Friday, March 4, 2016

Hamilton on Velocity

You can’t increase inflation by creating more money if velocity falls proportionately

In an old Econbrowser post, James Hamilton said "when M1 goes up, the velocity of M1 goes down by an almost exactly offsetting amount."

Hamilton showed a couple graphs that opened my eyes. But you know me: I had to make my own:

Graph #1: Percent Change from Year Ago for M1 Money (blue) and M1 Velocity (red)
with the red line moved down to separate the lines for clarity
Interesting stuff.

Okay. Velocity is GDP divided by the money number. Other changes aside, when the money number gets bigger the GDP-to-Money ratio gets smaller. I understand that. I just didn't expect the mirror-image effect to be so strikingly evident. Changes in GDP would seem to have little effect.

I wanted to align the red and blue lines to get a better look. So I made the velocity number negative to flip the pattern. Like Hamilton did in his article. And I changed the constant, moving the velocity line up until the match was good in the 1985-1990 years. The resulting graph shows a lot of similarity between the two lines, even outside the 1985-1990 period:

Graph #2: M1 Growth Rate (blue) and M1 Velocity Growth Rate (red)
with the red line moved up to emphasize similarity
The fit seems different, better, after the early 1980s than before, for some reason. The changes are bigger; maybe that has something to do with it.

Okay. On Graph #1 there is a lot of "one goes up when the other goes down" action. So if you took and added those two lines together, a lot of the variations would cancel each other out. The resulting line would not be perfectly smooth, but the ups and downs would be smaller.

The blue line on Graph #3 shows money and velocity added together. Combined, the patterns do cancel each other out to a large extent.

Graph #3: Rate of M1 Growth + Rate of M1V Growth compared to GDP Deflator Inflation Rate
The red line shows inflation, as measured by the GDP Deflator. The blue line is moved down a bit to make visual comparison easier. I see a lot of similarity between the two.

First impressions:

1. The growth rates of money and velocity generally run in opposite directions. When one goes up, the other goes down. When the growth of M1 money goes up, the growth of M1 Velocity goes down. This is what you might expect, when you do the math, because money is the denominator in the velocity calculation. And it means that a change in velocity seems to be due mostly to a change in money.

2. M1 and M1V are not perfect mirror opposites. The difference from perfect must be due to variations of GDP.

3. When you arrange a calculation so that the changes in M1 and M1V tend to cancel each other out, the changes do not cancel perfectly. But what remains looks not perfectly, but powerfully related to inflation.

4. We're looking at nothing but GDP and Money here, and finding some relation to inflation.

Interesting stuff.

1 comment:

Oilfield Trash said...

My experience is that although MV = PY is a simple identity, people like to tinker with one variable or another while incorrectly assuming that the other parts of the equation are simply constant. For example, people often assume that doubling the monetary base will simply double the price level, but that requires V and Y to stay constant, which is hardly an accurate assumption. Likewise, advocates of easy money seem to believe that increasing the money supply will buy you more economic output, but this requires holding V and P relatively constant.

If you look at the historical data, neither of these arguments hold a great deal of water. Rather, what seems to be true is that the strongest effect of an increase in the money supply is to drive short-term interest rates lower, thereby increasing liquidity preference (i.e. reducing velocity). This isn't quite the whole story, but to a first approximation, the main effect of changes in the monetary base is to produce opposite and proportional changes in velocity.

The disturbing fact about this, however, is that inflation dynamics can potentially become unstable when a massive stock of base money is being kept in check by very low interest rates. This is because small increases in interest rates from near-zero levels imply huge changes in liquidity preference and velocity. If those changes are not offset by opposite and proportional changes in the monetary base, strong inflation pressures are likely to follow.

The wild card policy is the Fed does have the ability to raise the interest rate that it currently pays banks to hold idle reserve balances, in order to keep those balances idle.