1. The eyeball test suggests the Quantity Theory of Money (QTM) works dramatically better for high inflation countries than low inflation countries. (Also true of PPP and the Fisher effect, for much the same reason.) In fact, money growth affects prices in all countries, but other factors are relatively more important when inflation is low. Let’s suppose that the gap between money growth and inflation does not vary with the average rate of money growth. For instance, suppose the gap is 3% on average, when examining very long run data. In that cases the gap will seem almost trivial when money growth rates become very large, say more than 30%/year.
If you see the QTM as claiming money growth and inflation rates are highly correlated, then the theory works better for high inflation countries. If you view it as it claiming that a given one time increase in the money supply will cause a proportionate increase in prices in the long run, then it should work equally well in low and high inflation countries. Indeed even at the zero interest rate bound.
2. In the vast majority of countries the money growth rate exceeded the inflation rate. That means the money demand curve tends to shift to the right over time, at least when you describe money demand as a function of the value of money (1/P). Many people prefer to visualize this pattern with the Equation of Exchange: M*V = P*Y. If V is fairly stable, and Y increases over time, then inflation will be less than money growth. RGDP growth is deflationary!! (Something our textbooks ignore—and check out Singapore below.) In Barro’s sample of 83 countries, only one experienced falling RGDP on average over the entire 30 year period.
3. Why does the money growth/inflation gap exceed 10% in only one of the 83 cases? Partly because RGDP growth averages less than 10% in all 83 countries. But it also requires velocity to be relatively stable. Keep in mind that a 30% change in velocity over 30 years is fairly large, and yet is still less than 1% per year on average. For money growth to exceed inflation by more than 10% you need the RGDP growth rate minus the change in velocity to exceed 10%, which occurred only in Libya.
4 and 5. In order for the inflation rate to exceed the money supply growth rate you’d need the change in velocity to exceed the RGDP growth rate. That would be a fairly large increase in velocity, and occurred in only 12 of the 83 countries. The vast majority of these situations occurred in the high inflation countries. (Seven of twelve in the 13 highest inflation countries.) This is because velocity is positively correlated with nominal interest rates. For velocity to rise sharply you normally need a large increase in interest rates, which usually implies a large increase in inflation (or more precisely NGDP growth) expectations. Unfortunately the table doesn’t show the change in inflation expectations. However it stands to reason that a very large increase in inflation expectations is more likely to occur in countries where the average rate of inflation is higher, and that’s what we observe.
Below the answers illustrated. The data set is also from Barro (Macroeconomics – A modern approach (2008)) and differs somewhat from his previous data set. It covers, for most of the 82 (Libya is not included) countries, the 40 years between 1960-2000.
Q1. The high inflation countries are closer to the regression line. Money growth ‘dwarfs’ RGDP growth.
Q2/Q3/Q4/Q5. High RGDP growth countries tend to have a larger difference between money growth and inflation. Additionally, in countries such as Korea and Singapore, velocity decreased substantially. In very high inflation countries money becomes a “burning potato” and slow RGDP growth only makes it “hotter” i.e., velocity ‘rockets’ so that inflation is higher than money growth. Although it was the inflation ‘silver medalist’ Brazil, more than any other high inflation country, developed efficient ‘living with inflation’ mechanisms.
The last chart shows what happens when you move quickly (and credibly) from a high (and rising) inflation environment to a low inflation environment. This happened in Brazil in mid-1994. Before 1994 velocity was rising (Money/NGDP falling). From that point on, money growth was significant but not inflationary because it was compatible with the increase in money demand (fall in velocity) that accompanied the steep drop in inflation (and nominal interest rates).
Update: The following chart is basically consistent with the long-run neutrality of money. In the long run money growth only affects nominal variables (like inflation) having no effect (maybe slightly negative due to the inneficiences brought about by very high inflation) on real variables (like RGDP growth).