The social cost of carbon is the estimated present discounted value of economic damages from emitting one ton of carbon dioxide into the atmosphere today. This column proposes a straightforward way to calculate the cost which takes into account the damages to aggregate production, the risk of recurring climate disasters, and the risk of a climate tipping point. The new approach produces similar results to complex traditional models. The high estimates of the social cost of carbon imply there is strong case for implementing carbon taxes or other market-based policies to incentivise the reduction of carbon dioxide emissions.
In one of his first actions after taking office, President Joe Biden set out to reassess how the US government values the cost of carbon emissions. The concept of the social cost of carbon (SCC), which represents the estimated present discounted value of present and future economic damages from emitting one ton of carbon dioxide (CO2) into the atmosphere today, has long been a critical component in shaping climate policy. The SCC is a key factor in the cost-benefit analysis of climate investment projects aiming to curb emissions. To implement the SCC, policymakers can either set a carbon tax at a level equal to the SCC or set up markets for emissions permits in which case the price of the permit will end up equal to the SCC. President Biden has tasked economists with providing the best and most up-to-date evaluation of the SCC, taking account of the latest climate science, socioeconomic projections, and economic models.
The result of this inquiry is a significant shift in our understanding of the cost of climate inaction. A groundbreaking collaborative study by Rennert et al. (2022) has recalculated the SCC, and their findings are eye-opening: their preferred estimate for the SCC stands at $185 per ton of CO2, a staggering 3.6 times higher than the current US government estimate of $51 per ton. This new figure reflects a more sophisticated understanding of the risks associated with climate change, especially the possibility of sudden, irreversible damage to the global climate system arising from, for example, a reversal of the Gulf Stream, melting of the tundra, melting of the Greenland Ice Sheet (so-called tipping points), and the increased intensity of recurring climate disasters such as floods, droughts, storms, and extreme heat events.
Why the new social cost of carbon matters
So, why does the SCC matter so much? It’s not just a number—it’s a guidepost for policymakers making decisions about climate action. If the true cost of emitting carbon is significantly higher than previously thought, it means the benefits of reducing emissions outweigh the costs by a larger margin. In practical terms, this implies that stronger climate policies, including carbon taxes and regulations, are needed to mitigate the far-reaching consequences of global warming.
The calculation of the SCC is a highly complex process, involving detailed economic and climate models that project the potential expected present and future damages from rising global temperatures. The challenge is made harder by the uncertainty of how the climate will evolve over time. Different models use different assumptions, and the risks associated with climate change—such as the possibility of reaching tipping points where the climate undergoes irreversible shifts—are difficult to quantify. These tipping points are potentially catastrophic, triggering feedback loops that could accelerate warming and make future mitigation efforts much more difficult. One tipping point can also set in motion another tipping point, thus leading to the phenomenon of cascading tipping points.
To account for these risks, Rennert and his colleagues have refined the SCC calculation by incorporating advanced methods and up-to-date data. Their approach is important because it emphasises the uncertain, but highly impactful, nature of climate change, something that many previous models have underestimated.
The complexity of calculating the social cost of carbon
Calculating the optimal SCC is no easy task. In the past, researchers used sophisticated mathematical equations and dynamic programming methods to model the expected impacts of climate change on the economy and ecosystems and to calculate the optimal SCC and price of carbon. However, these models can be computationally expensive and difficult to interpret. More recently, economists have turned to simpler methods, such as Monte Carlo simulations, which repeatedly solve for the optimal SCC given a particular realisation of future outcomes and then take the average of those values of the SCC. This procedure provides faster results but can often give misleading conclusions and biases in climate policy.
One of the key challenges in calculating the SCC is understanding the impact of climate tipping points. These are the thresholds beyond which climate change could spiral out of control. For instance, the melting of the Arctic ice sheet could trigger a chain reaction, accelerating global warming and leading to further ice melt. Similarly, massive wildfires in places like the Amazon rainforest could release enormous amounts of CO2 into the atmosphere, further heating the planet. While these tipping points are well-known, incorporating them into climate models is incredibly difficult.
In Hambel et al. (2024), we propose and derive a much simpler way to calculate the SCC using what’s called a rule of thumb. This rule distils the key factors that drive the SCC into an intuitive formula that can be easily applied in real-world policymaking and turns out to be surprisingly accurate. In essence, such a rule is designed to take account of three adverse effects of global warming on the economy:
- The impact of global warming on economic productivity: how climate change reduces the ability of the economy to produce goods and services by lowering total factor productivity, including productivity of workers.
- The risk of recurring climate-related disasters: the increased likelihood of extreme weather events like hurricanes, floods, and wildfires as the climate warms. The frequency of such disasters rises with global warming.
