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Even though the rate of growth in the monetary base decelerated — and the money multiplier decreased for the most part — from 1993-96 in the United States, the growth rate of the M2 money stock still progressively sped up. How is this possible?

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Reference to second graph:

https://www.alt-m.org/2016/07/21/why-the-money-multiplier-remains-so-low/

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So long as the growth rate of the monetary base is greater than the growth rate of M2, the ratio of M2 over the base (velocity) will decrease. (The numerator of M2/MB is growing less slowly than the denominator.)

That is what happened during (most of) the period shown. It was only in 1996 that M2 was growing faster than the base, which would increase velocity.

Your question is effectively attempting to characterise the second time derivative (acceleration) of M2 in terms of the acceleration of the monetary base and velocity. In my answer to another question, I give the relationship for acceleration in the money supply, and it is related to the acceleration in the monetary base and the acceleration of velocity. The data shows the level of velocity, which is not enough to characterise the relationship.

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