Haute Lumière

Commerce · II.02 · MMXXVI · daylight

La Bourse  /  Volume II  /  Nº II.02  /  Workbook — the student

WORKBOOK — THE STUDENT

Chapter II.02 · Markets as Living Systems

For the person studying this alone, or in a seminar, with no organisation to change yet. This chapter is the one that will make you useful in a room before you have any authority in it, because almost nobody in any room can estimate a tail exponent, and the person who can changes what the room is able to decide.

---

WHY THIS WORKBOOK IS DIFFERENT

The chapter is a piece of mathematics with an argument wrapped around it. That means it can be checked, and checking it is the assignment.

You are not being asked to believe that markets are living systems. You are being asked to do six things with your own hands: reproduce a theorem's counterexample, fit a distribution, estimate an exponent, run a stochastic model, find the point where the argument fails, and write the failure down as clearly as the success. If you do those six, you will hold this chapter the way you hold a tool rather than the way you hold an opinion.

And you have an advantage the executive does not: nothing depends on your answer, so you can afford to find out that it is inconvenient. Use that while you have it. It is the most expensive thing in professional life to buy back.

---

PART ONE — DISCOVERY

Weeks 1–4: find the systems that are already visibly alive

Exercise 1.1 — Five markets you already inhabit (90 minutes)

You are inside more markets than you think, and several of them produce data you can get. Write five, with the series each one would give you.

Choose one where you can get at least 500 observations. Five hundred is the floor below which a tail estimate is noise pretending to be a finding.

Exercise 1.2 — The appreciative interview, for a market (45 minutes)

Find someone who trades, prices or allocates something for a living — a market trader, a bookings manager, a buyer, a bar manager, a ticket tout. Ask exactly this:

"Tell me about a time you got a price right when the obvious answer would have been wrong. What were you reading? What did you know that a formula would not have?"

Then stay quiet and take notes on what they were reading, not on the outcome.

This is Hayek's argument for the price system heard from the inside, and it is also the chapter's argument about heterogeneous expectations heard from the inside. You will find they were reading other people's reading. Write down every instance of that; it is the mechanism the Santa Fe market formalises.

Exercise 1.3 — Locate the five Discovery cases (2 hours)

The chapter names five programmes. Find the primary source for two of them — the actual paper, not a summary — and read the methods section.

Then answer one question in writing for each: what did this model have to get right that it could have got wrong? A model that could not have failed did not succeed.

---

PART TWO — THE ARITHMETIC

Weeks 5–9: compute everything before you argue anything

Exercise 2.1 — Reproduce the chapter's figures (3 hours)

Open lib/verify/II_02.py, read it, and then compute these independently — by hand, in a spreadsheet, or in whatever language you use. Do not import the module. Rewriting it is the exercise.

1. Scarf's orbit. Implement the three excess demand functions, run Euler from (1.4, 0.8, 0.8), and confirm that the distance to the equilibrium ray never falls below about 0.457. Then confirm the invariant: p₁p₂p₃ should change only by the size of your time step.
2. The tail. Confirm that a twenty-sigma move has Gaussian probability 2.0 × 10⁻⁹³ and cubic-tail probability 2.5 × 10⁻⁵.
3. The exponents. Confirm 2^0.75⁻¹ = 0.841 and 2^1.15⁻¹ = 1.110.
4. Robustness. Plot R(a) = −a·ln a and confirm the maximum at 1/e.
5. The urn. Run 4,000 Pólya urns and confirm the deciles are flat.

Then do the thing that matters most: find one figure in this chapter you can check against an outside source, and check it. If you find a discrepancy, write it down and bring it to your seminar. This edition wants to be checked.

Exercise 2.2 — Estimate a tail exponent on your own data (3 hours)

Take the series from Exercise 1.1. Do this:

1. Sort the observations descending. Rank them 1, 2, 3, …
2. Plot log(rank) against log(value).
3. If the top of the plot is straight, the tail is a power law, and the slope of the straight part is −α.
4. Estimate α a second way, with the Hill estimator on the top 5 percent: α̂ = (1/k) Σ ln(x_i / x_k+1), inverted.

Report both estimates and the difference between them. Two estimates that disagree is a finding; one estimate quoted alone is a claim.

Then answer: does the variance of your series exist? If α̂ < 2, it does not, and every standard-deviation-based statement anyone has made about that series is referring to a quantity that is not there.

Exercise 2.3 — Find the honest negatives (90 minutes)

The chapter contains four. Find all four and write, in your own words, why each is included. Then rank them by how much damage each does to the chapter's own thesis, and defend the ranking in three sentences.

Then practise the move: take a claim you personally believe about how markets or economies work, and write the strongest honest negative against it. Not a straw version — the version that troubles you. If you cannot write it, you do not yet understand your own position well enough to defend it. That is not a criticism. It is the assignment.

Exercise 2.4 — The special-case argument (60 minutes)

Write 400 words on this claim: the rational-expectations equilibrium is the low-adaptation limit of the Santa Fe artificial market.

Constraints:

• You may not use the word "wrong" about equilibrium theory.
• You must state the condition under which the orthodox model is correct.
• You must say what would have to be observed for the claim to be false.

This is the hardest exercise in the workbook and the most valuable. A theory that contains its predecessor as a special case is in a far stronger position than one that contradicts it, and learning to make that argument is learning to be listened to by people who disagree with you.

