The Origins of Velocity Functions

L ike any practical, policy-oriented discipline, monetary economics employs useful concepts long after their prototypes and originators are forgotten. A case in point is the notion of a velocity function relating money’s rate of turnover to its independent determining variables. Most economists recognize Milton Friedman’s influential 1956 version of the function. Written v = Y/M = v(rb, re, 1/PdP/dt, w, Y/P, u), it expresses income velocity as a function of bond interest rates, equity yields, expected inflation, wealth, real income, and a catch-all taste-and-technology variable that captures the impact of a myriad of influences on velocity, including degree of monetization, spread of banking, proliferation of money substitutes, development of cash management practices, confidence in the future stability of the economy and the like. Many also are aware of Irving Fisher’s 1911 transactions velocity function, although few realize that it incorporates most of the same variables as Friedman’s.1 On velocity’s interest rate determinant, Fisher writes: “Each person regulates his turnover” to avoid “waste of interest” (1963, p. 152). When rates rise, cashholders “will avoid carrying too much” money thus prompting a rise in velocity. On expected inflation, he says: “When . . . depreciation is anticipated, there is a tendency among owners of money to spend it speedily . . . the result being to raise prices by increasing the velocity of circulation” (p. 263). And on real income: “The rich have a higher rate of turnover than the poor. They spend money faster, not only absolutely but relatively to the money they keep on hand. . . . We may therefore infer that, if a nation grows richer per capita, the velocity of circulation of money will increase” (p. 167). Finally, with respect to the catch-all variable, Fisher cites all of the following