## Monday, October 24, 2011

### Big V

#### Velocity

Velocity is the "miles per hour" of the economy. It is spendings per dollar, or how many times the average dollar was spent. Easy, right? But which money? And what spending? Let's start with MZM money.

FRED says

Velocity is a ratio of nominal GDP to a measure of the money supply.

and for MZM they figure it as GDP divided by MZMSL:

the ratio of quarterly nominal GDP
(http://research.stlouisfed.org/fred2/series/GDP)
to the quarterly average of MZM money stock
(http://research.stlouisfed.org/fred2/series/MZMSL).

Graph #1 shows percent change from year ago for the velocity of MZM money, for the quantity of MZM money, and for GDP -- in other words, for the velocity ratio and the two components of that ratio:

 Graph #1: MZM Velocity and Components
Graph #1 shows a big red spike in the quantity of MZM money immediately after the 1982 recession, which pretty well mirrors a major down-spike in the Velocity of MZM money. Why's that? Because Velocity is how many times the average dollar is spent, and if the spending is relatively constant -- as the green line is -- then an increase in the number of dollars will calculate out as a decrease in the number of times each of those dollars is spent.

After the tall red spike, there are five more significant peaks by my count. Each red line peak is matched by a sag in the blue line. As the quantity of money rose, the velocity of money fell. This graph shows the pace of those changes.

The same mathematical fact (the quantity of money is the denominator of the Velocity ratio) holds true before the 1982 recession, though it is less clear from the graph. But you can see between the 1974 and 1980 recessions an up-and-down in the red line corresponding to a down-and-up in the blue. Same thing between the 1970 and 1974 recessions. And again, though smaller, one can see the same thing between the near-recession of 1966 and the recession of 1970.

Before 1966 we seem to lose it, but those numbers are all made up anyway. (MZM is a fairly recent invention.) Still, for a brief span in the 1960s, MZM growth appears as a flat red line. So the Velocity of money (the blue line) varies in proportion to spending (the green line). During those years the blue line and the green line move in parallel.

Graph #2 is just like Graph #1 except based on M1 money rather than MZM:

 Graph #2: M1 Velocity and Components

In the years after 1980 it is again very clear that the red and blue lines tend in opposite directions. There is no magic to it, only simple arithmetic: The money number is the denominator of the ratio, so the money number and the ratio value tend to move in opposite directions.

I should point out that if there is any difference between the red uptrends and the blue downtrends, that difference must be because of the changes in GDP (the green line).

Note that in the years before 1980 the green line is the highest of the three on Graph #2. (That was not so obvious on Graph #1). Thus before 1980 the green line plays a larger role on #2, creating greater differences between the red and blue lines.

To finish the exercise, a look at M2 velocity and its components:

 Graph #3: M2 Velocity  and Components
Here everything is much less clear. Nonetheless, the same arithmetic applies. The red and green lines trend together (though they vary differently), so both contribute more or less equally to the variations in the blue line Velocity.

If you change the elapsed time of your drive to work, and there is no change in the distance traveled, then as the driving time increases your average speed must decrease. It cannot be helped. That is the way the ratio works.

If you increase the quantity of money, and assume no change in spending, then as the quantity of money increases the velocity of money must decrease. It cannot be helped. That is the way the ratio works.

If quantitative easing increases the quantity of money, we should expect to see a slowdown of velocity. Unless spending increases faster than the money.

nanute said...

Art,
You wrote:
I should point out that if there is any difference between the red uptrends and the blue downtrends, that difference must be because of the changes in GDP (the green line)

Well, I'm not sure, but if I look at the effects of increasing the money supply it seems to have had a positive impact on GDP in the past. In the latest trend at the end of your graphs it shows a major negative impact on GDP. Not sure why, but I'm wondering if it has something to do with interest rates and paying interest on excess reserves.

I'm still digesting the rest of your excellent explanation of the relationship between the variables.

The Arthurian said...

"...if I look at the effects of increasing the money supply it seems to have had a positive impact on GDP in the past."

Fair enough. Oddly, that did not occur to me during the writing. But the effect of Quantitative Easing on the Velocity ratio is immediate, direct, and certain. The effect of QE on output and prices is gradual, indirect, and uncertain.

The Arthurian said...

As Milton Friedman wrote: "what happens to the quantity of money tends to dwarf what happens to output" [Money Mischief, Chapter 8]