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Commerce · III.08 · MMXXVI · daylight

La Bourse  /  Volume III  /  Nº III.08

Velocity, Circulation, and Health

Volume III — Money, Energy, Information

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THE PLATE

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THE LETTER

You have almost certainly seen the chart. A single line, quarterly, running from the middle of the last century to now — the velocity of the M2 money stock. It rises through the nineties, turns over in 1997, and then falls, and falls, and keeps falling, until by the middle of 2020 it has lost half its height. It is one of the most-shared charts in economics, and it is usually captioned with a sentence about a slowing, sickening, seizing-up economy: the blood is not moving.

This chapter is about that line, and it does two things with it.

The first is arithmetic. We will compute the line ourselves rather than quoting it, from the two published series it is made of, because the moment you do that by hand you discover what it is: velocity is not a measurement. It is a definition. No one has ever timed a dollar. V is whatever number makes the identity balance, and the identity was arranged to balance. The falling line is a real fact about two other things and it is not a fact about speed.

The second is the more interesting half, and it is appreciative. Circulation is a real property. It can be measured, it is measured, and the people doing the measuring properly are mostly not macroeconomists — they are town councils, regional currency schemes, a Swiss clearing bank that has been at it since 1934, and treasurers running supplier finance. What they measure is not how fast money moves but where it goes next, and how much of it is still here after three rounds. That has a closed-form answer, it is a geometric series, and it is one of the most useful pieces of arithmetic in this volume.

By the end of this chapter you will be able to compute a local multiplier from a retention rate in your head, you will know the threshold at which a higher multiplier stops being worth having, and you will never again read a velocity chart as a diagnosis.

— The Editors

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DISCOVERY

What is already working

The WIR Bank, Basel, since 1934. A mutual credit clearing circle of Swiss small and medium enterprises, still operating after ninety years, in which members extend each other credit denominated in a unit that is not the franc and cannot leave the circle. Because it is a closed ledger, every unit and every transaction is known exactly — which means WIR is one of the few systems on earth where turnover is observed rather than inferred. James Stodder's analysis of the accounts found something that ought to be better known: WIR turnover is countercyclical. When Swiss GDP falls, trade inside the circle rises; when the franc economy is buoyant, the circle quietens. A circulation system that fills up exactly when the main one empties is not a curiosity. It is a shock absorber that has been in continuous service since before the Second World War.

Preston, Lancashire, from 2013. Six anchor institutions — the council, the university, the college, the constabulary, two housing associations — put their combined procurement on one table and asked a question nobody had asked: where does this land? In the 2012/13 year £38.0 million of £750.0 million was spent with organisations based in Preston, which is 5.07 percent. By 2016/17 it was £111.0 million of £616.0 million — 18.02 percent — and the total base had fallen by £134.0 million over the same period. That is £73.0 million a year more landing in the town, out of a smaller pot. No new money was raised. The programme is arithmetic and paperwork: unbundle the large contracts into lots a local firm can bid for, publish the pipeline early, pay quickly.

Sardex, Sardinia, from 2009. A mutual-credit circuit for a few thousand small Sardinian firms, zero-interest, with balances required to settle within the year. Like WIR, it is a closed ledger, so the circuit knows precisely how many units exist and precisely how many times each moved. The design choice worth noticing is not the currency; it is that the brokers actively match members — they find the member who buys what you sell, rather than waiting for a market to clear. Circulation, in Sardex, is somebody's job description.

The LM3 instrument itself. In 2002 the New Economics Foundation published The Money Trail — a method, built for a parish council rather than a research department, for following a pound through three rounds of local spending. You ask the recipient of your money where they spent theirs, and you ask their recipients the same, and you stop at the third round because that is where response rates die. It is unglamorous and it is genuinely a measurement: real payments, real counterparties, a real proportion. Every figure in the next movement that has a claim to be observed rather than defined comes from this family of methods.

Four systems, four countries. In each one, somebody made circulation countable — by closing a ledger, by mapping a procurement spend, by matching counterparties by hand, by knocking on the third door. None of them made money faster. All of them made its route visible, which turns out to be the property that does the work.

