There is increasing interest among economists in thinking about the implications of catastrophic scenarios and what we might wish to do limit the risk of these today. This is particularly relevant given that the weight of scientific opinion supports the proposition that a range of geophysical changes induced by emissions of greenhouse gases place the world at risk of catastrophic changes which threaten human well-being (van der Ploeg and De Zeeuw 2014). A key policy issue is how much current generations should be willing to sacrifice consumption to reduce the risk of a future catastrophe, given that the probability of it occurring increases with delay. Mr Trump seems unconvinced of the need for public action, but even he and those advising him might wish to think what the cost might be if they get things wrong and a disaster strikes down the line. We believe that debates about the optimal sacrifice to make can usefully be informed by calculating the discounted flow of benefits that accrue from any mitigation strategy. This should help to focus the minds of concerned citizens and policymakers when deciding how much to invest in scientific research or to impose taxes on emissions.

## The interaction between economic activity and climate change

Existing research has identified some important features of the dynamic interaction between economic activity and climate change.

- There is much structural uncertainty, which is not satisfactorily captured in a normal distribution but has fat tails. The Stern Review (2007: xiv) characterised the issue as "the economics of the management of very large risks."
- There are dynamics with a stock effect: the probability of a rare environmental disaster increases as the stock of greenhouse gases accumulate in the atmosphere.
- There is irreversibility on both sides of policy action: if we do nothing and the problem proves serious, the climate and economic activity will suffer long-term damage, but if we spend resources to mitigate or counter a problem that later proves to be less important or non-existent, we will have sacrificed resources unnecessarily.

Thus there are embedded options in both the decisions to act and to wait, and the two must be balanced to determine the optimal policy.

## How much consumption should we sacrifice?

In a new paper, we develop an approach where we capture the idea of fat-tailed uncertainty of a rare disaster in the simplest and most extreme form, namely as a Poisson process (Besley and Dixit 2017). The stock effect is captured by making the arrival rate of this process an increasing function of a state variable that represents the accumulated stock of greenhouse gases in the atmosphere. We then offer a quantification of the benefits from mitigation – how it depends on the underlying parameters of the problem, but without having to be specific about risk aversion or needing to take a strong stance on the discount rate (although we can examine the sensitivity of our results to varying it). We provide software for interested readers to download and explore any set of parameter values that they regard as plausible.

To get at policy implications, we ask what would be the loss in real consumption that society should be willing to make in perpetuity in order to achieve a given discounted gain if a particular parameter of the problem could be changed in a favourable way.

To get at quantitative implications, we propose a range of parameters since, as emphasised in reviews of integrated assessment models such as Metcalf (2015), there is a considerable uncertainty about the right assumptions to make about the likely damages from higher carbon emissions. There is also a debate about the about the right level at which to set the discount rate, with competing views suggested a range of 1-5%. For example, there are those who advocate near-zero discounting (e.g. Stern 2007) and those who favour rates of 5% or higher (e.g. Weitzman 2007). We set the discount rate at 2% per year. At our core parameter values for the emissions process and arrival rate for a catastrophe, the probability that a disaster occurs will reach 90% in 58 years. We also suppose that there is a probability that a ‘magic’ technology comes along which fixes the problem, which we set at 0.3% a year. This still gives around a 25% chance of this technology being found in the next 100 years.

In our core case, we suppose that catastrophe results in a permanent 5% fall in consumption, which is equivalent to sacrificing about five years of productivity growth based on the US historical average over the past 150 years. So arguably, this is still quite a benign definition of a catastrophe. We suppose that this occurs along with a ‘lump-sum’ loss in consumption with a discounted present value of one year’s consumption, although we are unspecific about the timing of this loss. This is not out of line with standard estimates from the Intergovernmental Panel on Climate Change for output loss based on the status quo based on a 4°C increase in global temperatures. This baseline translates into a loss (in expectation) of about a 16% of the total productive potential of an economy due to the risk of the catastrophes of the magnitude that we are contemplating. Put another way, if there were a way of eliminating the risk of all future catastrophes immediately and completely, society should be willing to sacrifice 16% of its consumption in perpetuity to achieve this.

To illustrate the impact of policy change, suppose that there is a 30% reduction in the rate of greenhouse emissions. This is the order of magnitude of reductions in carbon emissions that have been contemplated in international agreements such as the Kyoto Protocol. A number of countries have responded to this with binding targets on carbon emissions backed up by regulations and tax incentives. Increased use of renewables and nuclear power in electricity generation form a key part of this strategy. This change increases the time until the probability of a catastrophe occurring hits 90% from 58 to 74 years, and we calculate that we should be willing to sacrifice 5.8% of annual consumption to bring about this reduction in emissions. Given that US GDP is around $18 trillion, this means that the US should be willing to spend $1.05 trillion to achieve this Kyoto-type reduction. Even though this is substantial number, it is purely illustrative. Even if a catastrophe only reduces consumption by 1% a year with a one-off component of 20% of GDP, the willingness to sacrifice would still be 1.8% of GDP which would correspond to $324 billion.

Of course, a model is just that but our download allows us to be completely transparent about how different scenarios affect the results. The approach that we are suggesting also allows us to think about which parameters really matter for thinking about the willingness to sacrifice. If climate change is irreversible (over the relevant time scale) then a precautionary approach has value in sharpening the mind.

## References

Besley, T and A Dixit (2017), “Comparing Alternative Policies Against Environmental Catastrophes,” CEPR Discussion Paper No. 11802.

Metcalf, G (2015), The Role of Integrated Assessment Models in Climate Policy: A User's Guide and Assessment.

Stern, N H (2007), *The Economics of Climate Change: The Stern Review.* Cambridge, UK: Cambridge University Press.

van der Ploeg, R and A De Zeeuw (2014), “Climate tipping requires precautionary accumulation of capital and an additional price for carbon emissions”, VoxEU.org, 31 July.

Weitzman, M L (2007), “A review of the `Stern Review on the Economics of Climate Change”, *Journal of Economic Literature* 45(3): 703-724.