[Read my previous post first, if you have not already done so. Also note that **Marcus Nunes** has some excellent graphs illustrating these points.]

I didn’t get as many answers as I expected, but there were a few good ones. Phil got the ball rolling but fell a bit short on the last two questions. George wins the gold star for getting there first, with honorable mention to Don and Steve who also nailed it. Others came close.

Here’s how I analyze the Barro data set (which I’ll reproduce on the bottom of this post.)

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.

To summarize, in equilibrium:

P = Ms/(Md/P)

Let’s assume real money demand is k*Y. The parameter ‘k’ is the share of gross income that the public chooses to hold in the form of base money. In that case:

P = M/(k*Y) (or MV=PY, if you prefer.)

Now let’s assume that k is negatively relative to the opportunity cost of holding base money, and that base money doesn’t earn interest:

P = M/[k(i)*Y],

where i is positively related to both the level of NGDP relative to trend, and the expected rate of NGDP growth.

If you are more interested in NGDP than the price level (and if you aren’t you should be), then we have:

P*Y = M/k(i)

That’s my version of the QTM. Until I see something better I’m not interested in alternative Keynesian, MMT or fiscal theories of inflation/NGDP. Barro’s data set is the one I use to judge all competing theories of money and inflation.

However the fact that expectations play a role in the inflation process makes things far more complicated than the early QTM proponents assumed. In the next post we’ll see how expectations shifts can lead to some results that look wildly inconsistent with the simple QTM.

PS. Lars Christensen is forming a **Global Monetary Policy Network**. I’ve already joined.

**Country MB growth RGDP growth Inflation Time period**

Brazil 77.4% 5.6% 77.8% 1963-90

Argentina 72.8% 2.1% 76.0% 1952-90

Bolivia 49.0% 3.3% 48.0% 1950-89

Peru 49.7% 3.0% 47.6% 1960-89

Uruguay 42.4% 1.5% 43.1% 1960-89

Chile 47.3% 3.1% 42.2% 1960-90

Yugoslavia 38.7% 8.7% (FWIW) 31.7% 1961-89

Zaire 29.8% 2.4% 30.0% 1963-86

Israel 31.0% 6.7% 29.4% 1950-90

Sierra Leone 20.7% 3.1% 21.5% 1963-88

. . .

Canada 8.1% 4.2% 4.6% 1950-90

Austria 7.1% 3.9% 4.5% 1950-90

Cyprus 10.5% 5.2% 4.5% 1960-90

Netherlands 6.4% 3.7% 4.2% 1950-89

U.S. 5.7% 3.1% 4.2% 1950-90

Belgium 4.0% 3.3% 4.1% 1950-89

Malta 9.6% 6.2% 3.6% 1960-88

Singapore 10.8% 8.1% 3.6% 1963-89

Switzerland 4.6% 3.1% 3.2% 1950-90

W. Germany 7.0% 4.1% 3.0% 1953-90