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THE ARITHMETIC

What the quantity equation can and cannot tell you

Start with the identity, because the trouble begins in how it is written.

  Fisher (1911), transactions form     M · V_T  =  P · T
  income form                          M · V    =  P · Y   =  nominal GDP
  Cambridge form                       M        =  k · P · Y,   k = 1/V

P, Y and M are each produced by an independent procedure: a price index, a national accounts aggregation, a monetary aggregate assembled from bank returns. V is produced by no procedure at all. It is defined as nominal GDP divided by M. There is one degree of freedom in the equation and it is V, which is to say: the identity is true the way 2 = 2 is true, and any statement of the form velocity fell is the statement the money stock grew faster than nominal income, translated into the vocabulary of speed.

Compute it yourself and the translation becomes obvious.

  quarter     nominal GDP $bn     M2 $bn     V = GDP/M2     1/V in months
  1997Q3            8,542.2        3,897.0        2.192              5.5
  2019Q4           21,747.4       15,254.0        1.426              8.4
  2020Q2           19,913.1       18,109.0        1.100             10.9
  2025Q2           30,331.0       21,900.0        1.385              8.7

Peak to trough is 2.192 to 1.100 — a fall of 49.8 percent, the famous halving. Now take logs, which makes the decomposition exact:

  ln(nominal income ratio)   ln(19,913.1 / 8,542.2)  =  0.8464    ×2.331
  ln(money stock ratio)      ln(18,109.0 / 3,897.0)  =  1.5362    ×4.647
  ln(V ratio)                0.8464 − 1.5362         = −0.6898
  V ratio                    e^−0.6898               =  0.5017

The halving is that pair of numbers. Nominal income multiplied by 2.331 and the money stock by 4.647, and nothing else happened. Read the last column of the table instead and the same arithmetic says something a reader can act on: the American economy held about 5.5 months of its income as money in 1997 and about 10.9 months of it in mid-2020. Not money slowed down. People and firms chose to hold twice as much liquidity, which is a decision with reasons, and the reasons are the subject of Chapter III.10.

Here is the cut. The steepest fall ever recorded in a velocity series is not in M2 at all. It is in M1, between the first and second quarters of 2020.

  2020Q1   M1, old basis    4,002.0 $bn    V = 21,538.0 / 4,002.0  = 5.382
  2020Q2   M1, new basis   16,206.0 $bn    V = 19,913.1 / 16,206.0 = 1.229

A collapse of 77.2 percent in one quarter. On 24 April 2020 the Federal Reserve amended Regulation D to remove the six-per-month transfer limit on savings deposits; from the following H.6 release, savings deposits were reported inside M1. The denominator quadrupled by publication. Split the fall multiplicatively, using an old-basis M1 for 2020Q2 of about 5,000.0 billion:

  V on the old basis                    3.983
  real factor        5.382 → 3.983      0.7400     ln = −0.3011
  definitional       3.983 → 1.229      0.3085     ln = −1.1759
  definitional share of the log fall              79.6 %

Walk that estimate from 4,600.0 to 5,400.0 and the definitional share moves only between 85.3 and 74.4 percent. Between three-quarters and six-sevenths of the sharpest velocity collapse on record is an amendment to a regulation, and not one transaction changed hands to produce it. That is the honest negative of this chapter and it is the load-bearing one: a great deal of writing about circulation health is describing an artefact of the definition.

And the empirical test of faster is healthier fails just as plainly. Over the window in which M2 velocity fell 49.8 percent, real output per person in the same country went from 43,551 to 62,434 chained 2017 dollars — a rise of 43.4 percent. The ratio is invariant to the base year, so a reader working in 2012 dollars gets the same answer.

