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WORKBOOK — THE STUDENT

Chapter VII.02 · Climate as an Economic System

For the person studying this alone, or in a seminar, with no organisation to change yet. You will finish this term able to reproduce, check and criticise the central number in environmental economics — which almost nobody who quotes it can do.

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WHY THIS WORKBOOK IS DIFFERENT

Most climate-economics teaching asks you to hold a position. This one asks you to hold a procedure. By the end of the term you will be able to take any published social cost of carbon, ask it four questions, and know within ten minutes whether the figure is usable, what its author left out, and which way the omissions run.

That skill transfers completely. It is the skill of reading a number whose uncertainty is structural rather than statistical, and you will use it on valuations, on actuarial assumptions, on clinical effect sizes and on anything else where a model's shape decides its answer.

You need no data you cannot get free, and no software beyond a spreadsheet.

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PART ONE — DISCOVERY

Weeks 1–4: find the number and its ancestry

Exercise 1.1 — Reproduce the damage function (60 minutes)

Open a spreadsheet. Column A: temperature from 0 to 6 °C in steps of 0.5. Column B: = 0.236 * A^2. Column C: = B / (1 + B/100).

You have just rebuilt the money side of the most influential climate-economic model in existence. Check it against the published figures: 2.1 percent of global income at 3 °C and 8.5 percent at 6 °C. If you get those, your sheet is right.

Now plot it, and write two sentences on the shape. Note what a quadratic cannot do: it has no threshold, no discontinuity and no tipping point. Ask yourself whether that is a claim about the world or a property of the chosen functional form, and write your answer down so you can revisit it in week 10.

Exercise 1.2 — Trace the ancestry (2 hours)

The coefficient 0.236 was fitted to a survey of 26 studies, of which 16 contained independent damage estimates and 9 received full weight — 34.6 percent of the survey. Find the Nordhaus and Moffat survey of global impacts, listed in the chapter's Works Cited, and answer three questions in writing:

1. How many of the underlying estimates sit above 3 °C?
2. What methods produced them — enumerative, statistical, computable general equilibrium — and do the methods disagree systematically?
3. What was the 25 percent upward adjustment for, and would you make it?

Exercise 1.3 — The unit audit (45 minutes)

Find five published statements of "the social cost of carbon" — a newspaper, a government document, a corporate report, an NGO, a textbook. For each, record: the figure, the discount rate, the dollar year, and whether the tonne is carbon or carbon dioxide.

Expect most to be missing at least one. Then convert any $/tC figure using 3.6667: Tol's literature mean of $207 per tonne of carbon is $56.45 per tonne of CO₂, and a reader who compares 207 with 190 is out by a factor of 3.67.

Exercise 1.4 — Find what is working (90 minutes, in a seminar)

Take the four evaluations the chapter leans on — Andersson on Sweden (10.9 percent total, 6.3 from the tax alone), Leroutier on Britain (20 to 26 percent, 143 to 191 MtCO₂), Colmer and colleagues on French manufacturing (14 to 16 percent, no output effect), Bayer and Aklin on the EU ETS (1.2 GtCO₂, 3.8 percent). Assign one per person. Each presents for five minutes on the identification strategy only — not the result. What is the counterfactual, and what would break it?

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PART TWO — THE ARITHMETIC

Weeks 5–8: compute the sensitivity yourself

Exercise 2.1 — The discount-rate multiplier (90 minutes)

Build this table from Nordhaus's Table 1, then compute the right-hand column yourself:

Then: 128.5 / 19.7 = 6.52× across 2.5 points, which is 6.52^(1/2.5) = 2.12× per percentage point.

Do the same for the EPA series — $120, $190, $340 — and get 1.58×, 1.79×, a geometric mean of 1.68×, and 2.83× across the full point.

Write the sentence you would say in a seminar to someone who has just claimed the field is hopelessly divided. One sentence, with one number in it.

Exercise 2.2 — The elasticity, and the trap in it (45 minutes)

Compute ln(340/120) / 0.01 = 104.1 per unit of rate — 1.04 percent per basis point. Now apply it to a 0.25-point move two ways: compounded over the twenty-five basis points, 1.30×; read linearly, 1.26×. The linear reading is wrong, and it is wrong low.

Write two lines on why the multiplicative reading is the correct one for a quantity that compounds, and where else you have seen the same error.

Exercise 2.3 — Locate the disagreement (2 hours)

Two multipliers, side by side:

• The discount rate, inside one model: 6.52×.
• The entire damage-function literature, from DICE to Howard and Sterner: 3× to 4× without catastrophic impacts — $31.2 to $93.6–$124.8 — and 4× to 5× with them, to $124.8–$156.0.

Now answer in writing: which of those two is a forecast, and which is a choice? Read Chapter III.05 on the Ramsey terms before you answer. Do not re-derive it — cite it.

Exercise 2.4 — The honest negative, worked (60 minutes)

Three measurements of how weakly the damage side is grounded:

1. Coefficient standard deviation 0.118 against a mean of 0.236.
2. A t statistic of −7.8, "extremely well determined", immediately qualified as not reflecting specification, parameter or study-dependence uncertainty.
3. A Monte Carlo standard deviation of $31.5 against a mean of $31.2 — a ratio of 1.01.

The exercise is this. Write 400 words arguing that these three facts mean the number should not be discarded. Use the EPA's own statement that omissions are "implicitly assigning a value of zero to the omitted climate damages", and make the argument that a quantity whose errors run one way is a bound, not an unknown. You may not use the word "nevertheless".

Exercise 2.5 — Price a constraint instead of a damage (75 minutes)

Go back to Nordhaus's Table 1 and find the rows almost nobody quotes. The baseline marginal damage is $31.2. The price consistent with holding 2.5 °C is $184.4 — 5.91× — and $106.7 if the cap is a hundred-year average rather than a peak. Running the same model with the Stern Review's discounting gives $197.4, or 6.33×.

