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The motivation, as argued for instance by Nordhaus , comes from the issue of accumulation already alluded to in section 2. This choice is questionable for two reasons. First, practically, it is not obvious which market interest rate is relevant for the IAM computation. The second reason why this is questionable is ethical.

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The market rate on any asset reflects the preferences of investors whose calculations may include some altruism for future generations. Yet, such private preferences have no reason in general to be up to the ethical standards of a social welfare evaluation. Investors are expected to be selfish in their decisions, thinking more of their own future and their children than worrying about their great-great-grand-children.

It is very dubious that social policy should embrace the same ethical and temporal myopia when assessing trade-offs across distant generations.

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But one can simultaneously argue that for trade-offs across generations, impartiality across individuals becomes imperative—and excludes a pure time discount other than the level derived from considering the risk of extinction. Finally, one interesting complication is that if one accepts extinction risk as the justification of a small present bias in SWF, then one needs to face the question of how to evaluate risks in a more comprehensive way.

Extinction risk is only one of many relevant risks. It is awkward to make a computation in a deterministic nonrisky framework while justifying certain parameters by reference to risk. Growth effect. The growth effect refers to the fact that the SWF may assign less priority to future dollars than present dollars, hence a greater SDR, if future generations are richer than the present one.

Indeed, along a growth path, a mitigation policy which transfers resources from the present mitigation costs to the future benefits of a preserved climate looks regressive. In this formula, the growth effect discussed here is captured by the product of the last two terms. The growth rate is the average growth rate of consumption between the present period and the contemplated future period. The Ramsey formula is widely used. It offers a convenient way to understand the basic components of the relative social value of dollars between different time periods.

It also helps in grasping how different authors reason. Adjusting intertemporal inequality for intratemporal inequality.

The Ramsey formula is usually applied in frameworks in which inequalities within generations are ignored and the analysis is done as if there were perfect equality in every generation. For example, while an individual living in a developing country in 50 years is likely to be richer than his compatriots living today, it is questionable to assume, for example, that all future South African people will all be richer than current US people. Knowing that not all future individuals will be wealthier than the present ones might warrant a greater effort in their favor.

To obtain a quantitative estimate of this inequality effect, one can perform the following simple thought experiment with the help of the Ramsey formula. The Ramsey formula applies to a framework in which every generation is perfectly equal in the distribution of consumption. So, let us ask what level of consumption, if equally given to everyone in the present generation, would produce the same social welfare as the current, unequal distribution.

One can do the same for any future generation and compute its EDE level of consumption.

In the Ramsey formula, one can simply replace the average growth rate of consumption per capita, between the two periods, by the average growth rate of their EDE between the two periods. So far, we have assumed that there was only one coefficient of inequality aversion, which embodied an attitude which could be utilitarian, prioritarian, or egalitarian in origin to inequality in consumption across and within generations.

But Schelling famously suggested that distance in time and distance in space might justify different degrees of receding priority. Do people worry more about a poor child alive today in a remote country than about their grand-grand-grand-child, or the opposite? From a philosophical standpoint, it seems hard to make a difference between individuals on the basis of where and when they live, but the debate about global justice and cosmopolitanism has been the occasion to hear voices justifying some bias against aliens in defining social priorities Rawls ; Nagel The existence of local and national bonds and institutions is itself endogenous to human decisions and cannot be taken as a basis for ethical assessment in evaluations where it is itself an object of assessment and possible reform Beitz That being said, there is no formal difficulty in transforming the SWF to incorporate a different degree of inequality aversion within and across generations.

This requires abandoning the simple additive form of utilitarianism discounted or not , computing a separate value of social welfare for each generation, and then computing intergenerational social welfare as an aggregate of these generational social welfare values.

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The generational social-welfare function would have its inequality aversion applied to inequalities within each generation , and the intergenerational aggregator would have a different inequality aversion Dennig ; Anthoff and Emmerling Such a transformation would modify either the intergenerational component of the SDR, or the intragenerational inequality component, depending on which coefficient of inequality aversion is greater. Intratemporal inequality in the costs and benefits of mitigation policy.

So far we have been working under the assumption that adding a ton of CO 2 today will produce climate damages but will have no large impacts on the underlying economy in particular, not on its distribution of income. However, climate damages may affect not only the level of consumption but also the distribution. The empirical relationship between damages from climate change and income is hard to predict. In particular, would climate damages increase or decrease with wealth?

The SDR depends on the correlation between wealth and damages. Because rich countries and individuals have more assets at risk, we might expect wealthy individuals and individuals living in rich countries to be more exposed to climate damages simply because they have more to lose. On the other hand, rich individuals can afford investments in adaptation and in risk-sharing that will reduce the size of the damages they bear. In contrast, because poor individuals have lower resources, their ability to adapt is reduced, which would lead us to expect a negative relationship between damages and income.

If the poor will bear the brunt of climate damages, then climate change is expected to increase the degree of inequality in the future population. As a consequence, introducing a mitigation policy would not only prevent economic and noneconomic losses, but it would also help to reduce the level of inequality. Once again, the magnitude of this effect depends on the degree of intragenerational inequality aversion in the SWF.

Similar considerations apply also to the distribution of costs of climate policy among members of the present generation, because this affects inequality in living standards now. A carbon tax or the elimination of fuel subsidies which are common in poor countries as part of social policy may be regressive if the mitigation policy raises energy costs and makes energy less accessible to the present poor. Redistributing the proceeds of the tax to the population, in cash or in public goods and services, may, in principle, counter this problem and render the policy progressive within the present generation.

Therefore, quite generally, a distribution-sensitive computation of the SDR depends on the distribution of the cost among members of the present generation and the distribution of the benefits among members of the future generations. A policy that makes the rich today pay for the benefit of the future poor may appear to be a progressive transfer if the future poor remain below the level of the current rich. In this case, such a policy would be evaluated with a negative SDR, because the future dollar for the poor has greater social value than the present dollar for the rich. In contrast, a policy that would cost the present poor for the benefit of the future rich would have a large SDR because it would amount to a starkly regressive transfer.

In order to compute the SCC, we need to be able to monetize the physical impacts of a changing climate. Clearly, some damages can be easily turned into monetary terms.


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For example, losses in the agricultural sector can be valued by using the market price of agricultural products. Some categories of damages, instead, are more difficult to evaluate. Think, for instance, of impacts on human health and mortality risk, or the extinction of species: what should be the price of preserving a human or nonhuman life or ecosystem?

In IAMs, nonmarketable goods are monetized and incorporated into the consumption figures. For instance, the value-of-statistical-life is used to value improvements in health and housing prices are relied upon to determine the value of environmental services.

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In other words, an anthropocentric perspective is taken, where goods with no market value matter only if they matter to individuals. Let us illustrate the latter issue with the example of the value of a life.


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It may make sense to give less importance to the life of individuals who genuinely care less about living long, but it seems repugnant to discount the lives of the poor; yet, unfortunately, both determinants are entangled into the WTP. An SWF, fortunately, offers an elegant solution.

It may give a greater priority to the plight of the disadvantaged population through its inequality aversion feature. Usual methods, however, do not involve marginal-social-value-of-money weighting, and therefore fail to appreciate the importance of giving special attention to the worse-off. But this is obviously less than rigorous. One further difficulty for the SCC is to determine the scope of damages induced by a ton of CO 2 emitted. The standard approach, on which we have focused here, is restricted to the climate change effects of the emission.