MV ≡ PQ
Where M is money, V is velocity, P is price level, Q is economic activity.
Assume V’ is constant; then:
MV’ = PQ
Take logs (where lowercase letters denote log values):
m + v’ = p + q
Take difference with respect to a fixed date, and call that Δ :
Δm + Δv’ = Δp + Δq
Since V’ is constant, we can rearrange to obtain:
Δp = Δm – Δq
Let’s plot the change in the price level and the change in M2 to real GDP, relative to 2020Q1, the onset of the pandemic in the US.
Figure 1: PCE deflator (blue), M2/real GDP (tan), both in logs relative to 2020Q1 values. M2 values are end-of-quarter. NBER defined peak-to-trough recession dates shaded gray. Source: BEA, Federal Reserve Board via FRED, NBER, and author’s calculations.
It’s been about 2 years since the Fed