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

Macroeconomics Chapter 11 1

Inflation, Money Growth, and Interest Rates

C h a p t e r 1 1


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



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.



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.



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%



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.



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.”


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



Actual and Expected Inflation π1 = ( P2 − P1)/ P1

π1 = ∆P1/ P1

π1 · P1 = P2 − P1

P2 = ( 1 +π1) · P1



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.



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.



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.



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)



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)



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)



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



Fisher Equation

i = r +π

Fisher Effect i π



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.



Actual and Expected Real Interest Rates The expected inflation rate determines

the expected real interest rate, ret

ret = it − πe

t

expected real interest rate= nominal interest rate − expected inflation rate



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




Livingston Survey

Ask a sample of people （ 50 economists ） about their expectations.




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.



Interest 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 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.



Assume fully anticipated inflation, so that the inflation rate, πt, equals the expected rate, πe

t .

Extend the equilibrium business-cycle model to allow for money growth.



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.



Intertemporal-Substitution Effects The expected real interest rate, re

t , has intertemporal-substitution effects on consumption and labor supply.

Therefore, for given it, a change in πt will have these intertemporal-substitution effects.



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)



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 )



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.



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.



Inflation and the Real Economy

Real GDP, Y, is determined by the production functionY= A· F(κ K, L)

We conclude that a change in π does not influence real GDP, Y.



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.



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.



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.



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.



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



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



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.



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.



Money Growth, Inflation, and the Nominal Interest Rate Determination of price level:

P1 = M1 / L( Y, i)

πt, is the constant π = µ.



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.



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)



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



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



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



A Shift in the Money Growth Rate Suppose that the monetary authority

raises the money growth rate from µ to µ’ in year T.



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’).



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.



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



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

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