1. Macroeconomics Chapter 11
Inflation, Money Growth,
and Interest Rates
Macroeconomics Chapter 11

2. 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
Macroeconomics Chapter 11

3. 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.
Macroeconomics Chapter 11

4. Macroeconomics Chapter 11

5. Macroeconomics Chapter 11

6. Macroeconomics Chapter 11

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.
Macroeconomics Chapter 11

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%
Macroeconomics Chapter 11

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.
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.
Macroeconomics Chapter 11

10. Cross-Country Data on Inflation and Money Growth
Macroeconomics Chapter 11

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.”
Macroeconomics Chapter 11

12. 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
Macroeconomics Chapter 11

13. Inflation and Interest Rates
Actual and Expected Inflation
π1 = ( P2 − P1)/ P1
π1 = ∆P1/ P1
π1 · P1 = P2 − P1
P2 = ( 1 +π1) · P1
Macroeconomics Chapter 11

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 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.
Macroeconomics Chapter 11

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.
Macroeconomics Chapter 11

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 + 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.
Macroeconomics Chapter 11

17. Inflation and Interest Rates
Macroeconomics Chapter 11

18. 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 + π1)
Macroeconomics Chapter 11

19. 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)
Macroeconomics Chapter 11

20. 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)
Macroeconomics Chapter 11

21. Inflation and Interest Rates
Real 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 − π1
Macroeconomics Chapter 11

22. Inflation and Interest Rates
Fisher Equation
i = r +π
Fisher Effect i π
Macroeconomics Chapter 11

23. 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.
Macroeconomics Chapter 11

24. 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
Macroeconomics Chapter 11

25. 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
Macroeconomics Chapter 11

26. Inflation and Interest Rates
Measuring expected inflation
Livingston Survey
Ask a sample of people（50 economists） about their expectations.
Macroeconomics Chapter 11

27. Inflation and Interest Rates
Macroeconomics Chapter 11

28. Inflation and Interest Rates
Macroeconomics Chapter 11

29. 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.
Macroeconomics Chapter 11

30. Inflation and Interest Rates
Macroeconomics Chapter 11

31. Inflation and Interest Rates
Macroeconomics Chapter 11

32. 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
Macroeconomics Chapter 11

33. 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.
Macroeconomics Chapter 11

34. 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.
Macroeconomics Chapter 11

35. 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.
Macroeconomics Chapter 11

36. 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 πt will have these intertemporal-substitution effects.
Macroeconomics Chapter 11

37. 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)
Macroeconomics Chapter 11

38. 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
Md / P = L( Y, i )
Macroeconomics Chapter 11

39. 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.
Macroeconomics Chapter 11

40. Inflation in the Equilibrium Business-Cycle Model
Macroeconomics Chapter 11

41. Inflation in the Equilibrium Business-Cycle Model
Macroeconomics Chapter 11

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 labor. Therefore, ( w/ P) * and L* do not change.
Macroeconomics Chapter 11

43. 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.
Macroeconomics Chapter 11

44. 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.
Macroeconomics Chapter 11

45. 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.
Macroeconomics Chapter 11

46. 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.
Macroeconomics Chapter 11

47. 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.
Macroeconomics Chapter 11

48. 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
Macroeconomics Chapter 11

49. 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
Macroeconomics Chapter 11

50. 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.
Macroeconomics Chapter 11

51. 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.
Macroeconomics Chapter 11

52. 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.
Macroeconomics Chapter 11

53. 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.
Macroeconomics Chapter 11

54. 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)
Macroeconomics Chapter 11

55. 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
Macroeconomics Chapter 11

56. 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.
growth rate of Mt/ Pt = µ − π
Macroeconomics Chapter 11

57. 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
Macroeconomics Chapter 11

58. Inflation in the Equilibrium Business-Cycle Model
Macroeconomics Chapter 11

59. 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.
Macroeconomics Chapter 11

60. Inflation in the Equilibrium Business-Cycle Model
Macroeconomics Chapter 11

61. 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’).
Macroeconomics Chapter 11

62. 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.
Macroeconomics Chapter 11

63. 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
Real money growth rate
µt = ∆ Mt/ Mt
Macroeconomics Chapter 11

64. Inflation in the Equilibrium Business-Cycle Model
Government Revenue from Printing Money
Real revenue from printing money
= µt·( Mt /Pt+1)
≈ µt·( Mt / Pt )
= (money growth rate) · (level of real money balances)
Macroeconomics Chapter 11

65. Macroeconomics Chapter 11