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Commerce · VII.02 · MMXXVI · daylight
TEN CONCEPT BRIEFS · Chapter VII.02 — Climate as an Economic System
One page each. A reader who reads only these ten pages has the chapter.
BRIEF 1 — The Integrated Assessment Model
The idea. An integrated assessment model is not a climate model with opinions. It is five ordinary modules wired in a loop, each handing one number to the next.
1 socioeconomics population, output per head, to 2300
2 emissions output x carbon intensity, minus abatement
3 carbon cycle emissions -> atmospheric concentration
4 climate concentration -> forcing -> temperature
5 damages temperature -> lost output, in money
then discount the losses back to todayThree families have carried the field: DICE (William Nordhaus), FUND (Richard Tol) and PAGE (Chris Hope). The United States estimates now rest on two newer open-source damage modules, GIVE and DSCIM, which is why two independent teams could reach $185 and $190 a tonne — a ratio of 0.97 — working separately.
Worked example. To get a social cost of carbon you do not solve anything exotic. You run the loop, add one tonne today, run it again, and take the difference in discounted damages. Two runs, one subtraction.
Why it matters. Knowing the loop tells you where a disagreement lives. Someone arguing about climate sensitivity is arguing in module four. Someone arguing about damages is in module five. Someone arguing about the discount rate is not in the model at all — they are arguing about the last line, which is arithmetic applied after the science has finished. Most public disputes about these models are disputes about the last line.
You already know this because you have built a business case that chained a volume forecast into a price into a margin into a cash flow, and you know that the argument is almost never about the chain. It is about one assumption, and the first job is always finding which link it sits on.
BRIEF 2 — The Damage Function
The idea. The entire money side of the most influential climate-economic model is one line with one fitted coefficient.
D(T) = a2 · T² a2 = 0.236 % of global income per °C²
Ω(T) = D / (1 + D) damages as a share of outputRun it and you reproduce Nordhaus's published figures exactly: 2.1 percent of global income lost at 3 °C, 8.5 percent at 6 °C.
Worked example. At 1 °C the loss is 0.236 percent; at 2 °C, 0.944; at 4 °C, 3.776; at 5 °C, 5.900. Note the shape. A quadratic is smooth: it contains no threshold, no discontinuity and no tipping point, because the estimates it was fitted to contained none. The function cannot produce a behaviour that was not in its functional form.
The base under it. The 2016 coefficient was fitted to a survey of 26 studies, of which 16 had independent damage estimates and 9 received full weight — 34.6 percent of the survey — with a 25 percent upward adjustment added for omitted, non-market and catastrophic damages. The competing meta-analysis, Howard and Sterner's, rests on a preferred dataset of 21 observations and excludes estimates above 4 °C as empirically shaky.
Why it matters. When somebody says "the models say damages are modest", they are quoting a quadratic fitted to a few dozen studies, mostly below 3 °C, and then evaluated well above it.
You already know this because you have seen a regression in a board pack carry a decision, and you know the first question is never the R². It is how many points, and over what range?
BRIEF 3 — The Social Cost of Carbon
The idea. The social cost of carbon is the discounted value of the damage done by one extra tonne of CO₂ emitted today, over its whole atmospheric life. It is a marginal quantity and it is not a price anyone charges.
The number, with its range. There is no single figure and there never was. What there is, is a set of figures each of which is honest about what produced it:
| Source | Figure | Basis |
|---|---|---|
| Nordhaus (2017), DICE-2016R baseline | $31.2 | 2015, 2010$ |
| EPA (2023) at 2.5 % | $120 | 2020 emission year, 2020$ |
| EPA (2023) at 2.0 % | $190 | 2020 emission year, 2020$ |
| EPA (2023) at 1.5 % | $340 | 2020 emission year, 2020$ |
| Rennert et al. (2022) at 2 % | $185 | 2020$ |
| Bilal and Känzig (2024) | $1,200 | global-temperature specification |
Worked example — the unit trap. Tol's meta-analytic literature quotes a weighted mean of $207 per tonne of carbon. That is not $207 a tonne of CO₂. One tonne of carbon is 3.6667 tonnes of CO₂, so the same figure is $56.45 per tCO₂. A reader who compares 207 with 190 without this line is out by a factor of 3.67.
Why it matters. A social cost of carbon quoted without its discount rate, its dollar year and its tonne is not a figure. It is a fragment. Quote the triple: $120 · $190 · $340.
You already know this because you would never accept a valuation without being told the discount rate and the currency, and this is a valuation.
BRIEF 4 — What One Parameter Does
The idea. Most of the famous spread in the social cost of carbon is one parameter, and its effect is multiplicative and computable.
Chapter III.05 does the Ramsey equation and what each of its terms claims. This brief does only the magnitude.
