## Friday, September 21, 2012

### Velocity and Other Funny Things

 Two kids behind a fence

When I go to FRED and type velocity in the search box, this is what I get:

Sorted by popularity (default), M2 Velocity is first on the list.

This, then, is "Velocity":

 Graph #1: The Velocity of M2 Money
Velocity is a measure of how fast money moves. Something like that. A measure of how often the average dollar is spent. But not just any dollar, and not just any spending. It is a measure of how often M2 money is used for final spending.

M2 money is like the tall kid behind the fence, but just the part you can see. Funny thing is, the short kid is M1 money, which is the money people spend. M2 money is the money we have in savings and the money we spend, all added together. The Velocity graph -- which supposedly shows how fast the average dollar is spent -- is based largely on money we don't even spend. On savings. Meanwhile, behind the fence, from the eyeballs down, is other money -- money not included in the Velocity calculation, whether we spend it or not.

The standard calculation for how often the average dollar is spent assumes that money in the spending stream and money in savings are spent alike -- but only a portion of that money is used in to figure Velocity. The rest is behind a fence.

Come to think of it, the other number, the spending used in the Velocity calculation is also behind a fence. The standard calculation uses final spending, but excludes intermediate spending behind some other fence.

And that, ladies and gentlemen, is Velocity. The ratio of two numbers behind fences.

Economists depend on it.

If you take the Velocity graph and invert it, it looks like this:

 Graph #2: Inverted Velocity
No no, that's not right. It looks like this:

 Graph #2: Inverted Velocity

To invert Velocity, divide the value 1 by the Velocity number.

Funny thing. Velocity is GDP divided by M2. Velocity is a fraction. When we divide 1 by Velocity we are dividing by a fraction. For me, this brings back memories of grade school math: To divide by a fraction, invert and multiply.

To calculate 1 divided by V, calculate 1 multiplied by 1/V.

But maybe it makes more sense this way: V is the fraction GDP/M2. To divide by the fraction GDP/M2, invert and multiply. So to calculate 1/(GDP/M2), figure it as 1 multiplied by (M2/GDP). The answer is M2/GDP.

Oh yeah, the funny thing: M2/GDP is the same as "the quantity of money divided by output." Perhaps you've heard of that one. Milton Friedman made it famous.

Friedman wrote:

"Changes in the quantity of money have important, and broadly predictable, economic effects. Long-period changes in the quantity of money relative to output determine the secular behavior of prices."

Definitive, don't you think? But when you compare prices (the red line) to M2/GDP, it's hard to see any similarity at all:

 Graph #3: Money Relative to Output, and Prices

Isn't that funny?