A Simple Formula for the Social Cost of Carbon

Abstract

The social cost of carbon (SCC), commonly referred to as the carbon price, is the monetized damage from emitting one unit of CO 2 to the atmosphere. The SCC is typically obtained from large-scale computational Integrated Assessment Models (IAMs) that consolidate interdisciplinary climate research inputs to obtain a carbon price estimate relevant for policy-making (1). However, the climateeconomy interactions of IAMs remain inaccessible to scientists in general. Here we develop a simple closed-form formula that captures the key physical and economic determinants of the SCC in the IAMs. For a mainstream IAM, it explains over 99 percent of the within-model variation originating from structural uncertainties; in an inter-model comparison, the structural variation captured by the formula matches closely a SCC distribution of previous SCC estimates (2). The precise replication of the SCC estimates is strikingly free of details such as those on future policy and technology options, or even carbon concentration levels; the size of the current economy and the emissions-temperature-damage response are the dominant SCC determinants in the IAMs. The structural interpretation given allows decision-makers to disentangle the subjective and structural determinants of the carbon price. Structural uncertainties alone lead to a strongly right-skewed density with median 15 €/tCO 2 , mean 31 €/tCO 2 , and more than 5 percent probability for higher than 100 €/tCO 2 for year 2015.3

Global Demographic Change and Climate Policies

“…Formula (18) for the carbon price is similar to carbon price formulas presented in Golosov et al (2014), van den Bijgaart et al (2016), and Gerlagh and Liski (2017b). The carbon price tends to increase proportionally with output as a larger economy values emissions more.…”

“…Time is discrete and runs to infinity. The economy's technology is based on Gerlagh and Liski (2017b), while our quantitative assessment employs the (median) climate-damage description listed in van den Bijgaart et al (2016). 10 It is important to mention that we model a closed economy and therefore the aggregate savings rate equals the investment rate.…”

“…10 It is important to mention that we model a closed economy and therefore the aggregate savings rate equals the investment rate. 11 For a discussion of the implications and robustness of simple carbon pricing rules see e.g., Barrage (2014), van den Bijgaart et al (2016), and Rezai and van der Ploeg (2015). 12 See also Iverson (2012); Belfiori (2013) for discussions on time preferences and the SCC formula.…”

“…We take the parameters from van den Bijgaart et al (2016), Table 6 and 7 sphere 'forever', while the same share very quickly transits to other carbon reservoirs (at about 30% per year). Also, about 22% of temperature adjustment is virtually immediate, while almost half of temperature adjustment only happens after more than a century.…”

“…Recently, van den Bijgaart et al (2016) presented an alternative discount rate measure. They show that the relative value of future output compared to present output, b t = Y t+1 r t+1 Yt (labeled the effective discount factor), where Y t is output and r t+1 is the marginal rate of substitution between the two periods, captures the most important discount information required to calculate the efficient carbon price.…”