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Commerce · III.08 · MMXXVI · daylight

La Bourse  /  Volume III  /  Nº III.08  /  Workbook — the student

WORKBOOK — THE STUDENT

Chapter III.08 · Velocity, Circulation, and Health

For the person studying this alone or in a seminar. A term of practice, a term project, and a way of marking your own work. Everything here is done with a spreadsheet, a bank statement and a pen — no data subscription, no software.

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WHY THIS WORKBOOK IS DIFFERENT

Most economics teaching hands you velocity as a fact about the world. This term you are going to build it yourself from its two inputs, and the building is the lesson: within an afternoon you will know, in your hands rather than as an opinion, that the famous line is a division.

Then you will do the harder and more useful thing. You will measure a real retention rate — yours — and compute what a pound you spend is worth to the place you live, over three rounds, with a boundary you defined and published. Almost nobody has ever done this for themselves, and the number is always a surprise.

Two habits carried the whole way through, and they are the term's real curriculum:

1. Never quote a ratio you have not computed from its inputs.
2. Say which of your numbers are measured and which are modelled, in the same sentence as the number.

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PART ONE — DISCOVERY

Weeks 1–4: build the series yourself

Exercise 1.1 — The division (2 hours)

Open a spreadsheet. Two columns, from public sources: nominal GDP, seasonally adjusted annual rate, and the M2 money stock, quarterly average. Compute V = GDP/M2 for these four quarters and check your answers against the chapter:

Then plot your column next to the published velocity series. They will lie on top of each other. Write one sentence in your notebook about what that means, before you read on.

Exercise 1.2 — The decomposition (1 hour)

Add two columns: ln(GDP ratio to 1997Q3) and ln(M2 ratio to 1997Q3). Their difference is ln(V ratio). For 2020Q2 you should get 0.8464 − 1.5362 = −0.6898, and e^−0.6898 = 0.5017.

Now write the sentence that the chart is usually given: velocity halved. Then write the sentence your two columns actually support: nominal income multiplied by 2.331 and the money stock by 4.647. Keep both sentences. You will need the pair in the seminar.

Exercise 1.3 — The inversion (30 minutes)

Compute k = 1/V and express it in months. You should find 5.5 months in 1997Q3, 10.9 in 2020Q2, 8.7 in 2025Q2. Write a paragraph describing the same period using only the holding-period language. Notice how hard it becomes to imply a diagnosis.

Exercise 1.4 — The denominator experiment (1 hour)

Repeat the division for 2020Q1 and 2020Q2 using M1 rather than M2: 4,002.0 then 16,206.0 billion, giving 5.382 then 1.229 — a fall of 77.2 percent in a single quarter. Find and read the Federal Reserve's April 2020 Regulation D interim final rule and the H.6 technical note on the composition of M1.

The question to answer in writing, in one page: if a ratio can fall 77.2 percent because of an amendment to a regulation, what is the class of claims that ratio can support?

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PART TWO — THE ARITHMETIC

Weeks 5–8: the series that actually measures something

Exercise 2.1 — Derive the closed forms yourself (1 hour)

Do not look them up. Start from 1 + r + r² + … and derive:

  L(n) = (1 − rⁿ)/(1 − r)        L = 1/(1 − r)        L(3)/L = 1 − r³

Then differentiate L and get dL/dr = 1/(1 − r)². Three lines of algebra, and they are the whole toolkit.

Exercise 2.2 — The table (1 hour)

Build it, and keep it where you can see it all term:

Exercise 2.3 — Your own retention rate (one week)

This is the term's central measurement and it is done on your own bank statement.

1. Define your boundary and write it down. A postcode district, a named town, a radius. Write the rule for the awkward cases before you look at the data — an online retailer with a local warehouse, a national bank with a branch on your street, a landlord who lives elsewhere. Publish the rule to your seminar group before you compute anything. This is the discipline the whole field turns on.
2. Take three months of outgoings. Classify each payment as inside or outside the boundary by the rule you just wrote.
3. Compute r₁ = inside spend ÷ total spend. That is round one, measured.
4. Compute your LM3 as 1 + r₁ + r₁², and state clearly that rounds two and three are modelled at a uniform rate, not measured.

Exercise 2.4 — Buy one real second round (one week)

Pick one local business you actually use and ask them, politely and in person, roughly what proportion of their own costs are paid to businesses inside your boundary. One conversation. Compare their answer with the uniform r₁ you assumed. Write down the difference and what it does to your LM3.

Exercise 2.5 — The back-out (30 minutes)

Solve 1 + r + r² = 2.50 and get r = 0.8229. Then compute 1 − r³ at that rate: three rounds capture only 44.3 percent of a true 5.65. Write two sentences: one on why this makes LM3 conservative, one on why it also makes a uniform-r reading of a published LM3 implausible.

Exercise 2.6 — The threshold (1 hour)

Compute p* = 1.7104/1.1596 − 1 = 0.4750. Then build the sensitivity:

Find a real case in your own spending where the local option is dearer. Estimate the premium honestly. Are you anywhere near 47.5 percent?