Worked example — inside one model. Nordhaus's own Table 1, same damage function, same climate module, 2015, 2010 dollars:
2.5 % 128.5 128.5 / 19.7 = 6.52x across 2.5 points
3 % 79.1 per percentage point: 2.12x
4 % 36.3 5 -> 4: 1.84x 4 -> 3: 2.18x 3 -> 2.5: 1.62x
5 % 19.7And at the EPA, on entirely different damage modules: $120 at 2.5 percent, $190 at 2.0, $340 at 1.5. 340 / 120 = 2.83× across one point; the two half-point steps are 1.58× and 1.79×, a mean of 1.68×. As an elasticity, ln(340/120) / 0.01 = 104.1 — one basis point off the rate moves the social cost of carbon by 1.04 percent.
Compare the other lever. Swapping in Howard and Sterner's damage function multiplies the DICE figure by 3× to 4× — $31.2 becomes $93.6 to $124.8 — and by 4× to 5× with catastrophic impacts, to $124.8 to $156.0.
Why it matters. Discounting moves the answer more than the entire damage literature does, and it is the one parameter that is not a forecast. It is chosen. Which means it belongs in minutes, not in a model file.
You already know this because you have watched a terminal-value assumption decide a valuation that three months of diligence could not shift.
BRIEF 5 — Marginal Damage Is Not the Price of a Constraint
The idea. There are two completely different questions people ask a climate model, and they have different correct answers.
- What does one more tonne cost, along the path we are on? — the marginal damage, the social cost of carbon.
- What does it cost to hold a temperature limit? — the shadow price of the constraint, which is a Lagrange multiplier, not a damage estimate.
Worked example, in one model, on one page. DICE-2016R, 2015, 2010 dollars:
baseline marginal damage 31.2
price consistent with a 2.5 °C cap 184.4 5.91x
the same cap as a 100-year average 106.7
with Stern Review discounting 197.4 6.33xThe whole famous gulf between the "low" and "high" camps is reproducible inside a single model without touching the science. One camp is pricing damage; the other is pricing a constraint.
Why it matters, operationally. If your organisation has a temperature-aligned target, the marginal-damage estimate was never your number. Your number is the shadow price of the commitment you have already made, and it is roughly 5.91× larger. A firm holding a 1.5 °C target and a $20 internal price is holding two positions that do not multiply out — and it does not have to win a single argument about damage functions to see that.
You already know this because the cost of missing a covenant has nothing to do with the economic damage of the missed ratio. It is the cost of the constraint, and you price it as such.
BRIEF 6 — Coverage, Price, and the Gap
The idea. Carbon pricing is now large enough to measure and small enough to mistake for a solution. Both facts are in the same table.
The record, at 1 April 2025. 80 carbon taxes and emissions trading systems, covering 28 percent of global greenhouse gas emissions — up from about 5 percent in 2005 — raising over $100 billion in 2024. That is about 15 gigatonnes priced out of 52. The emissions-weighted average price across covered emissions is $19 a tonne, against just above $10 ten years earlier. Across all emissions it is $5.
Worked example — the gap against $190.
Uruguay 158.8 83.6 % EU ETS 70.4 37.1 %
Sweden 144.6 76.1 % UK ETS 57.2 30.1 %
Switzerland 136.0 71.6 % California 29.3 15.4 %
Canada federal OBPS 66.2 34.8 % China ETS 11.8 6.2 %
average, covered 19.0 10.0 % Mexico 2.8 1.5 %
average, all 5.0 2.6 %At the global average, unpriced marginal damage runs at $9.62 trillion a year: (190 − 5) × 52 billion tonnes. The comparison is undeflated — nominal prices against a 2020-dollar benchmark — so every gap is a floor.
The second gap. $100 billion collected across 15 gigatonnes is $6.67 a tonne — 35.1 percent of the posted $19 average. Free allocation, exemptions and output-based rebating take the rest. The fiscal size of carbon pricing is about a third of its apparent size.
You already know this because you have seen a list price and a realised price differ by two-thirds, and you know which one to build a budget on.
BRIEF 7 — What the Evaluations Actually Measure
The idea. "Does carbon pricing reduce emissions" is no longer a matter of opinion. It has been answered by the whole ex-post literature at once.
The synthesis. Döbbeling-Hildebrandt and colleagues (2024) reviewed 80 causal evaluations covering 21 schemes and 483 effect sizes. Result: statistically significant reductions of 5 to 21 percent, or 4 to 15 percent after correcting for publication bias, with immediate reductions in 17 of the 21 schemes — 81 percent.
Four studies worth knowing individually.
| Study | Scheme | Effect |
|---|---|---|
| Andersson (2019) | Sweden, transport | 10.9 % total, 6.3 % from the tax alone |
| Leroutier (2022) | UK power | 20–26 % a year; 143–191 MtCO₂ over 2013–17 |
| Colmer et al. (2024) | EU ETS, French firms | 14–16 %, no output or employment effect |
| Bayer & Aklin (2020) | EU ETS | 1.2 GtCO₂ over 2008–16 = 3.8 %, at low prices |
Worked example — the honest sum. Apply the bias-corrected midpoint, 9.5 percent, to the 15 gigatonnes covered: 1.43 gigatonnes a year, or 2.74 percent of global emissions. The IPCC's 1.5 °C pathway requires 43 percent below 2019 by 2030 — about 22.36 gigatonnes a year. Delivered against required: 6.4 percent. One part in 15.7.
