Social cost of carbon

Adoption

Following Nordhaus's early work, the concept of the Social Cost of Carbon gained prominence through the Stern Review (2006) and the formation of the U.S. Interagency Working Group in 2009. The SCC became a standard tool for regulatory analysis under the Obama administration.

Use by Country

The SCC is distinct from carbon pricing tools such as taxes or cap-and-trade systems.

The Social Cost of Carbon or similar approaches have been adopted globally, though implementations differ:

• United States: Fluctuations under Obama ($51/ton, 3% discount rate), Trump ($1–$7/ton, focusing on domestic damages), and Biden (proposed >$190/ton, accounting for global damages at lower discount rates).
• Canada: Integrates SCC estimates directly into fuel pricing regulations.
• United Kingdom and France: Apply "shadow pricing" in regulatory impact assessments, embedding a cost of carbon without a direct market price.
• Germany: Introduced the GIVE model in 2024 to better capture long-term uncertainties.
• China, New Zealand, South Korea, and others: Operate emissions trading systems (ETS) that reflect implicit or explicit carbon costs.

Discount rates, scope of damages (global vs. domestic), and valuation methods vary substantially across 40 governments and 25 sub-governmental entities that currently employ some form of carbon pricing.

Calculation

Basic Process

SCC calculations typically involve:

1. Projecting Future Emissions: Based on economic growth, technological change, and demographics.
2. Modeling Climate Responses: Simulating atmospheric CO₂ levels, temperature increases, sea level rise and other changes.
3. Assessing Impacts: Evaluating effects on agriculture, health, energy use, infrastructure, and ecosystems.
4. Monetizing Damages: Converting impacts into monetary terms.
5. Discounting Future Damages: Applying a discount rate to reflect time preferences.

Key Factors that Influence Social Cost of Carbon

Sources:

• Climate sensitivity (how much warming one ton of carbon causes, estimated via IAMs)
• Economic assumptions/growth projections
• Discount Rate Choice
• Global vs. domestic damage scope
• Inclusion of non-market damages (i.e. ecosystem services)

Discount Rates

The discount rate affects how future damages are valued today. A simplified example: an offer to receive $100 now or $110 in a year implies a 10% simple discount rate. In climate economics:

• Low discount rate (1–2%): Future generations' welfare valued nearly equally with today's.
• High discount rate (4–5%): Present benefits are prioritized and future damages are heavily discounted.

Discounting formula:

${\displaystyle PV=\frac{FV}{(1+r{)}^t}}$

where PV = present value, FV = future value, r = discount rate, and t = time.

Recent literature supports declining discount rates, starting higher in the near-term but decreasing over time to reflect long-term uncertainty and ethical considerations.

Equations

Risk-Neutral Damages

Captures the central tendency cost of emitting 1 additional ton of CO₂ today without accounting for catastrophic risks or risk aversion

${\displaystyle SC{C}_1=MDR\times HDP\times TCRE\times \frac{1}{FDR}}$

• MDR: Marginal Damage Ratio- How much global GDP drops per degree Celsius of warming
• HDP: Horizon Discounted GDP- Present value of global GDP over time (used to weight future damages)
• TCRE: Transient Climate Response to Cumulative Emissions- How much global temperature increases (in degrees C) per 1,000 gigatonnes of CO₂ emitted (about 1.8 °C/1 trillion tons of carbon)
• FDR: Future Discount Rate- Applied to calculate the present value of future damages

Catastrophic Risk Premium

Adds a risk premium to account for potential catastrophic damage, uncertainty, and risk aversion

${\displaystyle SC{C}_2=SC{C}_1+\frac{(MCRD\times MDD)}{(1-RA\times MDD)}\times V\times TCRE\times \frac{1}{R}}$

• MCRD: Marginal Catastrophe Risk Density- Change in the probability of a disaster per ton of CO₂ emitted
• MDD: Mean Disaster Damage- Expected GDP loss if a catastrophe occurs
• RA: Relative Risk Aversion- How strongly society prefers to avoid risk
• V: Value of GDP- Total or marginal economic value at risk (often equivalent to global GDP)
• R: Discount rate for catastrophic events (may differ from FDR in SCC₁)

The final SCC combines risk-neutral and risk-adjusted components.

Integrated Assessment Models (IAMs)

Three principal Integrated Assessment Models - DICE, FUND, and PAGE - have historically underpinned SCC calculations. DICE emphasizes a globally-aggregated, deterministic pathway that optimizes mitigation costs against economic damages. FUND introduces more granular regional and sectoral variation, allowing for some beneficial warming effects in higher latitudes. PAGE, by contrast, is probabilistic, explicitly modeling uncertain catastrophic risks. These methodological differences can lead to dramatically different SCC values. Obama-era SCC relied on an average across multiple runs of DICE, FUND and PAGE.

