Integrated Assessment Models (IAMs) attempt to capture and describe the interactions of (i) human behaviour, (ii) economic activity, and (iii) and climate dynamics and impacts. However, IAMs are often treated as some sort of black-box when calculating solutions.

DICE model in continuous time © Michael Freiberger

Investigating IAMs from an analytical perspective

Investigating the outcomes of IAMs following the steps:

Enter system dynamics -> Press button -> Get numeric results -> Obtain social cost of carbon (SCC) as the optimal carbon price.

raises several questions:

  • Do we really understand, what is happening in IAMs and what the SCC actually is?
  • Are we aware what IAMs can and cannot do / what it should and shouldn’t be used for?
  • Is the SCC actually the optimal carbon price/tax?

In this work, EF researchers aim at opening the black box and revisiting some of the mathematical properties of the DICE model (as a basic example for IAMs in general) in order to establish (or perhaps reestablish) an understanding of some of the core properties of the social cost of carbon and the social marginal abatement cost as the two constituent components of the optimal abatement rule and their relevance for climate policy making. Specifically, they

  • derive a detailed and economically intuitive representation of the social cost of carbon, which in typical applications is simply read-off from the shadow price of emissions, and for this reason, does not allow the structured decomposition into its intuitive key components.
  • discuss different definitions for the social marginal abatement costs in different model settings.
  • show that when incorporating continuous time effects, the optimal abatement rule may not always equalize the social cost of carbon with the social marginal abatement cost.
  • formally prove in a decentralized setting that nevertheless, and intuitively, the optimal carbon tax should equal the social cost of carbon.

A working paper of this project is available upon request.

Diagram of DICE model © Michael Freiberger

How to prepare for and adapt to a climate tipping point

In other work YSSP-student Maddalena Muttoni introduced stochastic tipping points into the DICE model during her time at the Economic Frontiers Program in the summer of 2022. Using the 2SOCS model she investigate the various impacts of qualitatively different type of tipping points:

  • Melting of sea ice or ice sheets
  • Destruction of capital due to an environmental catastrophe
  • Transformation of a carbon sink into a carbon source
  • Increased impact of temperature on production

Her results consist of analytical conditions for the optimal savings and emission abatement policy and a decomposition of the growth rate of the social cost of carbon. Furthermore, numerical simulations for the different tipping point scenarios are provided.

Muttoni, M. (2022). How to prepare for and adapt to a climate tipping point. IIASA YSSP Report. Laxenburg, Austria: IIASA