A tautology:

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 – Δ

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

Keep reading this article on Econbrowser Blog - James Hamilton & Menzie Chinn.

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