Now the constructive half, which is where the arithmetic earns its keep. Retention is observable. A pound lands on a counterparty; a proportion r of it is respent inside the same economy; a proportion r of that is respent again. Local income generated per pound is a geometric series:

  after n rounds     L(n)  = (1 − rⁿ)/(1 − r) = 1 + r + … + r^(n−1)
  in the limit       L     = 1/(1 − r)
  LM3 is L(3)        LM3   = 1 + r + r²
  share LM3 captures L(3)/L = 1 − r³
  marginal value     dL/dr = 1/(1 − r)²

Put the measured rates in. Civic Economics' Andersonville study found independent retailers respending about 0.48 of revenue locally against about 0.14 for chains:

  r = 0.48    LM3 = 1 + 0.48 + 0.2304 = 1.7104     L = 1.9231
  r = 0.14    LM3 = 1 + 0.14 + 0.0196 = 1.1596     L = 1.1628
  ratio over three rounds  1.4750        in the limit  1.6538

A pound generates £1.71 of local income against £1.16 — a gap of 55.1 pence, compounding rather than moral. Applied to Preston's extra £73.0 million, rounds two and three are worth £51.86 million at the higher rate and £11.65 million at the lower: a difference of £40.21 million a year of local income, produced by routing and not by quantity.

Two disciplines before you use this. First, LM3 truncates. At r = 0.48 it captures 88.9 percent of the full series; at the 0.8229 implied by NEF's published local-food LM3 of 2.50 it captures only 44.3 percent of a true 5.65. The instrument the local-economy literature relies on understates its own case — and that same back-out is a warning, because a uniform 82.3 percent at every round is higher than any single-round rate anyone has measured. Field LM3 does not assume a uniform r, and the two methods are not interchangeable.

Second, and this is the threshold to carry: a multiplier counts transactions, and transactions are the cost of getting something done, not the getting-it-done. If the higher-retention supply chain needs proportionally more real input p to deliver the same basket, circulation per unit delivered is LM3/(1+p), and the breakeven is

  1.7104 / (1 + p) = 1.1596     →     p* = 0.4750 = 47.5 %

Below a 47.5 percent efficiency penalty the local route delivers more circulation per unit of goods. Above it the extra circulation is the sound of the same basket costing more to produce, and the town is poorer with a better multiplier. That number belongs on the front page of every community wealth programme, and almost none of them hold it.

Finally, the biology, checked in its own units, because the regenerative claim was imported from there. Cardiac output is rate times stroke volume: 60 beats a minute at 70 millilitres is 4,200 millilitres a minute, and so is 100 beats a minute at 42. Identical delivery, rate up 66.7 percent, stroke volume down 40.0 percent — and a clinician reading that pair calls it compensated shock, not fitness. The health variable in physiology is output, not rate. The economic analogue of cardiac output is real goods and services delivered. Faster money at constant delivery is the tachycardia, not the athlete.

So: is a faster-circulating currency healthier? No — not as a property of an aggregate, and the claim as usually stated is a category error. But retention is a real and measurable property with a real and compounding payoff, and that is what the regenerative literature was reaching for when it reached for the bloodstream.

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DREAM

What becomes ordinary

In the economy that has taken this seriously, nobody argues about velocity, because everybody knows how it is made.

A town knows where its money lands. Not sentimentally — the anchor institutions publish a quarterly table showing the proportion of third-party spend settling with counterparties inside the boundary, alongside the boundary's definition, because a retention figure without its boundary is not a figure. The table has three columns: this quarter, the same quarter last year, and the implied LM3. It fits on one page and it is read by the same people who read the housing numbers.

Every business of any size knows its own retention rate the way it knows its gross margin, and treats it as an operating variable rather than a value. It is computed from the purchase ledger, which already holds every counterparty's address, so it costs an afternoon of somebody's time once and then runs itself. When a procurement decision comes up, the retention consequence sits in the paper next to the price — and so does the efficiency penalty, so that nobody is allowed to buy circulation at any price.

Suppliers are paid in days rather than months, and everybody understands why: not because speed is virtuous, but because a small firm carrying sixty days of receivables is financing its customer at its own cost of capital, which is always the highest in the chain. When the payment terms shorten, the released working capital shows up on the supplier's balance sheet as a stock, is reported as a stock, and is spent on the thing the supplier had been deferring.

The regional clearing circuits are unremarkable infrastructure. A firm belongs to one the way it belongs to a trade association, and in a downturn its turnover there rises while its bank turnover falls, and this is understood as the circuit doing exactly what it was built for rather than as a sign of distress. Their published turnover figures are believed, because a closed ledger can produce one honestly.