Why it matters. The instrument works and is too small, and a claim that gives you only one of those halves is an advertisement.
You already know this because you have shipped a feature that measurably improved conversion and still did not move the quarter, and you know both sentences were true.
BRIEF 8 — Additionality
The idea. A tonne of offset is only worth a tonne of emission if the reduction would not have happened anyway. That counterfactual is unobservable, which is why the crediting record is the worst-performing part of climate economics — and the best measured.
The evidence. The European Commission's 2016 study of the Clean Development Mechanism found 85 percent of projects, and 73 percent of potential credit supply, had a low likelihood that reductions were additional and not overestimated. Only 2 percent of projects and 7 percent of supply had a high likelihood. Thales West and colleagues (2023, Science) examined 18 forest-conservation projects that had issued 62 million credits, of which 14.6 million had already been used to offset emissions, and found roughly 6 percent represented real additional reductions.
Worked example. Six percent of 62 million credits is 3.72 million real tonnes. Of the 14.6 million already used to discharge somebody's emissions, 13.72 million tonnes of claimed offsetting did not occur. Those tonnes are in the atmosphere and off a balance sheet.
The rule that follows. An offset that is not additional is not cheap abatement. It is an emission with a receipt. Offsets may fund abatement outside your boundary. They may not discharge a tonne inside it. Write that sentence into the policy; it is one line and it removes the entire failure mode.
You already know this because you have refused a cost saving that was really a deferral, and you knew the difference immediately even though both showed up the same way in the month.
BRIEF 9 — The Shadow Price and the Carbon Liability Reserve
The idea. You do not need a carbon market to act on a carbon price. You need a number, a policy, and one capital decision that uses it.
Worked example. A firm emits 250,000 tonnes of CO₂e in scope 1, of which 60 percent falls under a scheme at $70.4.
cash carbon cost 250,000 x 0.60 x 70.4 = $10.56 m 8.8 % of EBITDA
at a shadow price 250,000 x 190 = $47.50 m
unpriced exposure $36.94 m 30.8 % of EBITDAThat gap between 8.8 and 30.8 percent is the whole reason nobody senior is managing this. At the cash figure it is a procurement line. At the shadow figure it is a board item.
The instrument. An appropriated reserve — not a provision; absent a present obligation there is nothing to recognise under IAS 37 — funded in cash at a board-set fraction of the exposure, $3.69 million at 10 percent, released only against verified abatement, with no credit purchase eligible, and a published escalator. The EPA's own series rises 1.93 percent a year in real terms from $190 in 2020 to $230 in 2030.
The deciding number. Where your own abatement curve clears. For this firm, 45,000 tonnes clear below $70.4 and 115,000 below $190, so the shadow price puts an incremental 70,000 tonnes a year into the money. At an average cost of $130 the tranche costs $9.10 million and releases $4.20 million a year of value at the shadow price.
You already know this because you already run an internal transfer price for something — capital, floor space, engineering hours — and you know it changes behaviour long before any external market does.
BRIEF 10 — A Bound With a Known Sign
The idea. The damage functions under almost every published social cost of carbon are weakly grounded above about 3 °C, and their authors say so. The correct response is not to discard the number. It is to use it as the kind of number it actually is.
The three measurements.
- Nordhaus gives the damage coefficient a standard deviation of 0.118 against a mean of 0.236 — exactly half — to reflect "the great divergence today among different studies."
- The coefficient's t statistic is −7.8, "extremely well determined", and one sentence later: it "does not reflect specification uncertainty, parameter uncertainty, or study dependence."
- In his own Monte Carlo the standard deviation of the 2015 social cost of carbon is $31.5 against a mean of $31.2 — a ratio of 1.01. The spread is larger than the estimate.
And the omissions run one way. The EPA's own report states that data and modelling limits "restrain the ability of SC-GHG estimates to include all physical, ecological, and economic impacts of climate change, implicitly assigning a value of zero to the omitted climate damages."
Worked example of correct use. A project shows a net present value of −$2 million at a shadow price of $190 a tonne. It is dead, and the weak calibration does not save it, because every omission would make it worse. A project shows +$2 million at $190. It has cleared a floor, not a bar: run it again at $340 and see whether it still clears.
Why it matters. A quantity whose errors are all of one sign is not an unknown. It is a bound with a known direction, and bounds are perfectly usable in decisions — which is what an engineer does with a safety factor and what a credit officer does with a haircut.
You already know this because you have signed off an estimate you knew was conservative, and the knowing-which-way is precisely what made it signable.