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Macroeconomics Chapter 111 Inflation, Money Growth, and Interest Rates C h a p t e r 1 1

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Macroeconomics Chapter 112 Cross-Country Data on Inflation and Money Growth Key equation: M s = P · L(Y, i) Two possible reasons of inflation: Decrease of real demand for money Increase of money supply

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Macroeconomics Chapter 113 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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Macroeconomics Chapter 114

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7 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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Macroeconomics Chapter 118 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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Macroeconomics Chapter 119 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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Macroeconomics Chapter 1110 Cross-Country Data on Inflation and Money Growth

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Macroeconomics Chapter 1111 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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Macroeconomics Chapter 1112 Inflation and Interest Rates Actual and Expected Inflation Let π be the inflation rate. The inflation rate from year 1 to year 2, π 1, is the ratio of the change in the price level to the initial price level. π 1 = ( P 2 − P 1 )/ P 1 π 1 = ∆P 1 / P 1

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Macroeconomics Chapter 1113 Inflation and Interest Rates Actual and Expected Inflation π 1 = ( P 2 − P 1 )/ P 1 π 1 = ∆P 1 / P 1 π 1 · P 1 = P 2 − P 1 P 2 = ( 1 +π 1 ) · P 1

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Macroeconomics Chapter 1114 Inflation and Interest Rates Actual and Expected Inflation Since the future is unknown, households have to form forecasts or expectations of inflation. Denote by π e 1 the expectation of the inflation rate π 1. The actual inflation rate, π 1, will usually deviate from its expectation, π e 1, and the forecast error — or unexpected inflation — will be nonzero.

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Macroeconomics Chapter 1115 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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Macroeconomics Chapter 1116 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 + i 1. The interest rate i 1 is the dollar or nominal interest rate because i 1 determines the change over time in the nominal value of assets held as bonds.

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Macroeconomics Chapter 1117 Inflation and Interest Rates

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Macroeconomics Chapter 1118 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 year 2 = ( dollar assets in year 1 ) · (1+ i 1 ) P 2 = P 1 · ( 1 + π 1 )

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Macroeconomics Chapter 1119 Inflation and Interest Rates Real and Nominal Interest Rates (dollar assets in year 2 /P 2 )= (dollar assets in year 1 /P 1 ) · (1+i 1 )/(1+π 1 ) real assets in year 2 = (real assets in year 1 ) · (1+i 1 )/(1+π 1 )

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Macroeconomics Chapter 1120 Inflation and Interest Rates Real and Nominal Interest Rates Since the real interest rate, denoted by r 1, is the rate at which assets held as bonds change in real value: (1+r 1 ) = (1+i 1 )/(1+π 1 )

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Macroeconomics Chapter 1121 Inflation and Interest Rates Real and Nominal Interest Rates r 1 = i 1 − π 1 − r 1 · π 1 the cross term, r 1 · π 1, which tends to be small; real interest rate= nominal interest rate− inflation rate r 1 = i 1 − π 1

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Macroeconomics Chapter 1122 Inflation and Interest Rates Fisher Equation i = r +π Fisher Effect i π

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Macroeconomics Chapter 1123 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.

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Macroeconomics Chapter 1124 Inflation and Interest Rates Actual and Expected Real Interest Rates The expected inflation rate determines the expected real interest rate, r e t r e t = i t − π e t expected real interest rate= nominal interest rate − expected inflation rate

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Macroeconomics Chapter 1125 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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Macroeconomics Chapter 1126 Inflation and Interest Rates Measuring expected inflation Livingston Survey Ask a sample of people （ 50 economists ） about their expectations.

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Macroeconomics Chapter 1127 Inflation and Interest Rates

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Macroeconomics Chapter 1128 Inflation and Interest Rates

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Macroeconomics Chapter 1129 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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Macroeconomics Chapter 1130 Inflation and Interest Rates

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Macroeconomics Chapter 1131 Inflation and Interest Rates

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Macroeconomics Chapter 1132 Inflation and Interest Rates Interest Rates on Money real interest rate on money= nominal interest rate on money − π t real interest rate on money = −π t

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Macroeconomics Chapter 1133 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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Macroeconomics Chapter 1134 Inflation in the Equilibrium Business- Cycle Model Assume fully anticipated inflation, so that the inflation rate, π t, equals the expected rate, π e t. Extend the equilibrium business- cycle model to allow for money growth.

