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nullnullInflation, Money Growth, and Interest RatesC h a p t e r 1 1Cross-Country Data on Inflation and Money GrowthCross-Country Data on Inflation and Money GrowthKey equation: Ms = P· L(Y, i) Two possible reasons of inflation: Decrease of real demand for money Increase of money supply Cross-Country Data on Inflation and Money GrowthCross-Country Data on Inflation and Money GrowthInflation 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. nullnullnullCross-Country Data on Inflation and Money GrowthCross-Country Data on Inflation and Money GrowthHighlights 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.Cross-Country Data on Inflation and Money GrowthCross-Country Data on Inflation and Money GrowthHighlights 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% Cross-Country Data on Inflation and Money GrowthCross-Country Data on Inflation and Money GrowthHighlights 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.Cross-Country Data on Inflation and Money GrowthCross-Country Data on Inflation and Money GrowthCross-Country Data on Inflation and Money GrowthCross-Country Data on Inflation and Money GrowthOne 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.” Inflation and Interest RatesInflation and Interest RatesActual 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/ P1Inflation and Interest RatesInflation and Interest RatesActual and Expected Inflation π1 = ( P2 − P1)/ P1 π1 = ∆P1/ P1 π1 · P1 = P2 − P1 P2 = ( 1 +π1) · P1 Inflation and Interest RatesInflation and Interest RatesActual 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.Inflation and Interest RatesInflation and Interest RatesActual 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.Inflation and Interest RatesInflation and Interest RatesReal 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. Inflation and Interest RatesInflation and Interest RatesInflation and Interest RatesInflation and Interest RatesReal 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)Inflation and Interest RatesInflation and Interest RatesReal 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)Inflation and Interest RatesInflation and Interest RatesReal 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) Inflation and Interest RatesInflation and Interest RatesReal 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 − π1Inflation and Interest RatesInflation and Interest RatesFisher Equation i = r +π Fisher Effect i π Inflation and Interest RatesInflation and Interest RatesThe 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. Inflation and Interest RatesInflation and Interest RatesActual 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 Inflation and Interest RatesInflation and Interest RatesMeasuring 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 inflationInflation and Interest RatesInflation and Interest Rates Measuring expected inflation Livingston Survey Ask a sample of people（50 economists） about their expectations.Inflation and Interest RatesInflation and Interest RatesInflation and Interest RatesInflation and Interest RatesInflation and Interest RatesInflation and Interest RatesMeasuring 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. Inflation and Interest RatesInflation and Interest RatesInflation and Interest RatesInflation and Interest RatesInflation and Interest RatesInflation and Interest RatesInterest Rates on Money real interest rate on money= nominal interest rate on money − πt real interest rate on money = −πt Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelGoals 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.Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelAssume 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.Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelAssume 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.Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelIntertemporal-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 intertemporal-substitution effects.Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelBonds 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) Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelInterest 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 )Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelInterest 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. Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelInflation 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.Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelInflation 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.Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelInflation 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.Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelInflation 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.Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelWe 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. Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelMoney 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. Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelMoney 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)·PtInflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelMoney 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 = µInflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelMoney 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.Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelMoney 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.Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelMoney Growth, Inflation, and the Nominal Interest Rate Determination of price level: P1 = M1 / L( Y, i) πt, is the constant π = µ. Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelMoney 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.Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelMoney 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) Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelA 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 Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelA 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 Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelA 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 − γInflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelA Shift in the Money Growth Rate Suppose that the monetary authority raises the money growth rate from µ to µ’ in year T. Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelA 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’). Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelGovernment 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.Inflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelGovernment 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/ MtInflation in the Equilibrium Business-Cycle ModelInflation in the Equilibrium Business-Cycle ModelGovernment Revenue from Printing Money Real revenue from printing money = µt·( Mt /Pt+1) ≈ µt·( Mt / Pt ) = (money growth rate) · (level of real money balances)null