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

**Monetary velocity** is an important, often ignored 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. This site describes exactly what economic events determine it, and what its negative effect can be. 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 difficulty 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. The description below will bring complete clarity to its meaning. The explanation that follows will make obvious why the above quote in the last sentence about inflation and interest rates 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. Each agent in the economy has their own speed of spending money. When all individual choices are properly combined, this is the** only** factor that collectively determines the monetary velocity of an economy.

**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. However some who don’t trust investments to be safe may hold much more than they need for expenses. Monetary velocity can be thought of as how rapidly it takes to spend the amount of cash you on average typically like to hold. If only a short amount of time, that would represent high velocity. It’s determined for each person by knowing two numbers:

- How much average cash money each agent decides to hold for expenses.
- How rapidly that person spends that quantity of money.

Velocity is completely determined for one agent once you know how many months it takes to spend that average amount of cash money they typically hold. If it takes one month (1/12 of a year) to spend that much their velocity is 12. If they spend the same amount in just half a month (1/24 of a year), they are spending each dollar twice as fast, so their velocity is 24. If it takes 6 months, then their monetary velocity is much lower at 12/6 = 2.

It is pretty obvious that the amount of total money (M) in the economy is determined by adding together the amounts all agents hold together, either in hand or as cash in the bank. But it’s a little trickier how to combine all those velocities to get the velocity for the entire economy. The formula below shows how to combine each person’s velocity into a single velocity number that describes the velocity of the complete economy.

So there’s no mystery! That’s ALL there is to determine monetary velocity in an economy! Described mathematically: This formula is derived a little further down the page.

**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.

**What economic factors determine velocity? **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 low for people that hold a lot of non transactional cash.
- 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: