Some recent research suggests that uncertainty about the response of the climate system to atmospheric greenhouse gas (GHG) concentrations can have a disproportionately large influence on benefits estimates for climate change policies, potentially even dominating the effect of the discount rate. In this paper we conduct a series of numerical simulation experiments to investigate the quantitative significance of climate response uncertainty for economic assessments of climate change. First we characterize climate uncertainty by constructing two probability density functions—a Bayesian model-averaged and a Bayesian updated version—based on a combination of uncertainty ranges for climate sensitivity reported in the scientific literature. Next we estimate the willingness to pay of a representative agent for a range of emissions reduction policies using two simplified economic models. Our results illustrate the potential for large risk premiums in benefits estimates as suggested by the recent theoretical work on climate response uncertainty, and they show that the size and even the sign of the risk premium may depend crucially on how the posterior distribution describing the overall climate sensitivity uncertainty is constructed and on the specific shape of the damage function.