Tautology:
MV ≡ PQ
Where Meter is money, five is the speed, phosphorus is the price level, ask is economic activity.
Suppose V’ is constant; then:
MV’= PQ
Get logs (where lowercase letters represent log values):
m + v’ = p + q
Take the difference relative to a fixed date and call it Δ:
ΔMeter +Δv’ = Δp +Δq
since V’ is a constant, we can rearrange to get:
Δp = ΔMeter – Δq
Let’s plot the change in price levels and the change in M2 versus real GDP relative to the first quarter of 2020 (the start of the pandemic in the US).
figure 1: PCE Deflator (blue), M2/Real GDP (tan), both expressed as logarithms relative to first quarter 2020 values.Meter2 Values are quarter end. The NBER uses shades of grey to define the peak and trough dates of the recession. Source: BEA, Federal Reserve via FRED, NBER and author’s calculations.
It has been about 2 years since the Fed increased high-energy money and allowed it to manifest as an increase in broad money. However, the price level has only risen by about 7.9%, while the ratio of broad money to real GDP has risen by 27% (in logarithmic terms).
The lack of correlation between broad money and price levels is not a product of the COVID-19 era. This is a scatter plot of inflation and M2/GDP growth.
figure 2: Q4/Q4 PCE inflation and M2/real GDP growth rate (calculated in logarithmic form) and nearest neighbor fitted line (tan).Meter2 Values are quarter end. Source: BEA, Federal Reserve via FRED and author’s calculations.
A more sophisticated version of quantity theory would allow for velocity trends and/or interest sensitivity.I don’t think this is enough to make quantity theory empirically more efficient than other methods (see Comparing the Empirical Special Quantity Theory with the Phillips Curve).
This article was inspired by Words from Mr. Steven Kopits,and this Comment.