- The risk of irreversible climate tipping points: the possibility that climate change could reach a point where the climate system tips, and temperature abruptly becomes more sensitive to cumulative carbon emissions. Again, the probability of such an irreversible shift of the climate system increases with global warming.
Emissions by an individual firm or corporation can generate adverse effects on others, and thus correspond to external effects that are not internalised by the market. Governments should step in to correct for these market failures and price carbon via a carbon tax or an emissions market. The size of this carbon price will correspond to the SCC, which needs to be evaluated.
The new rule for the social cost of carbon
Taking account of damages to aggregate production
Let’s use the rule of thumb in Hambel et al. (2024) to estimate the SCC. If we ignore for the time being the risks of recurrent climate-related disaster and climate tipping points and focus on the first externality, the rule for the SCC will depend on three key factors.
The first factor is the marginal damage of a one-degree Celsius rise in temperature, which corresponds to the marginal damage ratio (MDR) times world gross domestic product (GDP). The MDR is thus the increase in the damage ratio of damages to world gross domestic product if temperature rises by one degree. We set this to 0.9% for each degree rise in global warming. World GDP in 2021 was about $115 trillion (based on evaluating the damages in Nordhaus and Moffatt (2017) at two degrees Celsius). Aerts et al. (2024) give a meta review of damage estimates and find that estimates of the marginal damage ratio vary between 1% for the DICE model and 25% for Bilal and Kaenzig (2024), so our estimate may be on the low side. A reason is that this estimate does not allow for risks of climate disasters and tipping points.
The second factor concerns the sensitivity of the climate system with respect to cumulative global carbon emissions, which is called the transient response to cumulative emissions (TCRE). A ballpark figure for the TCRE is 1.8 degrees of warming for every trillion ton of cumulative carbon emissions (e.g. Matthews et al. 2009; to express this in degrees per Gigaton of emitted CO2 instead of carbon (C) we must convert by multiplying by the factor 12/44).
The third factor is the rate by which the marginal damages should be discounted. This corresponds to the difference between the social discount rate and the expected trend growth of the global economy. The reason for the growth correction is that global warming damages rise in proportion to world gross domestic product. Many economists would agree on a figure for the social discount rate of 4% per year and a trend growth rate of 2% per year, so that the growth-corrected discount rate is r= 2% per year.
Combining these three factors, the expression for the SCC becomes:
This is like a much-used expression derived by Golosov et al. (2014). Substituting in the above numbers, we get
per ton of emitted CO2.
Risk of recurring climate disasters
If we also allow for the risk of recurring climate disasters, we need to know the marginal risk to the capital stock of a climate disaster when temperature increases by one degree: MRCD, say 9.6% per year for every degree of warming. We also need to know the mean damage of a disaster: MDD, say 1.5% of the global capital stock. This is smaller than the mean size of macroeconomic disasters at 20%. However, climate disasters occur more frequently (0.3% plus 9.6% times the temperature in degrees above preindustrial, per year) than macroeconomic disasters (at 8.8% per year). We need to adjust the MDD for risk, using the coefficient of relative risk aversion of RA = 5.35 by the factor
or 1.0872 which gives a risk-adjusted mean loss of 1.63% per year. Finally, we need the value of the global capital stock, i.e. V = $2,875 trillion in 2021, as climate disasters hit productive capacity.
The SCC that takes account of the first two externalities thus becomes
which gives SCC_(1&2)=135.9>25.5 dollars per ton of emitted CO2. In fact, the figure is a bit higher, namely 139.2 $/tCO2, as the rate of interest should be depressed to r = 1.953% to allow for precautionary saving in view of the risk of climate disasters and non-zero mean disasters. The risk of recurring climate disasters thus demands a SCC that is bigger by a factor of 5.5 corresponding to a risk premium of 450%.
Our exercise above corresponded to calculating an aggregate of all kinds of different recurring climate disasters. It is straightforward to allow for a multitude of recurring climate disasters corresponding to floods, disasters, storms, etc., each one with a different marginal risk to the capital stock of a climate disaster (MRCD) and mean damage of a disaster (MDD) when calculating the optimal social cost of carbon (SCC) simply by adding terms for each disaster.
Risk of a climate tipping point
Finally, we can allow for the temperature-dependent risk of a climate tipping point. Cai and Lontzek (2019) discuss how a wide variety of tipping points affect the optimal SCC. Here, we consider what happens if the transient response to cumulative emissions (TCRE) abruptly increases from 1.8 to 2.5 degrees Celsius per trillion ton of carbon of cumulative emissions. The annual risk of climate tipping rises by 0.6 percentage points for every degree. The new SCC is then the sum of S〖SC〗_(1&2) plus an additional term that captures the expected loss in welfare from the risk of this climate tipping point resulting from emitting one ton of CO2 more today (proportional to the marginal risk, 0.6%), and an additional term to reprice the SCC in view of the risk of climate tipping (proportional to the temperature-dependent risk of climate tipping itself).
