ECON102: Principles of Macroeconomics (2021.A.01)

Assume for the moment that velocity is constant, expressed as V¯. Our equation of exchange is now written as

Equation 11.6

$$M\overline{V}=PY$$

A constant value for velocity would have two important implications:

1. Nominal GDP could change only if there were a change in the money supply. Other kinds of changes, such as a change in government purchases or a change in investment, could have no effect on nominal GDP.
2. A change in the money supply would always change nominal GDP, and by an equal percentage.
   

In short, if velocity were constant, a course in macroeconomics would be quite simple. The quantity of money would determine nominal GDP; nothing else would matter.

Indeed, when we look at the behavior of economies over long periods of time, the prediction that the quantity of money determines nominal output holds rather well. Figure 11.6 "Inflation, M2 Growth, and GDP Growth" compares long-term averages in the growth rates of M2 and nominal GNP for 11 countries (Canada, Denmark, France, Italy, Japan, the Netherlands, Norway, Sweden, Switzerland, the United Kingdom, and the United States) for more than a century. These are the only countries that have consistent data for such a long period. The lines representing inflation, M2 growth, and nominal GDP growth do seem to move together most of the time, suggesting that velocity is constant when viewed over the long run.

Figure 11.6 Inflation, M2 Growth, and GDP Growth

The chart shows the behavior of price-level changes, the growth of M2, and the growth of nominal GDP for 11 countries using the average value of each variable. Viewed in this light, the relationship between money growth and nominal GDP seems quite strong.


Moreover, price-level changes also follow the same pattern that changes in M2 and nominal GNP do. Why is this?

We can rewrite the equation of exchange, M $\overline{V}$ = PY, in terms of percentage rates of change. When two products, such as M $\overline{V}$ and PY, are equal, and the variables themselves are changing, then the sums of the percentage rates of change are approximately equal:

$$\mathrm{\%\Delta M}+\mathrm{\%\Delta V}\cong \mathrm{\%\Delta P}+\mathrm{\%\Delta Y}$$
The Greek letter Δ (delta) means "change in". Assume that velocity is constant in the long run, so that %ΔV = 0. We also assume that real GDP moves to its potential level, Y_P, in the long run. With these assumptions, we can rewrite Equation 11.7 as follows:

Equation 11.8

$$\mathrm{\%\Delta M}\cong \mathrm{\%\Delta P}+\mathrm{\%\Delta }{Y}_{\text{P}}$$

Subtracting %ΔYP from both sides of Equation 11.8, we have the following:

Equation 11.9

Equation 11.9 has enormously important implications for monetary policy. It tells us that, in the long run, the rate of inflation, %ΔP, equals the difference between the rate of money growth and the rate of increase in potential output, %ΔY_P, given our assumption of constant velocity. Because potential output is likely to rise by at most a few percentage points per year, the rate of money growth will be close to the rate of inflation in the long run.

Several recent studies that looked at all the countries on which they could get data on inflation and money growth over long periods found a very high correlation between growth rates of the money supply and of the price level for countries with high inflation rates, but the relationship was much weaker for countries with inflation rates of less than 10%.For example, one study examined data on 81 countries using inflation rates averaged for the period 1980 to 1993 (John R. Moroney, " while another examined data on 160 countries over the period 1969–1999 (Paul De Grauwe and Magdalena Polan, "Is Inflation Always and Everywhere a Monetary Phenomenon?" These findings support the quantity theory of money, which holds that in the long run the price level moves in proportion with changes in the money supply, at least for high-inflation countries.