Inflation, Money Growth,

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C h a p t e r 1 1
Inflation, Money Growth, and Interest Rates
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Cross-Country Data on Inflation and Money Growth

• Key equation Ms P L(Y, i)
• Two possible reasons of inflation
• Decrease of real demand for money
• Increase of money supply

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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 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.

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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.
• 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.

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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 Friedmans famous dictum Inflation is
  always and everywhere a monetary phenomenon.

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Inflation and Interest Rates

• Actual and Expected Inflation
• Let p be the inflation rate. The inflation rate
  from year 1 to year 2, p1, is the ratio of the
  change in the price level to the initial price
  level.
• p1 ( P2 - P1)/ P1
• p1 ?P1/ P1

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Inflation and Interest Rates

• Actual and Expected Inflation
• p1 ( P2 - P1)/ P1
• p1 ?P1/ P1
• p1 P1 P2 - P1
• P2 ( 1 p1) 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 pe1 the expectation of the inflation
  rate p1.
• The actual inflation rate, p1, will usually
  deviate from its expectation, pe1, and the
  forecast erroror unexpected inflationwill 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 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 p1)

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Inflation and Interest Rates

• Real and Nominal Interest Rates
• (dollar assets in year2/P2 )
• (dollar assets in year1/P1)
• (1i1)/(1p1)
• real assets in year2
• (real assets in year1) (1i1)/(1p1)

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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
• (1r1) (1i1)/(1p1)

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Inflation and Interest Rates

• Real and Nominal Interest Rates
• r1 i1 - p1 - r1p1
• the cross term, r1 p1, which tends to be small
• real interest rate nominal interest rate-
  inflation rate
• r1 i1 - p1

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Inflation and Interest Rates

• Fisher Equation
• i r p
• Fisher Effect i p

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Inflation and Interest Rates

• The Real Interest Rate and Intertemporal
  Substitution
• When the inflation rate, p, is not zero, it is
  the real interest rate, r, rather than the
  nominal rate, i, 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 - pet
• expected real interest rate nominal interest
  rate - expected inflation rate

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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

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Inflation and Interest Rates

• Measuring expected inflation
• Livingston Survey
• Ask a sample of people(50 economists) 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

• 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

• Interest Rates on Money
• real interest rate on money
• nominal interest rate on money - pt
• real interest rate on money -pt

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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 labor 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, pt, equals the expected rate, pet
  .
• 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
  intertemporal-substitution effects on consumption
  and labor supply.
• Therefore, for given it, a change in pt will have
  these intertemporal-substitution effects.

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Inflation in the Equilibrium Business-Cycle Model

• Bonds and Capital
• i (R/P)? - d(?)
• Replace the nominal interest rate on bonds, i, by
  the real rate, r,
• r (R/P)? - d(?)

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Inflation in the Equilibrium Business-Cycle Model

• Interest Rates and the Demand for Money
• The tradeoff between earning assets and holding
  money is
• ( i - p) - (-p) 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
  intertemporal-substitution effects on consumption
  and labor supply.
• 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
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Inflation in the Equilibrium Business-Cycle Model
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Inflation in the Equilibrium Business-Cycle Model

• Inflation and the Real Economy
• A change in the inflation rate, p, does not shift
  the demand or supply curve for capital services.
  Therefore, ( R/P) and (?K) do not change.
• A change in the inflation rate, p, does not shift
  the demand or supply curve for labor. Therefore,
  ( w/ P) and L do not change.

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Inflation in the Equilibrium Business-Cycle Model

• Inflation and the Real Economy
• Real GDP, Y, is determined by the production
  function
• Y A F(? K, L)
• We conclude that a change in p 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, ?, determine the real rate of
  return from owning capital, (R/P) ? - d(?), and
  therefore the real interest rate, r,
• r ( R/ P) ? - d(?) .
• Since R/P and ? are unchanged, we find that a
  change in the inflation rate, p, does not affect
  the real interest rate, r.

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Inflation in the Equilibrium Business-Cycle Model

• Inflation and the Real Economy
• If we continue to ignore income effects from
  inflation, p, we know that C does not change.
• Since Y is fixed, we conclude that I does not
  change.

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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 labor
  and capital services, L and ?K 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.

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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,pt.
• 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 Mt1-Mt
• µt ?Mt/Mt
• Mt1 (1µt)Mt
• pt ? Pt/ Pt
• pt (Pt1-Pt)/Pt
• Pt1 (1pt)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.
  
• p 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 p
• 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)
• pt, is the constant p µ.

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Inflation in the Equilibrium Business-Cycle Model

• Money Growth, Inflation, and the Nominal Interest
  Rate
• The inflation rate, p, 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.
• P1 M1 / L( Y, i)

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Inflation in the Equilibrium Business-Cycle Model

• A Trend in the Real Demand for Money
• Assume that L(Y, i) grows steadily at the
  constant rate ? .
• 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 p.
• growth rate of Mt/ Pt µ - p

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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 ? , Mt/Pt must also grow
  at rate ?.
• ? µ - p
• p µ - ?

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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 µ 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
• 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).

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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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Inflation in the Equilibrium Business-Cycle Model

• Government Revenue from Printing Money
• Nominal revenue from printing money
• Mt1-Mt ?Mt
• Real revenue from printing money
• ?Mt/ Pt1
• Real 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 /Pt1)
• µt( Mt / Pt )
• (money growth rate) (level of real
  money balances)

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