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
S3. Equity weighting is based upon the utilitarian
ethic and the concept of diminishing marginal utility of consumptionpoor
people gain greater utility from consumption than rich people.
This is modelled by the parameter , the "elasticity of marginal
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 pointgiven 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
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.
EFFECTS OF INEQUALITY AVERSION WHEN YR=10YP
||0.5 ||0.8 ||1.0
||1.2 ||1.5 ||2.0
|Loss to R as a fraction of gain to P||1.0
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
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.
C. THE CASE
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
15. However, for investments spanning hundreds of years
and several generationssuch as climate change mitigationthere
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
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.
D. APPLYING EQUITY
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
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.
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 www.oft.gov.uk/NR/rdonlyres/
Pearce, D, (2003) "The social cost of carbon and its
policy implications", Oxford Review of Economic Policy
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