Following the money is fraught with difficulty. Numerous attempts to pin down the precise relationship between the amount of the stuff being printed, or deposited in accounts, and inflation have failed.
So much so that those attempts gave us the term Goodhart’s Law, which describes the annoying tendency for any variable to lose the capacity to tell us what we’d like it to about the economy once we attempt to regulate it.
Money’s wriggliness helps explain why most economists have ignored aggregates in recent decades. However there’s been a revival of late due to the surge in money growth that came after officials the world over flooded their economies with cash in the wake of the pandemic.