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PART THREE — DREAM AND DESIGN

Weeks 9–11: write it as though somebody will act on it

Exercise 3.1 — The one-page retention report (3 hours)

Write the page you would hand to a parish council. It has four elements and nothing else: the boundary and its awkward-case rule; the measured round-one rate with its coverage; the LM3 with a plain statement of which rounds were modelled; and the breakeven penalty. One page. No adjectives.

Exercise 3.2 — The cardiac paragraph (1 hour)

Compute both sides of the identity: 60 × 70 = 4,200 and 100 × 42 = 4,200 ml/min. Then write two hundred words arguing the strongest possible case for the "faster money is healthier" claim — steelman it properly — and two hundred words against. You are marked on the steelman, not the rebuttal.

Exercise 3.3 — The timestamped pound (2 hours)

Take a supplier billing £2,000,000 a year at 60-day terms: the receivable is £328,767. At 10 days it is £54,795, releasing £273,973. Write one paragraph explaining why the released stock is the benefit and the move from 6.08 to 36.50 turns a year is the artefact. This is the chapter's thesis at the scale of one ledger; if you can write this paragraph cleanly you have the chapter.

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PART FOUR — DESTINY AND DELIGHT

Week 12: make it last, and enjoy it

Exercise 4.1 — The boundary audit (1 hour)

Give your published boundary rule to someone who wants to make your number look better. Ask them to find three legitimate-sounding ways to move it. Write their three down. That list is what a standing measurement has to survive, and knowing it is worth more than the measurement.

Exercise 4.2 — The convexity note (30 minutes)

Write a target for your own retention rate that respects 1/(1 − r)². Not "five points a year". Something that says where the value is.

Exercise 4.3 — The good afternoon

Sort one dataset you already have by a field nobody has ever sorted it by. Your bank statement by postcode is the obvious one, but any will do. Notice the specific pleasure of a question you assumed was philosophical turning out to be clerical. That pleasure is the whole discipline, and it is available every week for the rest of your life.

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THE TERM PROJECT

One place, measured properly

The brief. Choose one bounded place — a high street, a campus, a village, a postcode district. Produce a retention and circulation report for it, in eight to ten pages, that a real council could act on.

What it must contain.

1. The boundary, published, with the multi-address rule, written before any data was touched.
2. Round one, measured. A real spend dataset — your own, a society's, a small business that will let you see the purchase ledger — classified by the rule. State the coverage: what proportion of total spend you actually classified, and what you could not.
3. Rounds two and three, either measured from at least five real counterparty conversations or modelled at a uniform rate. Say which, in the same sentence as the number.
4. LM3 and the limit, with the captured share 1 − r³.
5. The breakeven penalty p* for your case, computed, with a sensitivity table.
6. One velocity paragraph, computing V and k for your national economy from published GDP and money stock, and explaining in plain language why your local measurement is a measurement and the national one is a definition.
7. One honest negative about your own work. The place where your number is weakest and what it would cost to fix.

What it must not contain. A figure without a unit. A ratio you did not compute from its inputs. A modelled round presented as a measured one. The word circulation used as a compliment.

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SELF-ASSESSMENT

Mark yourself against these, honestly, at the end of the term.

The last row is the one that matters most, and a blank there at the end of a term usually means you were reading rather than checking.

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CARRYING IT FORWARD

Three things from this term that keep paying long after the exam.

The division habit. You will now compute ratios from their inputs before quoting them, and this will save you from a specific and very common humiliation at least twice in your career.

The boundary habit. You will ask what is the boundary of every local, regional, sustainable or ethical claim you meet, and you will find that a large fraction of them have never answered it.

The model-measurement sentence. You will say which is which, in the same breath as the number. It costs nine words and it is the single clearest signal of somebody who can be trusted with a figure.

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COMMON ERRORS, AND HOW TO CATCH THEM IN YOUR OWN WORK

Five things go wrong in almost every first attempt at this material. Four of them are catchable in under a minute if you know to look.

Quoting a ratio you did not compute. The commonest and the cheapest to fix. Before any ratio enters your writing, put its numerator and denominator in the sentence with it, or in a table beside it. If you cannot, you do not yet have the ratio — you have somebody else's.

Letting the boundary move. You will be tempted, about halfway through Exercise 2.3, to reclassify one awkward counterparty because the number would look better. Do not. Instead write the case down in a list titled cases I wanted to move, and put that list in your project. It is evidence of method, and a marker will value it more than a higher figure.

Presenting a modelled round as measured. 1 + r + r² at a uniform rate is a model. Round one from a bank statement is a measurement. Nine words — rounds two and three are modelled at a uniform rate — keep the two apart forever.

Reading truncation as conservatism only. LM3 captures 99.7 percent of the true series at r = 0.14 and 48.8 percent at r = 0.80. That makes it conservative, which is good, and it makes comparisons between very different retention rates misleading, which is not. Both are true at once.

Treating a rate as an outcome. If you find yourself pleased that a number of turns went up, stop and ask what stock changed and by how much. The stock is the finding; the rate is the shadow it casts.

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APPRECIATIVE QUESTIONS FOR YOUR SEMINAR

1. Which number in this term's reading did somebody in this room reproduce, and what did they find?
2. When has a measurement changed an argument in this seminar — and what made that particular measurement persuasive?
3. Whose boundary definition here was the most honest about its awkward cases, and what can the rest of us take from it?
4. What became possible for you this term that was not possible in September?