rates
– The real interest rate is the rate at which the real
value of assets held as bonds changes over time.
dollar assets in year 2 =
(dollar assets in year 1)·(1+ i1)
P2 = P1 · ( 1 + π1)
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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)
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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)
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Inflation and Interest Rates
• Real and Nominal Interest Rates
r1 = i1 − π1 − r1·π1
the cross term, r1·π1, tends to be small. Hence,
– real interest rate = nominal interest rate − inflation
rate:
r1 = i1 − π1
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Inflation and Interest Rates
• The Real Interest Rate and Intertemporal
Substitution
– When the inflation rate, π1, is not zero, it is the real
interest rate, r1, rather than the nominal rate, i1, that
matters for intertemporal substitution.
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Inflation and Interest Rates
• Actual and Expected Real Interest Rates
– The expected inflation rate determines the expected
real interest rate, ret
ret = it − πet
(expected real interest rate =
nominal interest rate − expected inflation rate)
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Inflation and Interest Rates
• Actual and Expected Real Interest Rates
– Measuring expected inflation
• Ask a sample of people about their expectations.
• Use the adaptive expectations hypothesis
• 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
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Inflation and Interest Rates
• Actual and Expected Real Interest Rates
– Measuring expected inflation
• Ask a sample of people about their expectations.
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Inflation and Interest Rates
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Inflation and Interest Rates
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Inflation and Interest Rates
• Actual and Expected Real 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.
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Inflation and Interest Rates
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Inflation and Interest Rates
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Inflation and Interest Rates in the United
States
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Inflation and Interest Rates in the United
States
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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
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Inflation in the Equilibrium Business-Cycle
Model
• Goals
– To see how inflation affects our conclusions about the
determination of real variables, including real GDP,
consumption and investment, quantities of labour and
capital services, the real wage rate, and the real
rental price.
– To understand the causes of inflation.
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Inflation in the Equilibrium Business-Cycle
Model
• Assume fully anticipated inflation, so that the
inflation rate, πt, equals the expected rate, πet .
• Extend the equilibrium business-cycle model to
allow for money growth.
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Inflation in the Equilibrium Business-Cycle
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.
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Inflation in the Equilibrium Business-Cycle
Model
• Intertemporal-Substitution Effects
– The expected real interest rate, ret , has intertemporalsubstitution effects on consumption and labour
supply.
– Therefore, for given it, a change in πt will have these
intertemporal-substitution effects.
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Inflation in the Equilibrium Business-Cycle
Model
• Bonds and Capital
– Households still hold two forms of earning assets:
bonds and ownership of capital and the rates of return
on these two assets have to be equal. Therefore,
when the inflation rate, π, was zero, we got the
condition:
i = (R/P)·κ − δ(κ)
(rate of return on bonds =
rate of return from owning capital)
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Inflation in the Equilibrium Business-Cycle
Model
• Bonds and Capital
– When the inflation rate, π, is nonzero, the expression
(R/P)·κ − δ(κ) gives the real rate of return from
owning capital.
– Replace the nominal interest rate on bonds, i, by the
real rate, r:
r = ( R/ P) · κ − δ(κ)
(real rate of return on bonds =
real rate of return from owning capital)
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Inflation in the Equilibrium Business-Cycle
Model
• Interest Rates and the Demand for Money
– The real interest rate on earning assets is r = i − π,
and the real interest rate on money is −π. The
difference between the two real interest rates 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)
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Inflation in the Equilibrium Business-Cycle
Model
• Interest Rates and the Demand for Money
– It is the real interest rate, r, that has intertemporalsubstitution effects on consumption and labour
supply.
– However, it is the nominal interest, i, that influences
the real demand for money, Md/P.
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Inflation in the Equilibrium Business-Cycle
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 labour. Therefore, (w/P)*
and L* do not change.
