A Brief Note on the Velocity of Money

Mathematicians understand the simple fact that in an equation containing a number of variables, at least one has to be a dependent variable. That is, when you have a number of properties you are measuring independently and try and relate them mathematically, you need a dependent variable to make the equation work. A classical relationship in economics is GDP = MV where GDP is just that, M is a measure of the money supply, and V is the velocity of the money being referenced.

As Wikipedia describes velocity, V:

The velocity of money (also called velocity of circulation) is the average frequency with which a unit of money is spent on new goods and services produced domestically in a specific period of time.

We would add spending to buy debt to the above definition. Velocity can be considered to be a function of the amount of our cash we intend to spend and the length of time we hold it before we spend it. It is inversely related to the duration of ownership of money based on whatever definition of ‘money’ is used.

Velocity increases when the economy is growing faster than the money supply. The inverse relationship also holds. Generally, V is viewed as an indication of the health of the economy. When V is decreasing, we are holding money in reserve longer and economic activity is slowing. The economy may be headed for a recession. If V is increasing, the economy is growing because we are spending our money faster.

We discuss the current state of V in our economy below and examine some aspects of its changes. Click on any graph to enlarge in a new window.

We can measure GDP and M but we can’t measure V which as the dependent variable, has to be calculated. We discussed various measures of the money supply in Understanding Money: Part 3 – Measures of the Money Supply. The growth in these various measures, M1, M2, and MZM plus MZMc and M3 are shown in Figure 1. We show their associated velocities in Figure 2. There we have included the calculated velocity for currency or MZMc shown in dark yellow.

Figure 1. The various measures of the money supply, M1, M2, M3, MZM and MZMc (CURRCIR). (Source: FRED)

We have use a vertical log scale. The resulting linearity is more informative than the exponential growth a linear vertical scale would show. Of all measures, the growth in MZMc is the most regular (linear). This is controlled by the Fed more directly than M1 and M2 which have components influenced by the behavior of players in the economy.

Figure 2. The velocity of M1, M2, MZM and MZMc. (Source: FRED)

Currency (MZMc) is the most liquid form of money since it is already in the form that most economic transactions occur in and has a true zero maturity. Since the consumer is responsible for roughly 70% of GDP in the US and the consumer uses MZMc widely, the yellow curve in Figure 2 shows healthy growth (consumer spending) of the economy relative to MZMc, up to the mid 1980s. After that point, the velocity of MZMc drops dramatically until about 2004 at which point it picks until the recession of 2009 causes it to drop the most on record establishing continuing record lows. As we have noted, the growth in MZMc is markedly uniform so the volatility in its velocity is due to changes in GDP.

We note without comment that as the measure of the money supply becomes more inclusive of more money types (M1 to MZM to M2) that have a low or effectively zero maturity, the changes in velocity becomes smaller. This suggests a degree of correlation between the money type and GDP.

To get a better idea of what is going on with the velocity of MZMc, we compare it with the Federal Funds rate (FEDFUNDS) which we have written about in the past (search on ZIRP). Shown in Figure 3, there appears to be a clear correlation between the velocity of MZMc (yellow line) and the FEDFUNDS rate (purple line with a scaling factor applied to improve the curve’s fit on the graph).

Figure 3. The velocity of currency compared with the Fed Funds rate.

We have written much on the failure of Fed policy and its tools (see the links at the end in the section Essays on Fed Policy). One of the Fed’s most important policy tools is the FEDFUNDS. The Fed raises rates to cool the economy and lowers rates to stimulate the economy. The apparent correlation of the two is counter-intuitive. From its peak around the 1980 recessions, the rate has declined to zero (ZIRP) at which point it becomes a broken tool. This descent should have have provided considerable stimulus to the economy with associated economic growth and increasing velocity of MZMc. Instead, the velocity of MZMc has fallen off a cliff.

We suspect the answer lies in the nature of the measurement of GDP but choose not to explore it at this time. In any case, we consider that MZMc velocity is further evidenc of the failure of Fed policy

Finally, in Figure 4, we calculate the velocity of total credit market debt outstanding (TCMDO) (red line) which as discussed in Understanding Money: Part 5 – It’s All Money, we consider to be a measure of the total money supply. We have overlaid this velocity with the TCMDO (blue line) and GDP (green line), both of which we have inverted with simple scaling transforms to create a more readable visual overlay. The result that we see is that this measure of the money supply outgrew the economy in a roughly linear fashion until the 2009 recession when the growth briefly reversed and the velocity consequently picked up slightly.

Figure 4. The velocity of TCMDO against TCMDO and GDP (both inverted).

The velocity curve tells us that TCMDO is growing faster than GDP (we used a multiplier of 3.6 to align the graphs of GDP and TCMDO). Recent research supports an argument we had made in past essays that high levels of credit market debt reduce future economic growth. This is intuitively obvious when future income must be used to pat back debt rather than fund new spending.

Our gut tells us thee are more jewels of insight to be mined in this topic but that’s for a future essay.

The Series

Essays on Fed Policy

We have written a number of essays on Fed policy and its failure including:


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