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 =(P 2 -P 1 )/P 1 P 2 =(1+  1 )P 1 Expected inflation rate:  Households’ expectation of the inflation rate. Rational expectations:  There is no persistent or systematic error in the expected inflation rate.

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: B 2 =B 1 (1+i 1 )  Price level in year 2: P 2 =(1+  1 )P 1

The Real Interest Rate and Intertemporal Substitution Original intertemporal budget constraint The intertemporal budget constraint in the presence of inflation

Actual and Expected Real Interest Rates The expected real interest rate is based upon the expected inflation rate Intertemporal consumption behavior is ultimately determined by the expected real interest rate.

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 r t =i t -  t. Bonds and capital  New equation: r=(R/P)  -  (  ) Demand for money  The difference between the real interest rates of money and interest-bearing assets: (i-  )-(-  )=i  Demand for money is again M d /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 interest rate  Assumptions Constant growth rate in nominal money supply M t+1 =(1+  )M t Constant real terms Y t =Y and r t =r  Conjecture:  t =  = 

Inflation in the RBC Model Money growth, inflation, and the nominal interest rate  Verification The nominal interest rate will remain constant i t =r+  =r+  The real money demand will remain constant M t /P t =L(Y, i t )=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.

The empirical evidence Correlation: 0.72

A Shift in the Money Growth Rate Assumptions  Real 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 =  = , i t =r+  After time T:  t =  =  ', i t =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:  M t =M t+1 -M t Real revenue from printing money:  M t /P t+1 = (  M t /M t )(M t /P t+1 )=  t M t /P t+1   t M t /P t Two effects:  Higher  higher real revenue;  Higher  higher  higher i  lower L(Y, i)  lower M/P;  Usually the first effect is stronger.