Climate Damage on Production or on Growth: What Impact on the Social Cost of Carbon?

Recent articles have investigated with integrated assessment models the possibility that climate damage bears on productivity (TFP) growth and not on production. Here, we compare the impact of these alternative representations of damage on the social cost of carbon (SCC). We ask whether damage on TFP growth leads to higher SCC than damage on production ceteris paribus. To make possible a controlled comparison, we introduce a measure of aggregate damage, or damage strength, based on welfare variations. With a simple climate-economy model, we compare three damage structures: quadratic damage on production, linear damage on growth and quadratic damage on growth. We show that when damage strength is the same, the ranking of SCC between a model with damage on production and a model with damage on TFP growth is not unequivocal. It depends on welfare parameters such as the utility discount rate or the elasticity of marginal social utility of consumption.