And the velocity chart is still published, quarterly, by a central bank — and it is read correctly, as a chart of how much liquidity the economy has chosen to hold. When the line falls, the question in the room is not why has circulation sickened but what are people insuring against, and is that reasonable? Which, most of the time, it is.

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DESIGN

The structure that gets there

Four pieces, in this order. The order matters more than any individual piece.

One — define the boundary before you measure anything. A retention rate is a proportion of payments landing inside a boundary, so the boundary is half the number. Write it down: a postcode district, a travel-to-work area, a thirty-mile radius, a named list of parishes. Then write down the rule for a counterparty with several addresses — which is where every such measurement actually breaks — and publish both. A figure whose boundary moves is a figure that can be produced to order, and it will be.

Two — compute round one from the ledger you already have. Your purchase ledger holds a counterparty and an address for every payment you made last year. That is round one, complete, retrospective and free. It is not a survey and it does not need anyone's cooperation. Do this before anything else, because it converts the whole question from advocacy into accounting, and because the number is nearly always lower than the room expects.

Three — buy rounds two and three, or model them and say which you did. Round two requires asking your suppliers where their money goes, and the honest route is to ask your largest twenty by value, weight the answers by spend, and state the coverage. If you model it instead — applying a uniform r and the 1 + r + r² form — say so in the same sentence as the result. The two methods give different numbers and both are legitimate; presenting a model as a measurement is what discredits this whole field.

Four — put the efficiency penalty in the same paper. Every retention decision has a price consequence, and p* = 47.5 percent is the point at which a higher multiplier stops paying for itself in circulation per unit delivered. In practice you will be nowhere near it — a local supplier ten percent dearer sits at 1.5549 against the chain's 1.1596 and wins comfortably — but the discipline of computing it is what keeps the programme from becoming a sentiment. A community wealth programme that cannot state its own breakeven penalty is not yet a programme.

Then the governance, which is three sentences long. The retention figure goes in the standing reporting pack, quarterly, with its boundary and its coverage. One named person owns the definition, and changing it requires the same authority as changing a revenue recognition policy. And the number is published, externally, because a retention figure that only circulates internally will be quietly optimised, and one that is published will not.

For the payments side, the design is simpler still: shorten terms for the suppliers with the highest cost of capital first, not the largest. The benefit is the spread between their funding cost and yours, so it is concentrated entirely among your smallest counterparties, and paying your largest supplier early is almost always a gift with no economics in it.

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DESTINY

How it holds when nobody is pushing

Three things make a circulation programme self-sustaining, and they are all structural rather than motivational.

The ledger does the work. Round one recomputes itself from the purchase ledger every quarter with no human input. Any measurement that requires an annual heroic effort gets done twice and then stops; any measurement that falls out of a system that runs anyway will outlive everyone involved.

The suppliers want it to continue. A supplier paid in ten days instead of sixty has £273,973 of working capital back per £2,000,000 of revenue, and will protect the arrangement more energetically than your own staff. Build the constituency outside the building.

The boundary is owned, published and hard to move. This is the one that decides whether the programme is honest in year three.

Now the failure modes, named plainly. It fails when the boundary is quietly redrawn to include the next town and the figure improves without anything changing — which is the most common death and the hardest to see. It fails when round two is modelled and reported as though it were measured, and one journalist takes ten minutes to find out. It fails when the retention target is written as a flat percentage-point increase, ignoring the convexity: moving from 0.22 to 0.45 is worth far less per point than moving from 0.60 to 0.80, because the marginal value 1/(1−r)² runs from 1.644 to 3.306 to 25.000 across that range, and a target that treats all points as equal will stop exactly where the points start being valuable. And it fails — most expensively — when somebody starts reporting velocity, because velocity is a residual and a residual can be made to say anything by choosing a different denominator, as an entire M1 series demonstrated in a single quarter.

