This, of course, leaves us none the wiser as to how to model velocity, as the equation of exchange is nothing more than an identity. MV=PQ just says that the money flow of expenditures is equal to the market value of what those expenditures buy, which is true by definition. The left and right sides are two ways of saying the same thing; it’s a form of double-entry accounting where each transaction is simultaneously recorded on both sides of the equation. Whether an effect should be recorded in M, V, P, or Q is, ultimately, arbitrary. To transform the identity into a tool with predictive potency, we need to make a series of assumptions about each of the variables. For example, monetarists assume M is determined exogenously, V is constant, and Q is independent of M and use the equation to demonstrate how increases in the money supply increase P (i.e. cause inflation).

The first practical problem with velocity is that it’s frequently employed as a catch-all to make the two sides of the equation of exchange balance. It often simply captures the error in our estimation of the other variables in the model.