Efficient carbon pricing under uncertainty

Any global temperature target must be translated into an intertemporal carbon budget and an associated cost-efficient carbon price schedule. This column uses an intertemporal asset-pricing approach to examine the impact of uncertainties surrounding economic growth and abatement technologies on the dynamics of efficient carbon prices. It finds evidence of a positive carbon risk premium and suggests an efficient growth rate of expected carbon prices of around 4% plus inflation. This is lower than the growth rates found in many public reports and integrated assessment models, and justifies a higher carbon price today in order to satisfy the carbon budget.

By Christian Gollier, 06 April 2021

The EU will come to the 26th United Nations Climate Change Conference (COP26) in Glasgow in November this year with a new ambitious climate commitment. Rather than promising to reduce emissions by 40% in 2030 (compared to 1990), it will now reduce them by 55%. Nobody knows exactly how this target can be attained, what the costs will be, and whether it is aligned with the long-term objective of 2°C. The EU Green Deal under discussion in Brussels will certainly produce a cocktail of climate measures combining an extension of the EU Emissions Trading System (EU-ETS) market for emission permits with a myriad of new norms, standards, bans, and subsidies. Because of the reluctance of EU citizens to sacrifice their welfare to fight climate change (Oswald and Nowakowsky 2020), it is crucial to attain our climate goal at minimal cost. These climate actions will thus require measuring their costs per tonne of CO2 saved, which will have to be compared to the shadow value of carbon associated to the carbon budget. What should the level of this carbon value be, and at what rate should it increase over time? I examine these questions in a recent paper (Gollier 2021).

Hotelling rule in carbon pricing

The Pigouvian approach to carbon pricing consists in estimating the present value of the flow of marginal damages of one tonne of CO2 emitted now. But today, under the auspice of COP21 and the Paris Agreement, the issue is no longer one of aligning private interests with the common good by forcing people to internalise the damage by a Pigouvian tax. Rather, the issue is to find a pathway of shadow carbon prices that are compatible with the 2°C target. Because this target can be translated into an intertemporal carbon constraint, the problem of the speed of decarbonisation and of carbon pricing becomes isomorphic to the ‘Hotelling problem’ of the optimal extraction of a natural resource. 

Under this cost-efficiency approach to carbon pricing, along any path compatible with the intertemporal carbon budget, what is abated today need not be abated tomorrow. This simple observation implies that the rate of return of frontloading the abatement effort equals the growth rate of the marginal abatement cost, i.e. of the carbon price. Under certainty, a growth rate of this carbon price that is above the interest rate signals that not enough abatement efforts are being made today. Along the optimal path, the growth rate of the carbon price should equal the risk-free rate. This is the well-known Hotelling rule.

This recommendation is not being applied in practice. In the UK, the carbon price recommended by the BEIS (2019) is 15% per year for the next ten years. In France, the Commission Quinet (2019) recommended a schedule for carbon prices that grow at 8% per year. And in the fifth report of the Intergovernmental Panel on Climate Change (IPCC), the carbon value also has a mean growth rate of 8%! This suggests that we are all playing the waiting game, with too low a carbon price today, and too high a carbon price in the future. This delay in reducing emissions will be costly (Furman et al. 2015).

But the necessary energy transition is surrounded by deep uncertainties. Nobody knows what a fully decarbonised world will look like in 2050. In the absence of a huge R&D effort to reduce the cost of green technologies, the price of carbon will have to grow fast to induce people to reduce their consumption of brown goods and services. On the contrary, if we find cheap solutions to capture and sequester atmospheric CO2, or if we succeed in solving the mass electricity storage problem in the face of the intermittency of renewable electricity, it could be possible to decarbonise our economy with a very limited carbon price in the future. This technological unpredictability means that an efficient climate policy has an important dimension of risk management, and in the future the carbon price will need to be adjusted to the evolution of the marginal abatement cost (MAC) function. This large uncertainty is documented in Figure 1, in which I draw the histogram of the 2030 carbon price compatible with the 2°C target estimated by 374 integrated assessment models (IAMs) from the IPCC database.

