Modeling Damages in Climate Policy Models : Temperature-Based or Carbon-Based?

Economists have analyzed potential for damages from climate change from theoretical analyses and with Integrated Assessment Models (IAMs). Analytical models typically write damages as a function of the carbon stock, while IAMs typically view damages as based on temperatures. In this paper, we evaluate the implications for adapting analytic models to include two state variables — temperature and carbon stocks. We first provide an analytical comparison of a model where damages are based on carbon stocks against a model where damages are based on temperatures. When damages are based on carbon stocks, the time path of optimal emissions is described by a first-order differential equation; when damages are based on temperatures, the time path of optimal emissions is described by a second-order differential equation. We then proceed to an empirical analysis of the link between temperatures and carbon stocks. Our empirical analysis strongly supports a relation between levels of carbon stocks and changes in temperatures, and indicates the virtual absence of a linkage between levels of carbon and levels of temperature. As such, it is broadly supportive of a more elaborate modeling structure, under which two state variables are included in the analytical framework