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Climate change, discounting, and the tragedy of horizons

by Andreas Charisiadis, Research Assistant, Cambridge Centre for Finance and Cambridge Endowment for Research in Finance

Aerial drone views high above flooding caused by climate change leaving entire neighborhood underwater and houses completely under water.

This year’s UN Climate Change Conference, COP26, has been in the centre of a controversial debate over the extent to which current climate change mitigation measures are (in)sufficient to limit the rise in average global temperatures to 2°c – let alone 1.5°c – above pre-industrial levels. Inherent in the discussion about the appropriate intensity of climate action is a fundamental social dilemma. While most of the costs associated with climate change mitigation measures are incurred today, their ensuing benefits are to a large extent enjoyed by future generations. Conversely, inaction today – while unlikely to generate material repercussions in the short run – is bound to have dramatic consequences in the more distant future. Climate change therefore poses an intergenerational challenge. Specifically, insufficient climate action today represents a manifestation of the ‘tragedy of horizons’, whereby the current generation avoids costly abatement policies to the detriment of future generations – a phenomenon Chichilnisky (1996) referred to as “dictatorship of the present”.

Exponential discounting and the welfare of future generations

Intertemporal choice problems are commonly analysed under the assumption of exponential discounting, whereby any future benefit or cost is discounted at a constant rate. Alas, relying on exponential discounting when conducting cost-benefit analyses for environmental action produces optimal policies which place almost negligible value on environmental damage materialising in the distant future, say several hundred years from now. At virtually any chosen discount rate, the future costs arising from climate change become unimportant in present-value terms so long as the horizon under consideration is sufficiently long. At constant discount rates, justifying large public expenditures on climate change mitigation therefore becomes an intricate endeavour. This gives rise to the question of how climate action – which is of sufficient scale to avoid disastrous consequences for future generations – can be motivated in an intertemporal optimisation framework.

Declining discount rates – a way forward?

One possible approach involves departing from exponential discounting at a constant rate and instead allowing for time-variation in the discount rate. For instance, hyperbolic (or quasi-hyperbolic) discount functions yield discount rates which decline with the length of the time horizon, ie impatience is larger in the short run than in the long run. In other words, benefits and costs arising in the distant future are discounted at lower rates than if they were to materialise sooner. The welfare of future generations thus receives a relatively larger weight under such discounting regimes. The use of declining discount rates might therefore be helpful in rationalising the need for more pronounced climate policy action today. Importantly, employing declining discount rates in environmental cost-benefit analyses need not rely on the assumption that all individuals have intertemporal preferences with declining impatience. In fact, even if all members of society are using a constant personal discount rate, the representative agent – who duplicates the optimal behaviour of the group of individuals – has a discount rate which decreases with the time horizon, so long as individuals exhibit decreasing absolute risk aversion (Gollier and Zeckhauser 2005). A similar conclusion is reached by Heal and Millner (2014), who analytically aggregate a set of heterogeneous discount rates into a single ‘consensus’ rate, wherein each preference is assigned an equal weight. This time-dependent aggregate rate is shown to decrease monotonically to the smallest discount rate in the population.

Achieving intergenerational equity

Equal treatment of current and future generations is at the heart of the debate around the appropriate choice of discounting regime when evaluating welfare across generations. Yet, the notion of equal treatment is far from unambiguous. For instance, Ramsey (1928) argued that discounting the utility of future generations would be “ethically indefensible” – yet, so long as there is positive economic growth and utility functions are concave (ie agents prefer to smooth their intertemporal consumption path), using a positive rate to discount future consumption streams (as opposed to utility) can be consistent with equal treatment of current and future generations.

However, not discounting the welfare of future generations at all – ie setting the social utility discount rate to zero as Ramsey (1928) suggested – is not uncontroversial. In fact, Arrow (1999) argued that failing to discount would produce logical fallacies. For illustration, he considered a stylised economy in which output takes the form of a continuous stream of perishable goods. In this economy, the current generation has access to an investment opportunity, whereby for each unit of consumption foregone, the investment yields a continuous consumption stream (say, α) in perpetuity. In the absence of discounting, any present value calculation would advocate foregoing consumption in order to invest a fraction arbitrarily close to 100% of the current generation’s income in the project, regardless of how small the value of α is. Arrow (1999) regarded such high sacrifices by the current (or, in fact, any) generation as morally unacceptable, and therefore concluded that the welfare of future generations should be discounted at a positive rate.

Reflecting the possibility of extinction

In a recent contribution, Chichilnisky et al. (2018) argue that – contrary to the findings of Arrow (1999) – refraining from discounting the welfare of future generations need not lead to logical inconsistencies. They derive that maximising the unweighted expected utility across all generations can, in fact, be logically coherent as long as (a) the expected total number of individuals who will ever live before extinction is finite and (b) each individual’s utility function is bounded above and below. In this framework, the only source of value decay stems from the possibility of extinction occurring at an uncertain future date. Consequently, the value placed on future consumption should reflect the fact that potential future generations may not come into existence. Chichilnisky et al. (2018) therefore argue that – when modelling the benefits and costs of climate policy – any discounting of future generations’ utility should purely reflect the risk of extinction. This results in an ‘extinction discounting rule’, whereby the weight placed on future generations declines in line with their decreasing probability of existence.

Overall, mitigating climate change is without doubt an intergenerational challenge. Standard (exponential) discounting regimes have been shown to be of limited usefulness for environmental cost-benefit analysis, given their negligible weight on the distant future. Different alternatives have been proposed in response to this dilemma, such as declining discount rates which place a relatively larger weight on future generations, or the assignment of equal weights to all potential future generations conditional on their existence. How such discounting regimes may be implemented in current and future policy making remains an open question.


Arrow, K.J. (1999) “Discounting, morality, and gaming. In: Portney, P.R. and Weyant, J.P. (eds.) Discounting and intergenerational effects. Washington, DC: Resources for the Future Press, pp.13-21

Chichilnisky, G. (1996) “An axiomatic approach to sustainable development.” Social Choice and Welfare, 13(2): 231-257

Chichilnisky, G., Hammond, P.J. and Stern, N.H. (2018) “Should we discount the welfare of future generations? Ramsey and Suppes versus Koopmans and Arrow.” Warwick Economics Research Papers No.1174.

Gollier, C. and Zeckhauser, R. (2005) “Aggregation of heterogeneous time preferences.” Journal of Political Economy, 113(4): 878-896

Heal, G.M. and Millner, A. (2014) “Agreeing to disagree on climate policy.” Proceedings of the National Academy of Sciences, 111(10): 3695-3698

Ramsey, F.P. (1928) “A mathematical theory of saving.” Economic Journal, 38(152): 543-559