Explaining the Velocity Decline

Our framework solves the enigma of the velocity decline that was observed in many countries during the 1980s, including Japan. The apparent decline in velocity is simply due to the fact that the equation of exchange has been erroneously defined. Researchers assumed that (1)<math display='block'> <mrow> <mi>M</mi><mi>V</mi><mo>=</mo><mi>P</mi><mi>Q</mi> </mrow> </math>$$MV = PQ$$ can be proxied reasonably accurately by (2)<math display='block'> <mrow> <mi>M</mi><mi>V</mi><mo>=</mo><msub> <mi>P</mi> <mi>R</mi> </msub> <mi>Y</mi> </mrow> </math>$$MV = {P_R}Y$$ However, this is true if and only if (3)<math display='block'> <mrow> <mi>P</mi><mi>Q</mi><mo>=</mo><msub> <mi>P</mi> <mi>R</mi> </msub> <mi>Y</mi> </mrow> </math>$$PQ = {P_R}Y$$ that is, all transactions for which money is used are part of and accurately measured by nominal GDP. This ignores the possibility that transactions that are not part of GDP, such as financial and real estate transactions, exist and may develop differently from GDP-based transactions. There is little empirical evidence that equation (3) can be considered to hold true. Instead, it is a special case that only applies when there are no real estate or financial transactions, or, in the case of changes, when these non-GDP transactions remain a constant proportion of all transactions. In general, we must expect that GDP-based transactions are a subset of all transactions. Thus instead of equation (3): (4)<math display='block'> <mrow> <mi>P</mi><mi>Q</mi><mo>&#x2265;</mo><msub> <mi>P</mi> <mi>R</mi> </msub> <mi>Y</mi> </mrow> </math>$$PQ \geqslant {P_R}Y$$