The current GDP deflator should be 18% higher (in log terms), or 154.2 instead of 128.2. To see this, consider the 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
In 2019Q4, V for M2 was 1.4245. Take logs (where lowercase letters denote log values).
p = m + v’ – q
Taking this manipulation literally, one obtains the following picture.
Figure 1: Log GDP deflator, 2012=0 (blue), and log M2 x V’/GDP where V’ takes on a fixed value of 1.42 (recorded on 2019Q4) (tan). GDP in bn Ch.2012$ SAAR, M2 in bn$. NBER defined peak-to-trough recession dates shaded gray. Federal Reserve, BEA via FRED, NBER, and author’s calculations.
The 2022Q3 GDP deflator was 25% higher than in 2012, while using the 2019Q4 value of velocity, the GDP deflator should have been 43% higher (in log terms), had the flex-price quantity theory held.
If you were wondering, there is little evidence of stability in velocity (either mean or trend stationarity). The Johansen maximum likelihood approach to testing for cointegration shows no evidence of a long run relationship between the GDP deflator on one side, and M2 divided by real GDP on the other (the tan series in Figure 1) over the 1960-2022Q3 period.