Select Committee on Economic Affairs Written Evidence

Memorandum by Dr Cameron Hepburn, St Hugh's College, University of Oxford

  This note reviews the theory on equity weighting and the application to climate change policy, particularly from a UK perspective.


  S1.  The utilitarian ethic places an equal weight on the welfare of every person in every country. It weighs the utility of a Ghanaian (rich or poor) the same as the utility of a UK citizen (rich or poor).

  S2.  No nation-state behaves with such an implicit utilitarian social welfare function. Every nation-state, including the UK, weights the welfare of its own citizens ahead of the welfare of other citizens. Global utilitarianism, whatever its moral appeal, provides a poor description of government decision making.

  S3.  Equity weighting is based upon the utilitarian ethic and the concept of diminishing marginal utility of consumption—poor people gain greater utility from consumption than rich people. This is modelled by the parameter , the "elasticity of marginal utility".

  S4.  Using a measure of the mean e for a country, it is possible to define equity weights to be applied to climate change damages for different countries. Damage to poor countries would be weighed more than damage to rich countries.

  S5.  The value of can be determined using a "descriptive" approach, which looks at evidence from individual behaviour, and uses a mean as the appropriate value for the country.

  S6.  Evidence from individual behaviour in the UK suggests = 1, which is commonly employed in the economic literature. This implies that we should value a marginal pound to poor countries at roughly 10 times more than a marginal pound to the UK.

  S7.  However, a moment's reflection indicates that this is vastly at odds with government practice, where the welfare of UK citizens weighs more (not less!) than citizens of other countries. The current rate of spending on foreign aid illustrates the point—given current rates of foreign aid, a value of e closer to zero, if not negative, would emerge.

  S8.  However, this does not imply that the estimate of is incorrect, but rather that policy making does not correspond with the underlying assumption of global utilitarianism.

  S9.  An intellectually honest approach would be to apply a factor to reduce the weight placed on impacts outside the UK. This would reflect the fact that the UK government places the welfare of UK citizens ahead of the welfare of other citizens. Having applied that factor, conventional equity weighting based upon wealth differences would then occur.


  1.  In a utilitarian framework, each person's utility is equally important. That is, there is no weighting of utilities.

  2.  Still operating with this utilitarian framework, however, it is almost universally accepted that there is diminishing marginal utility of consumption. That is, giving £1 to a rich person produces less utility ("welfare" or "happiness" may substitute as rough equivalents) than giving £1 to a poor person.

  3.  This implies that utility increases with consumption, but at a decreasing rate. A common way to represent this is when utility, u, of consumption, c, is represented by an isoelastic utility function: u(c) = c (1-) /(1-), where denotes the elasticity of marginal utility.

  4.  In this function, the higher , the more rapidly marginal utility falls with additional wealth. In other words, a high implies a strong aversion to inequality, as there is little additional utility gained from additional consumption to people who are already rich.

  5.  The impact of different choices for can be shown by considering two countries, one rich (R) and one poor (P). Suppose country R has an income 10 times that of country P. Then in Table 1, adapted from Pearce (2003), we calculate the value of a marginal pound to R relative to a marginal pound to P. For = 0 (no equity weighting), a pound to R is worth the same as a pound to P. For = 1.0 (commonly employed in the literature), giving 10 pence to P achieves the same utility increase as giving £1 to R: marginal income to P is valued 10 times more highly than to R.

Table 1

E0 0.5  0.8  1.0   1.2  1.5  2.0   4.0
Loss to R as a fraction of gain to P1.0 0.310.160.10 0

  6.  Hence even though a pure utilitarian would not weight utility (see 1 above), a utilitarian would weight consumption flows because of the diminishing marginal utility of consumption. The appropriate "equity weight" for consumption going to country R is (YN/YR) , where YN is a "numeraire" (benchmark) income level. The equity weight for consumption going to P is equivalently (YN/YP) .

  7.  This benchmark level is important. In the literature, an average world income benchmark is often used. This is appropriate provided that the equity weighted damages are then also compared to abatement costs which are equity weighted to the same benchmark.

  8.  For instance, it would be incorrect to compare climate change damages which have been equity weighted to a world income benchmark with unweighted marginal abatement costs in the UK. For UK policy, it is arguable that the benchmark level of income should be UK national income.


