## Tuesday, March 15, 2016

### Velocity and Interest Rates move together

Okay, I slept on it.

Oilfield Trash commented on my previous post:

the 3-month Treasury bill yield as a function of liquidity preference: I = EXP(4.27 – 45.5*M/PY) where M= Monetary Base and PY is Nominal GPD.

"You get a pretty good fit," he says. I drew it up:

 Graph #1: The Interest Rate (blue) and the Result of Calculation (red)
You get a pretty good fit.

The blue line is the 3-Month Treasury Bill: Secondary Market Rate. The red line is calculated using some carefully chosen constants along with the St. Louis Adjusted Monetary Base and a measure of GDP. I used annual data from FRED.

I showed the economic data, the M/PY from the calculation, in light gray, using the right-side vertical scale. It moves in the opposite direction from the calculated (red) line. Has to do with M/PY being subtracted in the calculation. If we were adding it, I expect the red line would move in the same direction as the gray, rather than opposite.

Looking at the red and blue lines, the first thing I noticed was that on the uphill, from 1934 to 1981, the red line tends to run low on the blue. On the downhill, after 1981, the red tends to run high on the blue. At first I thought that might be a fluke result of the calculation. But I don't see how that can be, because the red line comes from base money and GDP and a couple constants, and nothing else. There are no flukes in the calculation.

Looking at the graph again now, it occurs to me that on the way up the Fed was fighting inflation all the while. On and off, but all the while. So then the red runs relatively low on the uphill because the Fed kept pushing interest rates up to fight inflation. On the downhill side, then, it looks like the Fed kept trying to boost growth by repeatedly reducing interest rates. And the red runs relatively high as a result.

Or maybe it wasn't even the Fed doing it. Maybe it was the result of the mass of economic decisions made by, you know, people participating in economic activity. Some people say the Fed follows the market.

//

The red line is a lot less wiggly than the blue. The wiggles show the pattern of business cycles, draped over the longer term path established by the M/PY ratio.

As of course you know, the M of M/PY is money, P is the price level, and Y is real output. Together, those three variables constitute three quarters of the equation of exchange: MV=PY.

What's missing is V: velocity. If you take the equation of exchange and divide both sides by M, you get V=PY/M.

Invert both sides, and you get (1/V)=M/PY.

Wait a minute now: M/PY is part of the calculation.

The calculation from Oilfield Trash says that the interest rate is equal to the exponent of one number minus another number times M/PY. But M/PY is equal to (1/V). So the calculation says that the interest rate is equal to one number minus another number divided by the velocity of money.

So there is a relation between the interest rate and the velocity of money.

Why would that be?

It's pretty easy to say things that are more common are cheaper, things that are less common are more expensive. When money is moving fast -- when velocity is high -- does money seem more common, or less common?

What does the graph say?

The gray line M/PY is the same as (1/V). In recent years, for example, the line goes up like crazy because of all the QE. Money became more common, relative to GDP. And the interest rate went down. But that's (1/V). What about V itself?

When (1/V) goes up, like in the recent years, V goes down. V goes down, and interest rates go down. So, velocity and interest rates move together.

Velocity and interest rates move together, perhaps because things that are more common are cheaper and things that are less common are more expensive. It seems to work. But you know what? I shouldn't have asked. I shouldn't have asked "Why?"

The fact is, velocity and interest rates move together. That's the fact. It will probably help me to remember that fact, thinking things that are more common are cheaper. But I don't know if that's the reason. It's only a theory. The fact is, velocity and interest rates move together. Base velocity, anyway.

http://www.hussmanfunds.com/wmc/wmc110124.htm

jim said...

"Looking at the red and blue lines, the first thing I noticed was that on the uphill, from 1934 to 1981, the red line tends to run low on the blue."

That suggests the blue curve may be driving the red.
(or at least preceding the red in time}.

"What's missing is V: velocity."

Actually one could say, V (velocity of M0) is the only variable in the equation. It could be written as EXP(4.27 – 45.5/V)

Oilfield Trash said...

Art

Thanks you found my missing reference

http://www.hussmanfunds.com/wmc/wmc110124.htm"

I think I will have to dust off some of my older Hussman post. I have another individual that I have been reading on interest rates Jason Smith

http://informationtransfereconomics.blogspot.com/2014/03/the-effects-that-move-interest-rates.html

"The short run effect of monetary policy is called the liquidity effect. A change in the money supply causes interest rates to move in the opposite direction, in the short run. The long run effects of monetary policy are called the income effect, the price level effect and the expected inflation (Fisher) effect. These three effects all cause interest rates to move in the same direction as the money supply."

"If we look at the combined monetary effects in the right graph above, another pattern(or interpretation) emerges. The period before the early 1980s (blue) has a sizable contribution from the income/inflation effect, while data afterwards (purple) shows the liquidity effect dominating interest rates. This is broadly in line with the general path of interest rates over the post-war period: rising before the 1980s and falling afterwards."

Good stuff and I can confirm through Hussman this seems to be a correct interpretation by Jason.

Also this might be of use to you

http://informationtransfereconomics.blogspot.com/2014/03/the-diminishing-effect-of-monetary.html

"The diminishing effect of monetary expansion is seen as the curve bends downward as you move to the right. An additional point is that just because a country finds itself on the right side of the graph above, doesn't mean it is doomed to remain there. The US actually had a very large monetary base relative to the size of its economy during the period just before and after the Great Depression. A bout of accelerating inflation during/after WWII caused NGDP to grow much faster than the base, leading to an overall reduction in the ratio of MB/NGDP"

The Arthurian said...

"Actually one could say, V (velocity of M0) is the only variable in the equation. It could be written as EXP(4.27 – 45.5/V)"

Yeah. Thanks Jim. That is the point I was trying to get to.

"A bout of accelerating inflation during/after WWII caused NGDP to grow much faster than the base, leading to an overall reduction in the ratio of MB/NGDP"

Exactly, Oilfield. Inflation was the economy's way of correcting the imbalance between Base and NGDP.

The Arthurian said...