McCallum Chapter 6. Steady Inflation

  1. Introduction
  2. Our previous model did not track changes in variables from period to period; it was static.
  3. In this chapter we introduce a dynamic dimension in the simplest way, by analysis of steady states.
  4. In a steady state all variables are growing at constant percentage rates.
  5. We will develop a discrete time model.
  6. Growth rates will be measured as:

(log means natural logarithm).

  1. With this growth rate specification, if Xt =YtZt, then
  2. Steady growth in yt implies that or log yt= a + bt
  3. Let the real rate of interest be given by:
  1. Inflation in the Classical Model
  2. Assumptions
  3. No population growth,
  4. No technical progress
  5. Constant capital stock.
  6. Constant g and .
  7. Constant money growth:
  1. Analysis
  2. Conjecture that Pt will also grow at the rate .
  3. Recall the equations of the static classical model:
  1. The last three equations again determine yt, nt, and Wt/Pt .
  2. Now note that Rt belongs in the LM equation instead of rt.
  1. Write the IS equation as (note that rt is now the dependent variable):
  1. Now recalling the definition of real and nominal interest rates, i.e. that :
  2. Illustrate the IS curve (now plotting y vs. R) and IS-LM equilibrium in a steady state.
  1. Comparative Steady States
  2. Show the consequences of an increase in the steady rate of money growth.
  3. Note that the real money supply must decrease and the the price level goes up more than in proportion to the money supply.
  4. Inflation temporarily exceeds its steady state rate.
  5. Some Extensions
  6. Labor grows in a steady state (with capital absent from the model). The previous model now holds in “per capita terms.” Inflation now equals the growth rate of money per capita.
  7. Labor and capital grow at the same rate in a steady state. Again the previous model holds in per capita terms.
  8. With technical change (as specified in the earlier Solow papers), again a steady state can prevail.
  9. In a such a steady state, the inflation rate will be  - , where 1 is the elasticity of money demand with respect to y,  is the rate of output growth, and  is the rate of growth of money.

a)Approximate L by

b)In a steady state

  1. Welfare Costs of Inflation
  2. Plot the money demand curve (R vertical axis, m horizontal axis).
  3. Interpret the money demand curve as a marginal valuation function. At my optimum, I must value holding an additional dollar (assume P=1 so this is real) in the form of money as much as the marginal cost. Gains from holding additional money balances are represented by the area under the money demand function.
  4. Assuming super-neutrality (as in our version of the classical model with inflation), inflation leaves all real variables unchanged (except for real money balances).
  5. Higher money growth leads to higher inflation and higher nominal interest rates (point for point).
  6. There is a welfare loss associated with people holding lower real money balances
  7. Assuming printing money is essentially costeless in terms of resources, the loss of added inflationis measured by an area under the money demand function (between original and new values for m).
  8. Do a calculation
  9. Optimal inflation equals minus the real rate of interest.