DICE (Dynamic Integrated Climate Economy)

Source:

Optimizes emissions abatement based on cost-benefit balance, tends to produce lower SCCs because it ignores deep uncertainty and treats damage as reversible

Assumptions:

• Climate and economic systems are tightly coupled in a smooth, deterministic way
• Damages increase with the square of temperature (i.e., GDP loss = a × T²)
• Doesn't include tipping points or fat-tailed catastrophic risk

FUND (Framework for Uncertainty, Negotiation, and Distribution)

Source:

Shows wide variation in SCC depending on who's affected and when, can understate damages dure to assumptions about adaptation and potential warming benefits

Assumptions:

• Models multiple impact categories (e.g., agriculture, health, sea level rise) by region
• Includes some adaptation responses over time
• Allows for negative damages (i.e., benefits from warming in some regions/sectors)

PAGE (Policy Analysis of the Greenhouse Effect)

Source:

Produces higher SCC estimates with large uncertainty bands, complexity & uncertainty can make outputs difficult for policy communication

Assumptions:

• Uses Monte Carlo simulations to model thousands of futures
• Probabilistic treatment of catastrophic events and tipping points
• Damages increase sharply after certain thresholds
• Often uses declining discount rates

Tipping Points

Standard IAMs tend to assume smooth, continuous damages from warming, which may underestimate risk by ignoring climatic tipping points.

More recent models incorporate tipping elements using threshold functions or probabilistic catastrophe modules. This method accounts for the abrupt, irreversible impacts (ice sheet collapse, AMOC disruption) that occur when the climate crosses critical thresholds. Modeling studies suggest that including tipping points can double the SCC.

Tipping Point Additions to the Social Cost of Carbon Equation

Threshold function in damage term

${\displaystyle SC{C}_3=c\times 1(T>T^{\ast })+SC{C}_1+SC{C}_2}$

• T² = base damage function, meaning damages increase with the square of global temperature rise (i.e. 1 °C, little damage; 2 °C, 4x damage, 3 °C, 9x damage). This represents a smooth escalation of climate harm.
• T³ adds nonlinearity to the damage function, with the idea being that once warming passes 2-3 °C, damages might accelerate even faster than T². This accounts for feedback loops without jumping straight to tipping points
• ×1(T > T*) is an indicator function that activates when temperature exceeds tipping threshold T* (e.g. 3 or 4 °C). C = added cost from a tipping point event (e.g. polar ice sheet collapse). This kicks in suddenly, making the damage function discontinuous.

Stochastic Tipping Point Module

${\displaystyle SC{C}_4=BaseDamages+Pr(Tipping)\times ExpectedCatastrophicDamages}$

Adds a probabilistic tipping event that increases expected damages

Criticism

While the social cost of carbon is sometimes used in policymaking and economic analysis, it has been subjected to criticism from economists, scientists and ethicists. These critiques fall into three broad categories: methodological uncertainty, ethical limitations, and political vulnerability.

1. Extreme sensitivity to assumptions: SCC estimates are highly sensitive to a small number of assumptions, especially the discount rate, the climate damage function, and the climate sensitivity parameter. Philosophical choices about valuing future generations can dramatically influence SCC estimates.
2. Inadequate treatment of uncertainty and catastrophic risk: IAMs often overlook low-probability, high-impact climate events. This omission can lead to underestimating the true economic risks associated with climate change.
3. Ethical concerns and intergenerational injustice: the SCC has been criticized for embedding utilitarian and economically rationalist ethics that may not align with broader moral values.
4. Political manipulation and lack of transparency: the U.S. federal government under different administrations has produced wildly divergent SCC values, ranging from $1/ton under Trump to over $15/ton under Biden (using a 2% discount rate). This volatility undermines the credibility of SCC as a stable policy guide and suggests that it can be tailored to serve political ends rather than objective analysis. Further, some IAMs are not open-source or lack sufficient transparency, making it difficult for the public or policymakers to evaluate the quality of the estimates.
5. Marginal logic vs. Planetary boundaries: Some scholars argue that the marginal nature of the SCC is fundamentally mismatched to the climate crisis. The SCC estimates the cost of one additional ton of CO₂, assuming the rest of the system stays constant. In this view, carbon budgets or absolute emissions caps may be more appropriate than pricing frameworks based on marginal harm.

Proposed Alternatives and Emerging Directions

• Declining discount rates
• Carbon budgets
• Consumption-based greenhouse gas emissions accounting
• Intergenerational equity frameworks
• Global minimum carbon price proposals