Write 300 words on what this does to the public argument. The two camps are usually described as disagreeing about damages; the table shows their positions are reproducible inside one model, from one page, without touching a single scientific parameter. Then answer the operational question: if an institution has already committed to a temperature limit, which row is its number, and what follows for every appraisal it runs?

Exercise 2.6 — The fiscal size of a carbon price (45 minutes)

Revenue of $100 billion across 15 gigatonnes of covered emissions is $6.67 a tonne collected, against a posted emissions-weighted average of $19 — 35.1 percent. Free allocation, exemptions and output-based rebating account for the difference.

Compute it yourself, then write two sentences: one explaining why this is not evidence that the schemes are failing — the marginal price is what changes behaviour, and rebating the average cost is the design that keeps the marginal price politically alive — and one explaining why any proposal to spend carbon revenue must start from $6.67 rather than $19.

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PART THREE — DREAM AND DESIGN

Weeks 9–11: build something with it

Exercise 3.1 — Price a decision you actually face (2 hours)

Pick a real decision with an energy or materials component: a flight against a train, a device kept against replaced, a lease, a degree that requires relocation. Build three columns — cash, cash at the compliance price your tonnes actually face, and cash at a shadow price of $190.

You will usually find the carbon column changes nothing. Record when it does not change the answer, because that is the honest majority case and knowing it is what makes your judgement worth hearing when it does.

Exercise 3.2 — Audit an offset claim (90 minutes)

Find a product, an airline or an institution advertising offset emissions. Then ask the four additionality questions: what is the counterfactual, who verified it, what is the baseline method, and would the reduction have happened anyway?

Hold the answer against the record: 85 percent of CDM projects at low likelihood of additionality and 2 percent at high; 6 percent of credits from 18 forest projects genuinely additional, meaning 13.72 million of the 14.6 million tonnes already used to offset did not occur.

Write one paragraph you would actually send.

Exercise 3.3 — The gap table, redrawn for your country (2 hours)

Take the coverage data: 80 instruments, 28 percent of emissions, about 15 of 52 gigatonnes, over $100 billion raised, an average of $19 across covered emissions and $5 across all of them. Find your own jurisdiction's price and compute its share of $190 and its gap.

Then compute the world figure yourself: (190 − 5) × 52 billion = $9.62 trillion a year of unpriced marginal damage. Write one sentence stating what that number is and one stating what it is not.

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PART FOUR — DESTINY AND DELIGHT

Week 12: make it stick

Exercise 4.1 — The one-page instrument (90 minutes)

Write the price memo you would put to a board: the price, the basis, the escalator, the decision it governs, the review date. One page. The EPA's own series escalates at 1.93 percent a year in real terms — $190 in 2020 to $230 in 2030 — and that is a citable path.

Exercise 4.2 — Argue the other side (2 hours, in pairs)

One of you argues that carbon pricing has been a success; the other that it has been a failure. Both must use the same numbers: 5 to 21 percent measured reductions, 4 to 15 bias-corrected, 17 of 21 schemes, and 1.43 gigatonnes delivered against 22.36 required — 6.4 percent, one part in 15.7.

Then swap sides and do it again. The exercise is complete when neither of you can tell which side you believe, which is the state from which useful work gets done.

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THE TERM PROJECT

One piece of work, carried the whole way

Build a reproducible social cost of carbon sensitivity, and publish it.

The deliverable is a spreadsheet plus a memo, and it has four parts.

1. The damage function, rebuilt from D(T) = 0.236 · T², with its provenance documented: 26 studies, 16 included, 9 at full weight.
2. The discount sensitivity, computed both ways: the DICE constant-rate series to 6.52×, and the EPA Ramsey series to 2.83×, with the per-basis-point elasticity of 1.04 percent.
3. The alternative damage function, applying Howard and Sterner's 3× to 5× range to the DICE baseline of $31.2.
4. A one-page decision rule stating how you would use the resulting range — as a floor, with the rate always quoted, and with the constraint's shadow price used instead wherever a target exists.

Publish it where somebody can check it. A number that cannot be re-run by a stranger is an assertion, and this whole chapter is about the difference.

Assessment criteria, in order: does it reproduce the published figures exactly; are the inputs printed as well as the results; is every dollar year stated; and does the memo say what the model cannot see?

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SELF-ASSESSMENT

Score yourself honestly. Five points each.

Under 18 and the term's work is not finished. Over 25 and you should be teaching Exercise 2.1 to someone else, which is the fastest remaining way to improve.

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CARRYING IT FORWARD

Three things to keep after the term ends.

The four questions. Rate, dollar year, tonne, and what was omitted. They take ten minutes and they work on every number of this kind you will meet.

The two-multiplier habit. Whenever a range is presented as disagreement, ask which part of it comes from a forecast and which from a choice. 6.52× against 3× to 5× is the example; the habit is general.

The bound. When somebody tells you a number is too uncertain to use, ask which way its errors run. If they all run one way, it is a bound, and bounds are exactly what engineers and credit officers make decisions with every day.

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APPRECIATIVE QUESTIONS FOR YOUR SEMINAR

1. When has a number changed your mind about something you cared about? What made it credible?
2. Which of the four evaluations in Exercise 1.4 had the strongest identification, and what made it strong?
3. If our department had to publish one shadow price for its own decisions, what would we want it to be, and what would we want people to conclude?
4. What would it take for our cohort to produce one piece of work that a stranger could re-run?
5. Where else in economics is a chosen parameter doing the work that everyone thinks the evidence is doing?
6. What would we want the next cohort to inherit from what we built this term?