Climate damages on production or on growth: what impact on the social cost of carbon

Recent papers have investigated with Integrated Assessment Models the possibility that climate damages bear on productivity growth and not on production, the traditional route that follows Nordhaus's work. According to these papers, damages on growth lead to a higher social cost of carbon (SCC). Here, we reconsider the evidence with the introduction of a measure of the amount of damages, to allow the comparison between alternative representations of damages. We build a simple climate-economy model and compare three damages specifications: quadratic damages on production, linear damages on growth and quadratic damages on growth. We show that when total damages are the same, the ranking of SCC between a model with damages on production and a model with damages on growth is not unequivocal. It depends on welfare parameters such as the utility discount rate or the elasticity of marginal social utility of consumption. The difference in SCC comes both from when damages occur and from their total amount.