Owen F. Humpage and Margaret Jacobson write,

Over the short run—a year or two—excess-money growth explains very little of the changes in the GDP deflator. If excess-money growth explained all of the annual price changes, the dots in the scatter plot below would line up along the 45-degree line, and all price movements would be inflation—strictly a monetary phenomenon. Instead, the dots are spread about, showing almost no correspondence between the annual change in the GDP deflator and excess-money growth. The simple correlation coefficient is only 0.10. Moreover, the typical annual dispersion of price changes from excess-money growth is about 4 percentage points, but there are some enormous outliers. Many of the largest deviations occurred during the Great Depression and the Second World War, both highly disruptive and uncertain economic events. Likewise many dots associated with the recent Great Recession years also seem well off the mark. Clearly, central banks do not have much control over aggregate-price movements on a year-to-year basis.

Pointer from Mark Thoma.

Some comments.

1. To see what the authors did, start with MV = PY, and solve for P. P = V(M/Y). Convert to approximate percentage changes by taking logs of both sides: growth rate of the price level equals growth rate of velocity plus the difference between the growth rate of money and the growth rate of real output. The latter is what they call excess money growth.

2. Most economic models do not allow for such wide fluctuations in velocity.

3. I think this supports my view that the Fed does not have firm control over macroeconomic aggregates.

4. The authors say that in the long run, inflation can be linked to excess money growth. I gather that long-run velocity growth is much more stable than short-run velocity growth.