A key feature of the financial crisis was a massive fall in the velocity of money.  But what exactly is “money velocity”?  By definition, V=PY/M.  In English: Velocity=Nominal Income divided by the Money Supply.  When asked for some intuition, economists often respond that velocity is the “average turnover” of a dollar.  A velocity of 2, for example, means that the average dollar gets spent twice per year.  Except in a world without resale, however, this explanation is incorrect.  Suppose all new production ceased.  Money would still “turnover” as assets change hands, but nominal income would be zero – and velocity would be too.

I think I have a better way to explain velocity.  Forget turnover.  Velocity is the inverse of the percentage of income that people keep in the form of money.  If nominal income is $100B and the money supply is $10B, then velocity is 10 – which means that average money holdings equal 10% of annual income. 

Velocity is therefore essentially a measure of income-adjusted money demanded.  The higher velocity, the lower income-adjusted money demand.  When velocity plummets, as in 2008, this means that income-adjusted money demand has spiked.

What measure of money do I have in mind?  All of them.  For every monetary aggregate, there is a corresponding velocity.  Velocity of the monetary base might equal 100, indicating that people hold 1% of their annual income in (cash plus reserves).  Velocity of M3 might equal 2, indicating that people hold 50% of their annual income in (cash plus reserves plus checkings plus savings plus whatever).  Usually the various velocities move in tandem, but they don’t have to.

Pedagogically, the best feature of my explanation is that you can calculate person-specific velocities.  If a student has annual income of $10,000, and on average holds $2000 in cash plus checking, then his corresponding velocity for M1 equals 5.  You can then ask the student questions like: What would happen to your velocity if interest rates fell?  If credit cards became more widely available?  If you suddenly got nervous about your financial security?

Once the student “gets” the microeconomics of his own velocity, it’s a lot easier to grasp the macroeconomics of velocity.  There’s just one crucial intellectual bridge to cross: An individual can reduce his personal velocity simply by increasing his money holdings; for people in general to reduce velocity, in contrast, there has to be a corresponding change in nominal income (unless, of course, the quantity of money changes).  So if the average person decides he’d rather hold 40% of his income in the form of cash rather than 20%, and everything else stays the same, the nominal income of the economy has to halve.

Economists occasionally dismiss MV=PY as a mere tautology.  Whenever I’ve taught macroeconomics, however, I’ve found that it’s an immensely useful tautology – especially once students intuitively understand all four variables in the equation.