chapter 11 inflation, money growth, and interest rates
TRANSCRIPT
Chapter 11 Inflation, Money Growth, and Interest rates
Empirical Evidence of Inflation Inflation is a world-wide phenomenon; Nominal currency grows in all countries; Cross-sectional differences:
Inflation rate: 3.2%83%;Growth rate of currency: 3.7%84%.
Growth rate of M/P is usually positive; Strong correlation between the inflation rate
and the growth rate of nominal currency.
Empirical Evidence of Inflation
Actual and Expected Inflation The inflation rate
1=(P2-P1)/P1
P2=(1+1)P1
Expected inflation rate:Households’ expectation of the inflation rate.
Rational expectations:There is no persistent or systematic error in the
expected inflation rate.
1e
1 1e
Real and Nominal Interest Rates The nominal interest rate: i
The interest rate of the face value. The real interest rate: r
The interest rate on the purchasing power. Evaluating the real interest rate
Dollar asset in year 2: B2=B1(1+i1)
Price level in year 2: P2=(1+1)P1
2 2 11 1 1 1
1 1 1
11
1
B P ir r i
B P
The Real Interest Rate and Intertemporal Substitution Original intertemporal budget constraint
The intertemporal budget constraint in the presence of inflation
2 2
202 11 0 0
1 1 1
(1 )1 1 1
w BP PL KBC w
C i K Li P P i i
2 2
2 2 202 11 0 0
1 0 1 1 1
(1 )1 1 1
w BP PL KBC w
C r K Lr P P r r
Actual and Expected Real Interest Rates The expected real interest rate is based upon th
e expected inflation rate
Intertemporal consumption behavior is ultimately determined by the expected real interest rate.
e et t tr i
The empirics Actual and expected inflation rates
The empirics Nominal and expected real interest rates
The empirics Real interest rates on U.S. indexed bonds
The empirics Expected inflation rate as the difference between the
interest rates on nominal and indexed bonds.
Inflation in the RBC Model Objectives:
How inflation impacts real terms;What causes inflation.
Assumptions:Rational expectations;New money is transferred to households in the
lump-sum way.
Inflation in the RBC Model Intertemporal substitution effects
Now determined by rt=it-t.
Bonds and capitalNew equation: r=(R/P)-()
Demand for moneyThe difference between the real interest rates of m
oney and interest-bearing assets:
(i-)-(-)=iDemand for money is again Md/P=L(Y, i).
Inflation in the RBC Model The rental market remains unchanged
The demand for capital services remains unchanged
We will verify that labor input remain unchanged; does not alter MPK.
The supply of capital services remains unchanged is determined by R/P only.
(R/P)* and (K)* both remain unchanged.
Inflation in the RBC Model The rental market remains unchanged
Inflation in the RBC Model The labor market remains unchanged
The demand for labor remains unchanged The input of capital services remains unchanged; does not alter MPL.
Assuming away the income effects The labor supply remains unchanged.
(w/P)* and L* both remain unchanged.
Inflation in the RBC Model The labor market remains unchanged
Inflation in the RBC Model Real GDP remains unchanged
Y=AF(K, L) Real interest rate remains unchanged
r=(R/P)-() Assuming away the income effects
Both C and I remain unchanged.
Inflation in the RBC Model Money growth, inflation, and the nominal inter
est rateAssumptions
Constant growth rate in nominal money supply
Mt+1=(1+)Mt
Constant real terms
Yt=Y and rt=r
Conjecture: t==
Inflation in the RBC Model Money growth, inflation, and the nominal
interest rateVerification
The nominal interest rate will remain constant
it=r+ =r+ The real money demand will remain constant
Mt/Pt=L(Y, it)=L(Y, i)
Conjecture verified: t=.
A Trend in the Real Demand for Money Real GDP is growing over time
L(Y, i) should be growing over time. Growth rate of real demand for money
is generated by the growth of real GDP.
1 1 11
1t t
t t
M P
M P
The empirical evidence Correlation: 0.72
A Shift in the Money Growth Rate
AssumptionsReal GDP fixed;t= up to time T;
Unexpected increase in the money growth rate at time T;
t=' is expected beyond time T.
A Shift in the Money Growth Rate
Before time T: t==, it=r+ After time T: t==', it=r+'
Jump in price at time T:i='-;L(Y, i) decreased at time T;P jump upward at time T.
A Shift in the Money Growth Rate
Seignorage Government revenue from printing money. Nominal revenue from printing money:
Mt=Mt+1-Mt
Real revenue from printing money:
Mt/Pt+1= (Mt/Mt)(Mt/Pt+1)=t Mt/Pt+1
t Mt/Pt
Two effects: Higher higher real revenue; Higher higher higher ilower L(Y, i)lower M/P; Usually the first effect is stronger.