# Implications for the quantity theory of elastic price

The current GDP deflator should be 18% higher (in terms of logarithms), or 154.2 instead of 128.2. To see this, consider padding:

MV ≡ PQ

where M is money, Fifth is speed s is the price level, s It is an economic activity.

Supposedly Fifth’ Fixed and then:

MV’ = PQ

In 2019Q4, V for M.2 was 1.4245. Take logs (where lowercase letters indicate log values).

p = m + v’ – q

Taking this manipulation literally, one gets the following picture.

Figure 1: GDP contraction log, 2012 = 0 (blue), AD log2 x V’/GDP where V’ takes on a constant value of 1.42 (recorded in 2019Q4) (tan). GDP in billions of cz 2012 dollars, M2 in billions of dollars. The National Bureau of Economic Research has peak-to-trough recession dates highlighted in grey. Federal Reserve, BEA via FRED, NBER, and Author Accounts.

The GDP deflator in Q3 2022 was 25% higher than it was in 2012, while using the velocity value for Q4 2019 the GDP deflator would have been 43% higher (in terms of logarithms) , while retaining the quantity theory of price elasticity.

In case you were wondering, there is very little evidence for stability in velocity (either intermediate or directional stability). Johansen’s maximum likelihood cointegration test approach shows no evidence of a long-run relationship between the GDP deflator on the one hand, and M2 divided by real GDP on the other (tan series in Fig. 1) over the period 1960–2022 Q3.