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DELIGHT

What it feels like

There is a specific pleasure in the afternoon you first run the purchase ledger by postcode. It is the pleasure of a question you assumed was philosophical turning out to be clerical. The file was always there. Nobody had ever sorted it that way.

And then the better one, which comes a few months later: you are in a room where someone is arguing about local sourcing in the usual terms — loyalty, community, fairness — and you can put an actual number on the table, with its boundary and its coverage stated, and the argument changes register entirely. Not because the number wins. Because it makes the conversation finite.

The third pleasure is the smallest and the most durable. A supplier — someone who runs eleven people out of a unit on an industrial estate — tells you, some months after the payment terms changed, what they did with the money that came back. It is never what you would have guessed. That is what circulation actually is, and it never once appeared in the chart.

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OPERATIONALIZE THIS

At the level of finance

The instrument: a buyer-funded early payment facility, with the discount priced off the spread and a retention covenant attached.

This is not a supply chain finance programme sold by a bank, and the difference is the whole point. You are using your own balance sheet, in the ordinary course, to buy something you want — shorter chains and a measurable retention rate — out of a spread that already exists between your cost of funds and your suppliers'.

The mechanics. One supplier makes the case. Take a supplier billing £2,000,000 a year on 60-day terms. Their receivable against you is £2,000,000 × 60/365 = £328,767. Move to 10-day terms and it is £54,795, so £273,973 of working capital is released — and note carefully that the benefit is that stock, not the 6.08 to 36.50 change in turns per year, which is the artefact. At their 9.0 percent cost of capital that stock is costing them £24,658 a year. Offer to pay fifty days early for a 0.9 percent discount: £18,000 to you, against a funding cost of £2,000,000 × 50/365 × 5.5 percent = £15,068. The supplier is £6,658 better off, you are £2,932 better off, and the discount annualises at 0.9 × 365/50 = 6.57 percent, sitting neatly between the two costs of capital. Nobody has been squeezed.

The number that decides it. One figure, on the front page:

      supplier's cost of funds  −  your cost of funds  −  running cost
                            >  1.5 points

On a programme paying £20,000,000 early at fifty days, the average balance outstanding is £2,739,726. A £30,000 running cost across that is 1.095 percent annualised. A gross spread of 3.50 points therefore nets to 2.405. Below about one and a half points of gross spread the administration eats the trade and the facility should not be built — which is precisely why it should be offered to your smallest and dearest-funded suppliers first, and why offering it to your largest is a gift with no arithmetic behind it.

The balance sheet treatment, and the trap. Since the IASB's 2023 amendments to IAS 7 and IFRS 7 on supplier finance arrangements, effective for periods beginning on or after 1 January 2024, these arrangements carry specific disclosure requirements — terms, carrying amounts, the range of payment dates, and non-cash changes. A buyer-funded early payment scheme run on your own cash is ordinarily a trade payable settled early and stays in operating cash flow. A bank-intermediated scheme where the bank pays the supplier and you repay the bank later can look economically like borrowing, and auditors and rating agencies increasingly treat it as such. Decide which one you are building before you build it, and put the answer in writing in the first memo. This is the trap that has embarrassed several large buyers, and it is entirely avoidable.

The counterparty and the covenant. Attach one condition, and only one: the supplier reports, annually, the proportion of their own third-party spend landing inside the defined boundary. Not a target — a report. That single line buys you round two of your LM3 from the counterparties themselves, at no cost, with a commercial reason for them to answer accurately. It is the cheapest measurement instrument in this chapter, and it arrives as a by-product of a trade that was already profitable.

The first ninety days.

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APPRECIATIVE QUESTIONS

Twelve, for a room

Discovery — what is already working

1. Think of a supplier relationship here that has lasted far longer than procurement would predict. Where does their money go when it leaves us, and who in this room already knows?
2. When have we paid someone faster than we had to, and what came back that we did not expect?
3. Where in this organisation is somebody already tracking where money lands — in a spreadsheet, unofficially, because they wanted to know?

Dream — what becomes possible

1. If our retention rate sat next to our gross margin in the monthly pack, what decision would change first?
2. Imagine our suppliers each reporting where their own money goes, willingly, because it is worth something to them. What would we learn in the first year that we cannot learn any other way?
3. If everyone here could see the route a pound takes through this town after we spend it, what would we want that route to look like?