---

PART THREE — DREAM AND DESIGN

Weeks 10–13: build something that could be wrong

Exercise 3.1 — The smallest model that answers something (6 hours)

Build an agent-based model of one thing you can observe. Not a general economy — one question.

Candidates that work well at this scale: seat choice in a lecture theatre; which queue people join; how a rumour spreads through a group chat; how a second-hand market prices an item nobody has a reference price for; how study-group membership forms and dissolves.

The rules:

1. The question first. Write it down before you write any code. One sentence, with a number in it.
2. The fewest agent attributes that make the question answerable. Three is usually enough. Ten means you have stopped modelling and started decorating.
3. Withhold data. Collect observations, put a third of them in a sealed file, and do not look at them until the model is frozen.
4. Report three quantities: the median outcome, the tenth percentile, and the fraction of runs in which something breaks. Report the last even when it is zero.

Exercise 3.2 — The out-of-sample test (2 hours)

Now open the sealed third.

Write up what happened in one page, including the case where the model missed. A model that matched the withheld data is a result. A model that missed it, and whose miss you can explain, is also a result. A model whose author quietly retuned it after opening the file is not a result at all, and the discipline of not doing that is the entire content of this exercise.

Exercise 3.3 — Your own ascendency (60 minutes)

Ulanowicz's axis, applied to a life.

List every significant channel through which something you need arrives: income, learning, friendship, exercise, information about opportunities. For each, write what share of the total runs through the single largest channel.

• One income source, one social circle, one source of news, one route into work: your a is near 1, and R(a) is near zero.
• Six of everything, none of them developed: coordination cost, and nothing works well.

Estimate your own a honestly. Then write one sentence: the channel I would most want a second of is ___. Build the second one this term. This is the only exercise here that will still be paying in ten years.

---

PART FOUR — DESTINY AND DELIGHT

Weeks 14–16: make it hold, and enjoy it

Exercise 4.1 — The metaphor audit (45 minutes)

Collect five sentences from public writing — journalism, a company report, a politician, a textbook, a post — that use a biological metaphor about the economy. For each, answer:

1. What specific result is being carried across?
2. What assumption does that result need?
3. Does the assumption hold here?

Most will fail at step one, because no specific result is being carried. That is the finding, and it is what separates the analogy the chapter defends from the one it refuses. When you cannot name the theorem, you are using a figure of speech.

Exercise 4.2 — Publish one thing (this term)

Write up Exercise 2.2 — your series, your two exponent estimates, your disagreement between them — as one page, and put it somewhere another person can read it: a seminar, a blog, a departmental noticeboard, a preprint server.

Small and irreversible beats large and provisional. Once it is out, someone can check it, and being checked is the only route to being trusted.

Exercise 4.3 — Delight, on purpose (ongoing)

There is a specific pleasure in this chapter and you should go and get it: plot your own data on log-log axes and watch the scatter you had been apologising for come out straight.

Do it with the nicest plotting you can manage, at a time you are not rushed, somewhere you like being. This is not indulgence. Delight is the adoption mechanism, and it determines whether you are still doing this in March.

---

THE TERM PROJECT

One market, carried the whole way

Choose one market you have genuine access to and run the chapter's full method on it.

Deliverables.

1. Discovery memo (800 words). The market, why it is a market, who trades in it, and two appreciative interviews with people who do. Name what they are reading.
2. The distribution (1 page plus workings). At least 500 observations. Mean, standard deviation, 99th percentile, expected shortfall beyond it, and two independent estimates of the tail exponent with the disagreement stated.
3. The model (code plus 600 words). The smallest agent-based model that answers one stated question, with a third of the data withheld and opened only once.
4. The honest negative (400 words). One condition under which your own conclusion fails, worked to the same depth as the conclusion.
5. The comparison (400 words). What would a simple equilibrium model have said about this market, and where would it have been right? A project that cannot find anything the orthodox tool does better has not looked.
6. The reflection (600 words). What you expected, what happened, what the gap tells you.

How it is assessed. Not on whether your model worked. On whether the measurement was honest — whether a reader could reproduce your numbers, and whether you reported the out-of-sample result you actually got.

A model that missed and was reported cleanly is a first-class piece of work. A model that fitted and cannot be reproduced is not.

---

SELF-ASSESSMENT

Score yourself honestly. This is for you.

The two that matter most are the fourth and the last. Everything else can be learned in a term. Those two are habits of attention, and they will keep you out of most of the errors this literature is capable of producing.

---

CARRYING IT FORWARD

What you will have at the end of a term, if you do this properly:

• One real series, fitted, with an exponent and an honest disagreement between two estimators.
• One agent-based model that was tested on data it had never seen, and a written account of how it did.
• Two appreciative interviews with people who make prices for a living.
• The ability to say, in a room, "before we use that average — does the variance of this series exist?"

That last sentence is worth more than it sounds. It is short, it is polite, it is answerable, and it changes what a room decides. You can ask it before you have any authority at all, and asking it well is the fastest route to being given some.

---

APPRECIATIVE QUESTIONS FOR YOUR SEMINAR

1. Which of us found a figure in this chapter that did not hold, and how did you find it? What would we have to do to find one more?
2. When has one of us correctly predicted something the standard model missed — and what were we reading that it was not?
3. What is already working in how this seminar checks each other's numbers, and what would it take to have more of that?
4. If every one of us published one honest exponent this term, what would this group have at the end of a year that no course could have given us?