Figure 1 Histogram of the world marginal abatement costs for 2030 (in USD2005/tCO2) extracted from the IPCC database

Sources: Gollier (2021) and IPCC database (https://tntcat.iiasa.ac.at/AR5DB)

Carbon pricing under uncertainty

Thus, the future carbon price is uncertain by nature if we want to be serious about the EU carbon constraint. How does this affect the timing of the mitigation effort and of the Hotelling rule for carbon pricing? Because frontloading the mitigation effort becomes an investment with an uncertain social return, its expected rate of return should be adjusted for risk. The key insight of modern asset-pricing theory is that one should collectively favour actions that reduce the macroeconomic risk, i.e. those actions whose net benefit is negatively correlated to aggregate consumption. Let me apply this idea to the problem of the timing of our mitigation efforts. If the future MAC is negatively correlated with aggregate consumption, abatement frontloading will save a larger MAC in the future when consumption will be smaller; it is thus a more socially desirable policy. In that case, the consumption-based capital asset pricing model (CAPM) beta of green investments is negative. This justifies a higher carbon price today, and a lower expected growth rate for this price. In contrast, if the MAC is positively correlated with aggregate consumption, abatement frontloading does not hedge the aggregate risk, and the expected growth rate of carbon prices should be adjusted upwards, above the interest rate.

What can we say about the statistical relationship between future MAC and consumption? I may propose here two opposing stories. In the ‘negative beta’ story, I suppose that the main source of uncertainty is the intensity of green innovations. If this is greater than expected, the MAC will be smaller when consumption is larger (because we will have to spend less to decarbonise). This yields a negative correlation between MAC and consumption. In the ‘positive beta’ story, suppose alternatively that the main source of uncertainty is the future prosperity of our economy (for example, measured by the total factor productivity). If this is greater than expected, consumption will be higher, emissions under ‘business as usual’ will be higher too, and more abatement efforts will be required. Because the MAC curve is increasing, this yields a positive correlation between MAC and consumption.

To solve the ambiguity over the sign of this correlation, I calibrate a simple two-period mitigation optimisation problem with uncertainty affecting both technological progress and economic prosperity. This realistic calibration yields a consumption CAPM (C-CAPM) beta for mitigation efforts that is very close to one. The positive beta story dominates. This is related to the observation that during economic downturns, the equilibrium carbon price on emissions trading system (ETS) markets goes down because of the reduced demand for allowances. This justifies recommending a growth rate of expected carbon prices close to the average cost of capital in the economy – around 4% plus inflation.


By almost systematically exhibiting a growth rate of carbon prices of 8% or more for the next few years and decades, IAMs and public reports on carbon prices that are compatible with the 2°C target imply playing a waiting game that I believe should be reserved for our politicians. I show that the growth rate of expected carbon prices should be higher than the interest rate because carbon allowances are a risky asset whose return is positively related to the business cycle. But this rate of return should be around 4% per year. Compared to the recommendation by the IAMs, this reduced growth rate justifies recommending a much higher carbon price today in order to satisfy the carbon budget.

My model also shows that this Hotelling approach to carbon pricing yields a much larger price uncertainty than when using the Pigouvian approach to the social cost of carbon. Indeed, if the necessary green innovations do not materialise in the future, a steep increase in carbon prices will be needed. In contrast, if great green innovations allow us to produce renewable energies at a cost no higher than that of fossil fuels, the carbon price could converge to zero in the future, thereby ruining many green entrepreneurs who have bet on a large carbon price to make their investment profitable. In my model, this justifies compensating this green investment risk with a risk premium. The alternative (second-best) approach would consist of imposing a carbon price floor and ceiling (Metcalf 2018).  


Note: This article is a re-post of the original posted on the VoxEU website.