Design — what we build

1. What is our boundary, and who would we trust to own the definition of it for the next five years?
2. Which twenty suppliers have the highest cost of capital, and what would it take to find out by Friday?
3. What is the honest coverage of the number we are about to publish — and what would make us proud to state it out loud?

Destiny — how it holds

1. What would have to be true for this measurement to still be running when everyone in this room has moved on?
2. If the number improved next year without anything real changing, who would notice, and how?
3. What is the smallest part of this that runs itself out of a system we already operate — and could we start with only that?

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WORKS CITED

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Barnett, W. A. (1980). "Economic Monetary Aggregates: An Application of Index Number and Aggregation Theory." Journal of Econometrics, 14(1), 11–48.

Barnett, W. A. (2012). Getting It Wrong: How Faulty Monetary Statistics Undermine the Fed, the Financial System, and the Economy. MIT Press.

Board of Governors of the Federal Reserve System. H.6 Money Stock Measures, and the interim final rule amending Regulation D (Reserve Requirements of Depository Institutions), 24 April 2020, with the accompanying technical Q&A on the composition of M1.

Bureau of Economic Analysis. National Income and Product Accounts, Tables 1.1.5 (Gross Domestic Product) and 1.1.6 (Real Gross Domestic Product, Chained Dollars).

Centre for Local Economic Strategies and Preston City Council (2019). How We Built Community Wealth in Preston: Achievements and Lessons. CLES.

Civic Economics (2004). The Andersonville Study of Retail Economics. Chicago.

Federal Reserve Bank of St. Louis. FRED series M2V, M1V, M2SL, M1SL, GDP, GDPC1.

Fisher, I. (1911). The Purchasing Power of Money. Macmillan.

Fisher, I. (1933). Stamp Scrip. Adelphi.

Friedman, M. (1956). "The Quantity Theory of Money — A Restatement", in Friedman, M. (ed.), Studies in the Quantity Theory of Money. University of Chicago Press.

Gelleri, C. (2009). "Chiemgauer Regiomoney: Theory and Practice of a Local Currency." International Journal of Community Currency Research, 13, 61–75.

Goodhart, C. A. E. (1975). "Problems of Monetary Management: The U.K. Experience." Papers in Monetary Economics, Reserve Bank of Australia.

Guyton, A. C. and Hall, J. E. Textbook of Medical Physiology. Elsevier, successive editions. (Cardiac output = heart rate × stroke volume.)

International Accounting Standards Board (2023). Supplier Finance Arrangements — Amendments to IAS 7 and IFRS 7. IFRS Foundation.

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Littera, G., Sartori, L., Dini, P. and Antoniadis, P. (2017). "From an Idea to a Scalable Working Model: Merging Economic Benefits with Social Values in Sardex." International Journal of Community Currency Research, 21.

Lucas, R. E. (2000). "Inflation and Welfare." Econometrica, 68(2), 247–274.

Sacks, J. (2002). The Money Trail: Measuring Your Impact on the Local Economy Using LM3. New Economics Foundation.

Stodder, J. (2009). "Complementary Credit Networks and Macroeconomic Stability: Switzerland's Wirtschaftsring." Journal of Economic Behavior & Organization, 72(1), 79–95.

Stodder, J. and Lietaer, B. (2016). "The Macro-Stability of Swiss WIR-Bank Credits: Balance, Velocity, and Leverage." Comparative Economic Studies, 58, 570–605.

Tobin, J. (1956). "The Interest-Elasticity of Transactions Demand for Cash." Review of Economics and Statistics, 38(3), 241–247.

Ward, B. and Lewis, J. (2002). Plugging the Leaks: Making the Most of Every Pound that Enters Your Local Economy. New Economics Foundation.

Note on figures. Every figure in this chapter is computed in lib/verify/III_08.py from the inputs named there with their units and sources. Velocity is computed from published GDP and money stock rather than quoted from the published velocity series, because the argument of the chapter is that the published series is that division and nothing more.