  9. Evidence on the "correct" value of could be sourced from a variety of places: (a) lab experiments on individual behaviour; and (b) revealed preferences of individuals. One might also infer a value of by examining (c) revealed social preferences by government spending on programs designed to reduce inequality in the UK; (d) UK government spending on programs designed to assist other countries.

  10.  Evidence from individual behaviour in categories (a) and (b) above, collected in Cowell and Gardiner (1999), suggests values between 0.5 and 4 are plausible. A value of = 1 is commonly used.

  11.  For social programs in category (c), Pearce (2003) argues that values above = 2 are unreasonable. This is persuasive, as based upon the results in Table 1 above, a value of = 2 implies that £1 to someone earning £100,000 a year is valued 100 times less than £1 to someone on £10,000 a year. Pearce (2003) concludes that values between 0.5 and 1.2 seem reasonable.

  12.  For foreign aid in category (d), cursory inspection indicates that = 1 seems very high indeed. The UK government is a sovereign state which places the welfare of its citizens well above the welfare of foreign nationals. Even a value of = 0.5 seems extremely high in this context. Given that the UK is richer than developing nations, any positive value of implies the UK government values benefits to developing nations above benefits to UK citizens. As this seems unlikely, one might infer an equity weight of zero, or possibly even a negative number, seems to apply in foreign aid contexts.

  13.  However, the very low estimates of arising from evidence in (d) most likely arise from the fact that the UK government does not employ a global utilitarian framework: it does not weight the welfare of non-UK citizens as highly as UK citizens. It would be more descriptively accurate to retain the values of = 1 from individual evidence, and drop the assumption of global utilitarianism, which evidently no government follows.


  14.  For small projects spanning relatively short periods, cost benefit analysis need not consider distributional effects because the taxation system can be employed to achieve equity. In such circumstances, there is no compelling reason to employ equity weights.

  15.  However, for investments spanning hundreds of years and several generations—such as climate change mitigation—there are three considerations that suggest this conventional logic does not hold, and that equity weights ought to be applied.

  16.  First, investment in climate change mitigation is not "small", and the corresponding distributional effects are potentially large enough that is not possible, in practice, to correct them using the taxation system.

  17.  Second, climate change mitigation provides an international public good with distributional effects that cross borders. Given the absence of an international tax system, equity considerations may be legitimately incorporated into investments that are directed at the global good.

  18.  Third, climate change mitigation has distributional effects across generations. As such policy instruments that redistribute wealth between generations are required to correct for these effects. Some economists question whether such instruments would be effective, because they rely upon the goodwill of intervening generations to implement plans which they may not have an incentive to implement. Even if they effective intergenerational instruments do exist, it might be argued that climate change policy is no more costly (in the sense of deadweight losses) than other possible intergenerational transfer mechanisms.

  19.  These three considerations— that climate change is non-marginal, international, and intergenerational— provide grounds for arguing that equity weighting ought to be employed in the assessment of climate change investments.


  20.  Given that climate change policy is largely concerned with preventing damages to other nations (damages to the UK are a very small proportion of total damages), an analytical structure that generates policy consistent with foreign aid behaviour seems appropriate.

  21.  As such, an appropriate framework would apply a factor to reduce the weight placed upon impacts outside the UK, after which conventional equity weighting would be employed. The notion of placing a greater weight on those who are close to us (by citizenship or otherwise), while not utilitarian, is hardly new to ethics. [30]

  22.  The appropriate factor to reduce the weight on impacts outside the UK is a decision that must be made at the political level. Political and diplomatic considerations might, however, necessitate that the factors used to weigh impacts in different countries are not transparent.

  23. Some commentators argue that climate change poses particular ethical problems because it involves both challenges of free-riding and past responsibility on the part of industrialised nations. If this argument is accepted (at a political level), then a higher factor should be used to weight impacts in other countries, justifying a degree of divergence with UK foreign aid programmes.

28 February 2005


  Augustine (329), De Doctrina Christiana, 1.28.29. Trans. RPH Green (Clarendon: Oxford, 1995)

  Cowell, F, and Gardiner, K. (1999), Welfare Weights, Report to the UK Office of Fair Trading, available at

  Pearce, D, (2003) "The social cost of carbon and its policy implications", Oxford Review of Economic Policy 19(3): 362-384.

30   See, eg, Augustine (329): "All people should be loved equally, But you cannot do good to all people equally, so you should take thought for those who by the chance of place or time or anything else are, as if by lot, in particularly close contact with you." Back

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