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Inflation in the Equilibrium Business-Cycle
Model
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Inflation in the Equilibrium Business-Cycle
Model
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44
Inflation in the Equilibrium Business-Cycle
Model
• Inflation and the Real Economy
– Real GDP, Y, is determined by the production
function
Y = A· F(κ K, L)
– We know that a change in the inflation rate, π, does
not affect the inputs of capital services and labour, κK
and L. Since the technology level, A, is fixed, we
conclude that a change in π does not influence real
GDP, Y.
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Inflation in the Equilibrium Business-Cycle
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.
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46
Inflation in the Equilibrium Business-Cycle
Model
• Inflation and the Real Economy
– If we continue to ignore income effects from inflation,
π, we know that consumption, C, does not change.
– Since Y is fixed, we conclude that investment, I, does
not change.
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47
Inflation in the Equilibrium Business-Cycle
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 labour 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.
• Therefore, our earlier results on the neutrality of money—which
referred to a one-time change in the nominal quantity, M—apply, as
an approximation, to the entire path of money growth.
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48
Inflation in the Equilibrium Business-Cycle
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.
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Inflation in the Equilibrium Business-Cycle
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
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Inflation in the Equilibrium Business-Cycle
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
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Inflation in the Equilibrium Business-Cycle
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.
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Inflation in the Equilibrium Business-Cycle
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.
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Inflation in the Equilibrium Business-Cycle
Model
• Money Growth, Inflation, and the Nominal
Interest Rate
– Determination of price level:
P1 = M1 / L(Y, i)
πt, is the constant π = µ.
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Inflation in the Equilibrium Business-Cycle
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.
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Inflation in the Equilibrium Business-Cycle
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.
– Year 1’s price level, P1, equates year 1’s real money
balances, M1/P1, to the real quantity demanded, L(Y,
i).
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Inflation in the Equilibrium Business-Cycle
Model
• A Trend in the Real Demand for Money
– Assume that the real quantity of money demanded,
L(Y, i), grows steadily at the constant rate γ .
• This growth might reflect long-term growth of real
GDP
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Inflation in the Equilibrium Business-Cycle
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. Hence,
growth rate of Mt/Pt = µ − π
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Inflation in the Equilibrium Business-Cycle
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
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Inflation in the Equilibrium Business-Cycle
Model
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Inflation in the Equilibrium Business-Cycle
Model
• A Shift in the Money Growth Rate
– Suppose that the monetary authority raises the
money growth rate from µ to µʹ in year T.
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Inflation in the Equilibrium Business-Cycle
Model
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Inflation in the Equilibrium Business-Cycle
Model
• A Shift in the Money Growth Rate
– The red line shows that the nominal quantity of
money, Mt, grows at the constant rate µ before year
T. After year T, Mt grows along the brown line at the
higher rate µ.
– The blue line shows that the price level, Pt, grows at
the same rate as money, µ, before year T.
– After year T, Pt grows along the green line at the
same rate as money, µ. The price level, Pt, jumps
upward during year T. This jump reduces real money
balances, Mt/Pt, from the level prevailing before year
T to that prevailing after year T.
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Inflation in the Equilibrium Business-Cycle
Model
• A Shift in the Money Growth Rate
iʹ- i = µʹ − µ
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Inflation in the Equilibrium Business-Cycle
Model
• A Shift in the Money Growth Rate
– 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 iʹ).
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Inflation in the Equilibrium Business-Cycle
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.
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66
Inflation in the Equilibrium Business-Cycle
Model
• Government Revenue from Printing Money
– Nominal revenue from printing money
= Mt+1−Mt = ∆Mt
– Real revenue from printing money
= ∆Mt/Pt+1
– Money growth rate
µt = ∆Mt/Mt
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Inflation in the Equilibrium Business-Cycle
Model
• Government Revenue from Printing Money
– Real revenue from printing money
= µt·(Mt/Pt+1)
– Real revenue from printing money
≈ µt·(Mt/P)
= (money growth rate)·(level of real money
balances)
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