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

Carbon Prices for The Next Hundred Years

“…van den Bijgaart et al . () show that the analytical policies remain close to those obtained from numerical models but can deviate considerably under extremely convex or concave representations of losses. The assumption made in the current article can be seen to represent the central case.…”

“…Deviations from assumption ( iv ), the exponential loss of output, is extensively analysed in van den Bijgaart et al . (). Combined with the other assumptions, the exponential loss implies unitary elasticity of output losses with respect to income, from a given temperature increase, as will be seen as we derive the policy rules.…”

Power markets in transition: Decarbonization, energy efficiency, and short-term demand response

“…Complementing technologies that provide the necessary flexibility are either carbon-emitting (gas power), scarce regarding suitable sites (pumped hydro, biomass), still too expensive (batteries, power-to-gas), or difficult to incentivize (short-term demand re-1 Note that even a warming of 2°Celsius comes at enormous cost. Supposing social costs of carbon of 100 US$/tCO2 (see [64] for a survey and [5,52,53,65,55] for estimates that vary between 10 and 805 US$/tCO2) and future emissions of 500,000 Mt, leads to economic costs of US$ 50 trillion, which is 2,500 times the 2017 US GDP. sponse 2 ), and thus there is an increasingly strong focus on long-term demand response measures such as energy efficiency.…”

Economics of climate change: introducing the Basic Climate Economic (BCE) model

“… 6 Specifically, Dietz and Venmans (2017: 6), citing Matthews and Caldeira (2008) and others, state that ‘the temperature response to a pulse emission of CO 2 is approximately constant as a function of time, except for an initial period of adjustment that is very short, i.e., five to ten years’ and (citing Matthews et al , 2009) that the warming effect of an emission of CO 2 ‘does not depend on the background concentration of CO 2 in the atmosphere’. Conversely, other economics models have assumed growing effect of natural sinks (absorbing an increasing part of carbon emissions) and major delays in temperature response (e.g., van den Bijgaart et al , 2016) but we follow the most recent and accurate climate modelling here.…”

“…A linear relationship D ( P ) is commonly used in the literature for its analytical convenience (e.g., Grimaud and Rouge, 2014; Bretschger and Karydas, 2018). Analytical approximations of the social cost of carbon (SCC) using a complex damage structure similar to (4) have been provided by van den Bijgaart et al (2016). For the relevant range of the available polluting resources, Golosov et al (2014) approximate damages in GDP by an exponential function.…”