### Discussion Paper

## Abstract

It is well-known that the discount rate is crucially important for estimating the social cost of carbon, a standard indicator for the seriousness of climate change and desirable level of climate policy. The Ramsey equation for the discount rate has three components: the pure rate of time preference, a measure of relative risk aversion, and the rate of growth of per capita consumption. Much of the attention on the appropriate discount rate for long-term environmental problems has focussed on the role played by the pure rate of time preference in this formulation. We show that the other two elements are numerically just as important in considerations of anthropogenic climate change. The elasticity of the marginal utility with respect to consumption is particularly important because it assumes three roles: consumption smoothing over time, risk aversion, and inequity aversion. Given the large uncertainties about climate change and widely asymmetric impacts, the assumed rates of risk and inequity version can be expected to play significant roles. The consumption growth rate plays four roles. It is one of the determinants of the discount rate, and one of the drivers of emissions and hence climate change. We find that the impacts of climate change grow slower than income, so that the effective discount rate is higher than the real discount rate. The differential growth rate between rich and poor countries determines the time evolution of the size of the equity weights. As there are a number of crucial but uncertain parameters, it is no surprise that one can obtain almost any estimate of the social cost of carbon. We even show that, for a low pure rate of time preference, the estimate of the social cost of carbon is indeed arbitrary – as one can exclude neither large positive nor large negative impacts in the very long run. However, if we probabilistically constrain the parameters to values that are implied by observed behaviour, we find that the social cost of carbon, corrected for uncertainty and inequity, is 61 US dollar per metric tonne of carbon.

Paper submitted to the special issue “Discounting the Long-Run Future and Sustainable Development”

## Comments and Questions

see attached file

The referee makes three points:

1. The discussion on the triple role of the consumption elasticity of marginal utility (consumption smoothing over time, risk aversion, inequity aversion) should be moved up and extended.

Agreed. We'll also add a reference to the paper by Atkinson et al in the special ...[more]

... issue.

3. Refer to the hyperbolic discounting literature.

Agreed. Note that we do a Monte Carlo analysis on the growth rate of per capita income, so we implicitly have hyperbolic discounting. We'll try to make this explicit.

2. Discuss catastrophic risk as a reason for discounting.

Not agreed. Catastrophic risk should be modelled explicitly, not introduced through a backdoor, as this just muddles up the discussion. In the Monte Carlo analysis, the probability of the extinction of the human race is zero so the paper is internally consistent as it stands. We'd be happy to discuss this issue in a paragraph or two.