Revised 9-27-21. Corrected bank reserves statement to note they are not counted as M1.

Monetary velocity is a very important, often ignored “mystery” number that is an important determinant of GDP (gross domestic product) in an economy.  It represents how often, on average, each dollar in the economy is spent for final goods and services.  That number, combined with the amount of total money in an economy, determines nominal GDP which is money quantity times money velocity.  M x V = nominal GDP

Monetary velocity only counts money spent for final goods/services, and does not count dollars that are exchanged for any other reason, such as buying bonds or stocks, or making or receiving a loan, or exchanging 5 one dollar bills for a 5 dollar bill.

No one seems to have any problem visualizing what total money held M in an economy means.  However it seems most are mystified by what force in the economy causes monetary velocity to be what it is.  Here’s what one, completely perplexed economic commentator recently said about monetary velocity:

To paraphrase the Dread Pirate Roberts, anyone who claims that she fully understands what drives money velocity “is either lying or selling something.”  Technology certainly plays a role that is only dimly understood.  But without question two key inputs are inflation expectations and the level of interest rates.

The first two sentences in this statement are completely silly as I hope to show by the simple explanation to be given.  Monetary velocity no longer needs be “dimly understood.”  The explanation that follows will make obvious why the person’s last sentence is quite correct—no magic or difficult mathematical economic analysis will be required to understand why.  But an additional factor affecting velocity will also become evident: velocity will decrease with the perceived higher risk for investing (or saving) money.

To quickly give away the answer: Monetary velocity is crowd sourced, by the activity of each individual person in an economy.  It has to do with each person’s choice of how much cash money each person wishes to hold compared to how fast they spend such money in their possession.  When all individual choices are combined, this is the only factor that collectively determines the monetary velocity of an economy.

Two numbers for each person in the economy determine velocity:.

  1. How much cash money each one decides to hold for expenses.
  2. How long it takes each one to spend that amount of money for his/her normal cash expenses.

Once you know those numbers for every individual in their group, that group’s velocity is determined as shown in the math equation below.  Similarly, different subgroups can be combined together in a deterministic way to calculate velocity for an entire economy.  So it will become evident that not only does “monetary velocity” apply to an entire economy, it also can be measured for each individual that holds cash, and also for each subgroup such as “all people with wealth over ten million dollars.”  Velocities for different groups can be quite different. The main essay on this website: “A new macroeconomics to explain Wealth Inequality” describes how these numbers for different groups are distributed, such as among different wealth groups can determine how well an economy is working.

How to determine velocity for an individual: Everyone makes a choice about how much money they want to hold for their cash expenses.  Not too much, and not too little.  If too little, it can increase anxiety about having enough to cover ordinary expenses as they occur.  If too much, that extra money could be of more benefit if invested, which would then earn some interest.  Some may hold much more than they need for expenses because they don’t trust any investments to be safe.  A typical amount could be to hold enough cash to cover 1 month’s expenses.  If the total average amount of cash money held is $2000, and it takes four weeks to spend that much, that person’s velocity is 13.  To get that velocity number I divided 52 weeks in a year, by 4 weeks expenses to get 13.  Of course many may want to hold more or less than that example.  Monetary velocity can be thought of as how rapidly the cash you hold “escapes” from one’s grasp by spending.

Individual velocities combine deterministically to get an economy’s total velocity: To determine the total economic velocity: add up everyone’s velocity number, weighted by the money they hold, to get the total economic velocity.  For that last example with velocity of 13, that person’s portion is = 2000 x 13 divided by total money supply in the economy. People with high wealth may hold high amounts of cash compared to their spending, which means they hold money at low velocity, which can reduce velocity, and therefore GDP for an entire economy.

No mystery! That’s ALL there is to determine monetary velocity in an economy! Described mathematically:

Derivation formula

V = monetary velocity of M1 for entire economy
M = total M1 money in economy
Mk = individual M1 cash  held for expenses by person k
Vk= individual velocity for cash held by person k
n = number of people in economy

What about banks? It’s worth noting that a few of these “people” are banks.  They do hold reserves, but these are not counted as “money in circulation” so cash they hold does not affect velocity calculations.

Now the question of “what in the economy determines monetary velocity” has been transformed to a simple question: “what factors affect people’s decisions about how much cash money they decide to hold to cover expenses?”

Or you could ask “what makes you decide how much money you should hold?”  The question about velocity is no more (or less) complicated than answering that question.

What could make you want to hold more cash?  The LOW velocity choice.

Interest rates on saving cash as investment is too tiny to bother, so hold more cash instead.
You fear investments or loaning are risky, so hold more cash instead.
Interest rates may rise soon, hold cash money ready to invest later when interest rates rise.

What makes you want to hold less cash? The HIGH velocity choice.

Interest rates on savings is very high.  Hold less cash and invest (or loan) more to earn interest.
No fear about safety of the investment or loan.  Choose safe investment instead of holding money.
High inflation is happening.  Spend quickly before its value disappears.

Conclusion: 

Monetary velocity is correlated with interest rates: Low interest causes low velocity.
Monetary velocity is correlated with perceived safety of investment.
Monetary velocity is correlated with high active inflation.

Prediction 1: Very low interest rates cause low velocity and thus reduce GDP.  Here is empirical evidence for the assertion that interest rates strongly influence velocity: Thanks to Mr. Luca Benati, University of Bern for gathering this data into two informative pages.  Graphs for ten different countries’ economies show both velocity and interest rates.  Look at Figure 2a and Figure 2b just after page 10.  Interest rates are shown in black.  Velocity in red.  Note that velocity follows slightly behind interest rates.  http://www.hec.unil.ch/documents/seminars/deep/2362.pdf

Prediction 2: Japan was the first country to reduce interest rates to unprecedented low levels to attempt to boost GDP  from 2000 to 2017.  With low interest reward on money, people  held more money, velocity went down,  therefore GDP barely moved contrary to the expected increase.  The US and Europe experienced the same after 2010.

Prediction 3: Lowering interest rates too much to attempt to increase GDP is a very bad idea.  Velocity, and therefore GDP both go to zip. The lowest advisable interest rate is also called the low interest rate bound for effective monetary policy.

The Math: Here is how this formula is derived.  As expressed in this equation, GDP of an entire economy equals the sum of each person’s spending for goods and services.  Each person’s contribution to GDP is the product of their velocity times money they hold, expressing this mathematically:

mathematically expressing velocity times money