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Macroeconomics Chapter 1135 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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Macroeconomics Chapter 1136 Inflation in the Equilibrium Business- Cycle Model Intertemporal-Substitution Effects The expected real interest rate, r e t, has intertemporal-substitution effects on consumption and labor supply. Therefore, for given i t, a change in π t will have these intertemporal- substitution effects.

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Macroeconomics Chapter 1137 Inflation in the Equilibrium Business- Cycle 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)

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Macroeconomics Chapter 1138 Inflation in the Equilibrium Business- Cycle 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 M d / P = L( Y, i )

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Macroeconomics Chapter 1139 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, M d /P.

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Macroeconomics Chapter 1140 Inflation in the Equilibrium Business- Cycle Model

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Macroeconomics Chapter 1141 Inflation in the Equilibrium Business- Cycle Model

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Macroeconomics Chapter 1142 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 labor. Therefore, ( w/ P) * and L* do not change.

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Macroeconomics Chapter 1143 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 conclude that a change in π does not influence real GDP, Y.

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Macroeconomics Chapter 1144 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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Macroeconomics Chapter 1145 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 C does not change. Since Y is fixed, we conclude that I does not change.

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Macroeconomics Chapter 1146 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 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.

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Macroeconomics Chapter 1147 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, M t, determines the time path of the price level, P t, and, hence, the inflation rate,π t. We also assume for now that Y t and r t are constant over time.

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Macroeconomics Chapter 1148 Inflation in the Equilibrium Business- Cycle Model Money Growth, Inflation, and the Nominal Interest Rate ∆M t =M t+1 −M t µ t = ∆M t /M t M t+1 = (1+ µ t ) · M t π t = ∆ P t / P t π t = (P t+1 −P t )/P t P t+1 = (1+π t ) · P t

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Macroeconomics Chapter 1149 Inflation in the Equilibrium Business- Cycle Model Money Growth, Inflation, and the Nominal Interest Rate Show that When M t grows steadily at the rate µ, the price level, P t, will also grow steadily at the rate µ. π = µ

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Macroeconomics Chapter 1150 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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Macroeconomics Chapter 1151 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, M t /P t. L(Y, i) and M t /P t 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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Macroeconomics Chapter 1152 Inflation in the Equilibrium Business- Cycle Model Money Growth, Inflation, and the Nominal Interest Rate Determination of price level: P 1 = M 1 / L( Y, i) π t, is the constant π = µ.

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Macroeconomics Chapter 1153 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, M t /P t, are fixed over time. The nominal interest rate, i, equals r + µ, where r is the unchanging real interest rate.

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Macroeconomics Chapter 1154 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. P 1 = M 1 / L( Y, i)

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Macroeconomics Chapter 1155 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 γ. This growth might reflect long-term growth of real GDP

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Macroeconomics Chapter 1156 Inflation in the Equilibrium Business- Cycle Model A Trend in the Real Demand for Money Real money balances, M t /P t, increase because of growth in the numerator, M t, at the rate µ, but decrease because of growth in the denominator, P t, at the rate π. growth rate of M t / P t = µ − π

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Macroeconomics Chapter 1157 Inflation in the Equilibrium Business- Cycle Model A Trend in the Real Demand for Money If L(Y, i) grows at rate γ, M t /P t must also grow at rate γ. γ = µ − π π = µ − γ

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Macroeconomics Chapter 1158 Inflation in the Equilibrium Business- Cycle Model

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Macroeconomics Chapter 1159 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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Macroeconomics Chapter 1160 Inflation in the Equilibrium Business- Cycle Model

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Macroeconomics Chapter 1161 Inflation in the Equilibrium Business- Cycle Model A Shift in the Money Growth Rate i ’ − i = µ’ − µ M t /P t is constant before year T. M t /P t is constant after year T. M t /P t 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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Macroeconomics Chapter 1162 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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Macroeconomics Chapter 1163 Inflation in the Equilibrium Business- Cycle Model Government Revenue from Printing Money Nominal revenue from printing money = M t+1 −M t = ∆M t Real revenue from printing money = ∆M t / P t+1 Real money growth rate µ t = ∆ M t / M t

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Macroeconomics Chapter 1164 Inflation in the Equilibrium Business- Cycle Model Government Revenue from Printing Money Real revenue from printing money = µ t · ( M t /P t+1 ) ≈ µ t · ( M t / P t ) = (money growth rate) · (level of real money balances)

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Macroeconomics Chapter 1165

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