# Relationship between money growth and inflation

Reading: AB, chapter 7, section 4.

Recall, inflation is simply the growth rate of some aggregate price index like the CPI or the GDP deflator. If P(t) denotes the aggregate price level in year t then, symbolically, annual inflation from year t-1 to year t is given as: = %P(t) = (P(t) - P(t-1))/P(t-1).

We build a link between money growth and inflation through our model of money market equilibrium. In money market equilibrium, real money supply is equal to real money demand: M/P = Ld(Y, i). If we assume that the aggregate price level is free to adjust to keep the money market in equilibrium then we can use the money market equilibrium condition to solve for the aggregate price level: P = M/Ld(Y, i). That is, the price level is directly related to the nominal money supply and to real money demand (which is a function of real income and the nominal interest rate).

Using the above relationship between the aggregate price level, nominal money supply and real money demand we may derive a link between inflation, growth in the money supply and growth in money demand. Inflation is just the growth rate of aggregate prices and from the relationship P = M/Ld(Y, i) we get, using the fact that the growth rate of a A/B is equal to the growth rate of A minus the growth rate of B, = %P = %M - %Ld(Y,i). That is, inflation is equal to the growth rate in the nominal money supply (controlled by the Fed) minus the growth rate in real money demand.

Notice that if the growth rate of the nominal money supply is equal to growth rate of money demand then inflation is equal to zero. Now money demand grows over time primarily because the real economy grows over time (average real growth is about 2.5% per year on average). As Y grows individuals consume more and thus need more money to conduct transactions. Since money demand is a function of both Y and i we can use a trick from calculus - the total derivative - to decompose the growth of money demand as follows: %Ld(Y,i) = eY*%Y + ei*%i, where eY = income elasticity of money demand and ei = nominal interest rate elasticity of money demand. Economists estimate that eY is approximately 2/3, for the U.S., and that ei is approximately -1/10 so that money demand is much more sensitive to changes in income than to changes in the nominal interest rate. Further, the growth rate of the nominal interest rate is on average about zero (interest rate on average do not tend to go up or down). These data facts tell us that the nominal interest component does not contribute much to the growth rate of money demand and a reasonable good prediction model for inflation become: = %P = %M - (2/3)*%Y.

### An example

Suppose the Fed sets money growth, %M, equal to 6% per year, the annual real economic growth, %Y, is 3% and that the income elasticity of money demand is 2/3. Then our prediction for inflation is given by: = %M - (2/3)*%Y = 6% - (2/3)*3% = 4%.

## Empirical relationship between money growth and inflation

The tables below show the relationship between actual inflation and money growth in low money growth countries and high money growth countries.

 Inflation in low money growth countries: 1986-1989 Country money growth (% per year) inflation (% per year) Chad -2.1% -2.7% Switzerland 4.1% 1.8% Belgium 5.0% 1.8% France 5.5% 3.0% United States 7.0% 3.6%

 Inflation in high money growth countries: 1986-1989 Country money growth (% per year) inflation (% per year) Peru 425% 545% Yugoslavia 358% 305% Mexico 71% 82% Poland 47% 68% Nepal 20% 11.2%

Last updated on July 18, 1996 by Eric Zivot.