The present GDP deflator ought to be 18% higher (in log terms), or 154.2 rather of 128.2. To see this, consider the tautology:
MV ≡ PQ
Where M is money, V is speed, P is price level, Q is financial activity.
Assume V is consistent; then:
MV = PQ
In 2019Q4, V for M2 was 1.4245. Take logs (where lowercase letters signify log worths).
p = m + v– q.
Taking this manipulation literally, one obtains the following image.
Figure 1: Log GDP deflator, 2012= 0 (blue), and log M2 x V/ GDP where V takes on a repaired value of 1.42 (tape-recorded on 2019Q4) (tan). GDP in bn Ch.2012$ SAAR, M2 in bn$. NBER defined peak-to-trough economic crisis dates shaded gray.
Figure 1: Log GDP deflator, 2012= 0 (blue), and log M2 x V/ GDP where V handles a fixed worth of 1.42 (recorded on 2019Q4) (tan). GDP in bn Ch.2012$ SAAR, M2 in bn$. NBER specified peak-to-trough economic downturn dates shaded gray. Federal Reserve, BEA by means of FRED, NBER, and authors calculations.
The 2022Q3 GDP deflator was 25% higher than in 2012, while using the 2019Q4 value of speed, the GDP deflator ought to have been 43% higher (in log terms), had the flex-price amount theory held.
If you were wondering, there is little evidence of stability in speed (either trend or suggest stationarity). The Johansen optimum probability method to screening for cointegration reveals no proof of a long term relationship in 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 duration