EQUITY WEIGHTING
In a Climate Policy Context
Alex Dubgaard
Pearce, David (2003): The Social Cost of Carbon and Its Policy Implications, Oxford Review of Economic
Policy, Vol. 19, NO. 3, pp 362-366, 368-377. VII. Equity Weighting, pp 372-376
http://oxrep.oxfordjournals.org.ep.fjernadgang.kb.dk/content/19/3/362.full.pdf+html
Rationale behind equity weighting
Measurement of the social cost of carbon
•
The social cost of carbon refers to
– the monetary value of world-wide damage done by anthropogenic CO2 emissions.
•
Willingness to pay
– Losses are measured through willingness to pay (WTP) to avoid a loss
– Poor people generally have a lower WTP for avoiding the same amount of damage as
richer people
 even if the impact on utility may is the same for both groups.
•
This is due to the fact that
– an extra $ represents a greater marginal utility to a poor person than to a richer person.
•
Basing global warming damage estimates on willingness to pay
–
Implies that $1 of damage to a poor person should attract a higher weight than $1 of
damage to a rich person.
Choice of social welfare function I
•
To apply equity weighting
− A social welfare function (SWF) must be defined
•
Two broad classes of SWF are
– the utilitarian SWF and the ‘Rawlsian’ SWF.
Choice of social welfare function II
•
Applied to global warming damage (Dworld), these are given by
– (7) utilitarian SWF and (8) Rawlsian SWF:
where
− Y = income
− Y⎺ = average world per-capita income
− Yi = income of the ith person
− P = poor people
− D = damage
− ε = elasticity of marginal utility of income schedule, a measure of ‘inequality aversion’*.
* The term “inequality aversion” is used by Pearce – and other authors – in spite of the fact ε is
the elasticity of the marginal utility of income, which in principle at least can be estimated
empirically based on individuals’ utility maximizing behaviour.
Choice of social welfare function III
•
In (7) (the utilitarian SWF)
– damage to all individuals counts
– anyone below the average world per-capita income secures a weight greater
than unity
– anyone above secures a weight below unity
– the size of the weight varying with the degree of inequality aversion (ε).
•
In (8) (the Rawlsian SWF)
– only damage to poor people counts
– all other damage is given a weight of zero
– One paradox in using a Rawls-type welfare function is that global damages are
less than if no weights are used
 In the Rawlsian (maximin) social welfare function only the damage to the poorest region counts
in the global welfare function, whereas the damage in the better off regions is valued at zero.
The utilitarian SWF
•
Generally, SWFs of the utilitarian form (7) have been used
– in illustrating the effects of equity weighting on global warming damage.
•
What matters is
– the distribution of the initial level of damage between rich and poor regions
– the income disparity between rich and poor
– the value of ε.
•
To illustrate how the SWF is estimated, we rewrite (7) as:
where R = rich and P = poor.
Calculating weighted global damage
•
Crude estimates of the relevant magnitudes are then
– DR = $216 billion and DP = $106 billion for 2 × CO2
– YR = $10,000, and YP= $1,110; and Y⎺ = $3,333
•
Substituting in (9) produces estimates of world damage of
unweighted $ 322 billion
weighted, ε = 0.5 $ 307 billion
weighted, ε = 0.8 $ 343 billion
weighted, ε = 1 $ 390 billion
weighted, ε = 1.5 $ 600 billion
– Only if ε > 1 do the aggregate damages increase markedly
– When ε = 1 the effect depends on the distribution of aggregate damage between rich and
poor countries.
Value of the elasticity of marginal utility of income (ε)
•
Different approaches to the estimation of ε:
– savings behaviour implies a value of ε just below or just above one
– implied values of ε taken from UK tax schedules implies a range of 1.2–1.4
– experimental work produces values of around 4.
•
A value of ε such as 4 imply a dramatic degree of inequality aversion.
Thought experiment
Effect of different magnitudes of ε
•
Consider two nations, rich and poor, with utility functions of the form:
– The ratio of the two marginal utilities is given by:
•
Suppose YR = 10YP
– At ε = 1, a marginal unit of income to the poor is valued ten times the marginal gain to
the rich
– At ε = 2, the relative valuation is 100 times
•
On this basis values even of ε = 2 do not seem reasonable
– Values of ε in the range 0.5–1.2 seem reasonable.
Estimates of social cost of carbon depend on
Equity weighting as well as discount rate
•
‘Base case’ estimate of the marginal social cost of carbon is $4–9 tC
– Without equity weighting and using a constant discount rate.
•
Assuming ε =1
– and applying the lowest equity weight to the highest discount rate
– and the highest weights to the lowest discount rate
– equity weighting changes the marginal social-cost estimate to $3.6–22.5 tC.
•
The effect of allowing for time-varying discount rates
– is to raise both sets of estimates by perhaps 80 per cent again.