Copyright © 2010 by Nelson Education Limited 1 PowerPoint Slides to accompany Prepared by Apostolos Serletis University of Calgary

Copyright © 2010 by Nelson Education Limited 2 C h a p t e r 1 1 Inflation, Money Growth, and Interest Rates

Copyright © 2010 by Nelson Education Limited 3 Cross-Country Data on Inflation and Money Growth Inflation rates and money growth rates for 82 countries from 1960 to 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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7 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 –There is a broad cross-sectional range for the inflation rates and the growth rates of money.

Copyright © 2010 by Nelson Education Limited 8 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%

Copyright © 2010 by Nelson Education Limited 9 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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Copyright © 2010 by Nelson Education Limited 11 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.”

Copyright © 2010 by Nelson Education Limited 12 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

Copyright © 2010 by Nelson Education Limited 13 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

Copyright © 2010 by Nelson Education Limited 14 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.

Copyright © 2010 by Nelson Education Limited 15 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.

Copyright © 2010 by Nelson Education Limited 16 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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Copyright © 2010 by Nelson Education Limited 18 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+ i 1 ) P 2 = P 1 · ( 1 + π 1 )

Copyright © 2010 by Nelson Education Limited 19 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 )

Copyright © 2010 by Nelson Education Limited 20 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 )

Copyright © 2010 by Nelson Education Limited 21 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, tends to be small. Hence, –real interest rate = nominal interest rate − inflation rate: r 1 = i 1 − π 1

Copyright © 2010 by Nelson Education Limited 22 Inflation and Interest Rates The Real Interest Rate and Intertemporal Substitution –When the inflation rate, π 1, is not zero, it is the real interest rate, r 1, rather than the nominal rate, i 1, that matters for intertemporal substitution.

Copyright © 2010 by Nelson Education Limited 23 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)

Copyright © 2010 by Nelson Education Limited 24 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

Copyright © 2010 by Nelson Education Limited 25 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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Copyright © 2010 by Nelson Education Limited 28 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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Copyright © 2010 by Nelson Education Limited 31 Inflation and Interest Rates in the United States

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Copyright © 2010 by Nelson Education Limited 33 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

Copyright © 2010 by Nelson Education Limited 34 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.

Copyright © 2010 by Nelson Education Limited 35 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.

Copyright © 2010 by Nelson Education Limited 36 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.

Copyright © 2010 by Nelson Education Limited 37 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 labour supply. –Therefore, for given i t, a change in π t will have these intertemporal-substitution effects.

Copyright © 2010 by Nelson Education Limited 38 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)

Copyright © 2010 by Nelson Education Limited 39 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)

Copyright © 2010 by Nelson Education Limited 40 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: M d /P = L(Y, i)

Copyright © 2010 by Nelson Education Limited 41 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 labour supply. –However, it is the nominal interest, i, that influences the real demand for money, M d /P.

Copyright © 2010 by Nelson Education Limited 42 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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Copyright © 2010 by Nelson Education Limited 45 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.

Copyright © 2010 by Nelson Education Limited 46 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.

Copyright © 2010 by Nelson Education Limited 47 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.

Copyright © 2010 by Nelson Education Limited 48 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.

Copyright © 2010 by Nelson Education Limited 49 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.

Copyright © 2010 by Nelson Education Limited 50 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

Copyright © 2010 by Nelson Education Limited 51 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

Copyright © 2010 by Nelson Education Limited 52 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.

Copyright © 2010 by Nelson Education Limited 53 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.

Copyright © 2010 by Nelson Education Limited 54 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.

Copyright © 2010 by Nelson Education Limited 55 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.

Copyright © 2010 by Nelson Education Limited 56 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, P 1, equates year 1’s real money balances, M 1 /P 1, to the real quantity demanded, L(Y, i).

Copyright © 2010 by Nelson Education Limited 57 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

Copyright © 2010 by Nelson Education Limited 58 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. Hence, growth rate of M t /P t = µ − π

Copyright © 2010 by Nelson Education Limited 59 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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Copyright © 2010 by Nelson Education Limited 61 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 ʹ in year T.

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Copyright © 2010 by Nelson Education Limited 63 Inflation in the Equilibrium Business-Cycle Model A Shift in the Money Growth Rate –The red line shows that the nominal quantity of money, M t, grows at the constant rate µ before year T. After year T, M t grows along the brown line at the higher rate µ. –The blue line shows that the price level, P t, grows at the same rate as money, µ, before year T. –After year T, P t grows along the green line at the same rate as money, µ. The price level, P t, jumps upward during year T. This jump reduces real money balances, M t /P t, from the level prevailing before year T to that prevailing after year T.

Copyright © 2010 by Nelson Education Limited 64 Inflation in the Equilibrium Business-Cycle Model A Shift in the Money Growth Rate i ʹ - i = µ ʹ − µ

Copyright © 2010 by Nelson Education Limited 65 Inflation in the Equilibrium Business-Cycle Model A Shift in the Money Growth Rate –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 ʹ ).

Copyright © 2010 by Nelson Education Limited 66 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.

Copyright © 2010 by Nelson Education Limited 67 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 – Money growth rate µ t = ∆M t /M t

Copyright © 2010 by Nelson Education Limited 68 Inflation in the Equilibrium Business-Cycle Model Government Revenue from Printing Money –Real revenue from printing money = µ t ·(M t /P t+1 ) –Real revenue from printing money ≈ µ t ·(M t /P) = (money growth rate)·(level of real money balances)

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