Table 1 shows that the optimal SCC then becomes even higher. It rises from $139 to $182 per ton of CO2. Hence, the deterministic damages account for only 14% of the SCC, while the climate risk damages account for 86% of the SCC. Put differently, the climate risk premium in the SCC is 606%, so that if policy makers do not take account of climate risks, they underestimate the SCC by a factor of seven.
Table 1 The social cost of carbon is much higher if account is taken of climate risk
Projected time paths of the social cost of carbon
Figure 1 plots the projected mean path of the optimal social cost of carbon (SCC) up to the year 2050 on the vertical axis with years on the horizontal axis. If only account is taken of the normal adverse effects of production on aggregate production (the first externality), panel (a) indicates that the mean value of the SCC rises from $25 to about $80 per ton CO2 in 2050. However, if we also take account of the risks of recurring climate disasters and climate tipping, panel (b) indicates that the mean value of the SCC rises from $182 to almost $600 per ton CO2 in 2050.
Panel (a) indicates two downward jumps in the SCC around 2040 and just before 2050, which are due to the strike of a macroeconomic disaster unrelated to climate change. Panel (b) also shows an upward jump in the SCC towards the end of the 2020s, which is due to a climate tipping point leading to a higher temperature sensitivity and higher SCC. As disasters strike, the economy shrinks and thus there must be a discrete downward adjustment of the SCC; afterwards the economy continues to grow. This contrasts with a climate tipping point, which leads to an upward jump in the SCC before continuing to grow along this higher path.
Figure 1 Mean paths for the social cost of carbon (solid lines) and 5% and 95% quintiles (dashed lines)
Accuracy and robustness of this rule for the social cost of carbon
The beauty of this new approach is that we give an approximate, tractable solution to the complicated partial differential equations associated with the underlying dynamic programming problems. This gives an easy-to-interpret formula for the optimal social cost of carbon, which incorporates the economic cost of global warming, the risks associated with regularly recurring climate disasters, and the chance that the climate system crosses a tipping point.
If we compare this rule for the SCC to traditional numerical optimisation, Table 1 indicates that the rule produces remarkably accurate results even when the risks of climate disasters and tipping points are incorporated. This means that policymakers can use this rule to make better-informed decisions about climate policy without getting bogged down by the complexity of the models. Furthermore, the easy interpretation of the rule for the optimal SCC allows for a clear understanding of the drivers of the SCC.
Interestingly, the rule’s robustness can be tested by applying it to different models, where fossil fuel costs are falling or where the economy consists of multiple sectors and is growing in more complex ways. Even in these more complicated models, the rule continues to provide accurate estimates of the optimal SCC. This is an important finding because it shows that the rule is flexible and can be applied across a wide range of real-world situations.
Looking ahead: More stringent climate policies
By providing a more accurate and user-friendly way to calculate the social cost of carbon, our research can help policymakers develop more effective climate policies. If the cost of carbon emissions is as high as this new estimate suggests, there is a much stronger case for implementing carbon taxes or other market-based policies that incentivise the reduction of CO2 emissions. Governments should thus consider adopting policies that align more closely with the updated SCC, such as higher carbon taxes, stricter regulations on emissions, and increased investment in renewable energy technologies.
Furthermore, this new framework could help governments around the world better prepare for the economic and environmental impacts of climate change. The risks of extreme weather events and tipping points are not just theoretical—they are already beginning to manifest in real-world disasters like the Australian wildfires of 2019–2020, the increasingly severe hurricanes in the Atlantic, and the unprecedented heatwaves and floods hitting various parts of the globe. By incorporating the effect of these risks into the SCC, we can ensure that climate policy is more reflective of the true cost of inaction.
Proposals for a carbon tax have gained traction in recent years, but the actual price at which CO2 emissions should be taxed remains a contentious issue. With the new estimate of $185 per ton, the economic justification for such a tax becomes much clearer. It’s not just an abstract number — it is a reflection of the growing costs of a warming planet. It should serve as a wake-up call for policymakers and citizens alike: we need to take more immediate and decisive action to avoid the worst impacts of global warming. In the end, higher carbon prices are a crucial step forward in making climate change a priority in the global policy conversation. With a clearer understanding of the true costs of carbon emissions, the world has a better chance of avoiding the worst outcomes and building a more sustainable future.
Source : VOXeu
