Memorandum by Dr Chris Hope, Judge Institute
of Management, University of Cambridge
1. My work involves the construction and
use of an integrated assessment model of Climate Change called
PAGE (Policy Analysis of the Greenhouse Effect). The first version
of PAGE was produced in 1991 for the European Commission. It was
updated in 1995 to PAGE95 and most recently in 2002 to PAGE2002.
2. Integrated assessment models incorporate
knowledge from more than one field of study, with the purpose
of informing climate change policy. PAGE is typical in using relatively
simple equations to capture complex scientific and economic phenomena.
This is justified because the results approximate those of the
most complex climate simulations to within a few tenths of a degree,
and because many aspects of climate change are still subject to
3. To express the model results in terms
of a single "best guess" could be dangerously misleading.
Instead, a range of possible outcomes should inform policy. PAGE
builds up probability distributions of results by representing
over 50 key inputs by probability distributions, making the characterisation
of uncertainty the central focus.
4. The outputs of PAGE include estimates
of the impacts of climate change across the regions of the world
and over time, how these impacts change if measures are taken
to cut back the emissions of greenhouse gases, or adapt to changes
in climate, and what the costs of the abatement or adaptation
measures might be. In this note I shall concentrate mainly on
PAGE results for the social cost of carbon (SCC); that is the
extra impacts caused by the emission of one extra tonne of carbon
in the form of carbon dioxide. This is also the benefit of reducing
carbon emissions by one tonne. It is calculated by summing up
the extra impacts for as long as the extra tonne remains in the
atmosphere, and discounting them back to the year of emission.
5. Using scientific and economic inputs
taken mainly from the IPCC's 2001 Third Assessment Report, the
mean PAGE estimate for the SCC is $66 per tonne of carbon emitted
in 2001, in year 2000 dollars, with a 5-95 per cent range of $13-185.
These estimates use the Treasury Green Book assumptions on the
social rate of time preference, and an equity weight parameter
(the negative of the marginal elasticity of utility with respect
to income) of one, which has the effect of giving greater weight
to impacts in poor regions of the world. We see immediately just
how broad the range of plausible estimates is, even with these
fixed assumptions for discount rates and equity weights.
6. The figure below shows how the PAGE estimates
for the SCC vary with the date that the carbon dioxide is emitted.
The values increase by about 2.4 per cent per year; by 2060 the
mean estimate has risen to $265 per tonne of carbon.
7. Allowing discount rates and equity weights
to vary gives slightly different results. With pure time preference
rates in the range of 1 per cent to 3 per cent per year, and an
equity weight parameter in the range of 0.5 to 1.5, the mean PAGE
estimate for the SCC becomes $43 per tonne of carbon emitted in
2001, with a 5-95 per cent range of $7-128. The figures are lower
because the central value for the pure time preference rate, 2
per cent per year, gives a slightly higher discount rate than
the Treasury Green Book, and so the impacts that occur in the
far future have less weight.
8. All of these results assume the extra
tonne of carbon is emitted on top of an unconstrained emission
path, scenario A2 from the IPCC Special Report on Emission Scenarios.
But if climate change is taken seriously, it is unlikely that
emissions will be allowed to follow this unconstrained path, which
would lead to the atmospheric carbon dioxide concentration reaching
over 800 parts per million (ppm) by 2100, and continuing to rise
thereafter, compared to about 275 ppm in pre-industrial times
and 370 ppm in 2000.
9. One constrained emission path that has
been proposed aims to keep the atmospheric carbon dioxide concentration
below 550 ppm, double the pre-industrial level. The mean PAGE
estimate for the SCC superimposed on top of this emission path
is also $43 per tonne of carbon emitted in 2001, with a 5-95 per
cent range of $8-130, essentially identical to the result obtained
for the unconstrained scenario A2. The SCC appears to be insensitive
to the exact emissions scenario, within quite a wide range.
10. The reason why this is true is not straightforward.
It is caused by the interplay between the logarithmic relationship
between radiative forcing and concentration (which will tend to
make one extra tonne under the 550 ppm scenario cause more impacts),
the non-linear relationship of impacts to temperature (which will
tend to make one extra tonne under the A2 scenario cause more
impacts), and discounting (which will tend to make early impacts
more costly than late impacts). The insensitivity of SCC to the
emission path is rather counter-intuitive and is a strong argument
for using an integrated assessment model, as neither a scientific
nor an economic model would pick it up.
11. If the emission path does not affect
the SCC, what does? The chart below shows the major influences
calculated by PAGE; the longer the line, the larger the influence.
That the major influences divide into six scientific and seven
economic parameters is another strong argument for the building
of integrated assessment models such as PAGE. Models that are
exclusively scientific, or exclusively economic, would omit parts
of the climate change problem which still contain profound uncertainties.
12. The two top influences are the climate
sensitivity, which is the temperature rise that would occur for
a doubling of carbon dioxide concentration, and the pure time
preference rate. The climate sensitivity is positively correlated
with the SCC, so a rise leads to a higher SCC; the pure time preference
rate is negatively correlated with the SCC, so a rise leads to
a lower SCC, and so on.
13. As an example of the changes that new
scientific information can bring, the journal Nature has recently
published a new likelihood-weighted probability distribution for
the climate sensitivity, with a mean value of 3.6 degC, and a
5-95 per cent range of 2.4 to 5.4 degC. Using these values for
the climate sensitivity in PAGE, instead of the 1.5 to 5.0 degC
range given by the IPCC, increases the mean value of the SCC from
$43 to $68 per tonne of carbon emitted in 2001, with a 5-95 per
cent range of $11-202.
14. The PAGE model includes a range of greenhouse
gases, not just carbon dioxide, and can calculate the social cost
of each of them. Using the same assumptions as in paragraph 5,
the mean PAGE estimate for the social cost of methane is $280
per tonne emitted in 2001, in year 2000 dollars, with a 5-95 per
cent range of $80-750. In the future, the social cost of methane
increases faster than carbon dioxide, by 3.6 per cent per year.
This is because of the short atmospheric lifetime of methane;
any extra methane emitted today will have disappeared from the
atmosphere before the most severe climate change impacts occur,
but emissions that occur later will not.
15. What are the policy implications of
these results? If the social cost calculations are complete, efforts
to cut back the emissions of greenhouse gases should continue
as long as the marginal cost of the cutbacks is lower than the
social cost of the impacts they cause. If taxes are used, they
should be set at the social cost. If tradable permits are used,
their price should be the same as the social cost; if their price
turns out to be lower than the social cost, the total allocation
of permits is too large and vice versa. In any comparison between
greenhouse gases, the ratio of the social costs is the correct
figure to use.
16. Of course, the outputs from PAGE, and
other integrated assessment models, are only as complete as the
scientific and economic information that goes into the model.
PAGE does make an attempt to cover all five reasons for concern
about climate change identified by the IPCC, including a rudimentary
treatment of large-scale discontinuities such as the melting of
the West Antarctic ice sheet. It does not include the security
implications of any large-scale migration caused by climate change.
The social cost calculations presented here also assume that impacts
in poor countries are given the same weight as impacts in the
UK, or more weight if equity weights are used; this is not necessarily
consistent with our behaviour in other policy areas.
17. My main purpose in this short note has
not been to promote any one estimate of the social cost of greenhouse
gases. As I have shown, the social cost of carbon is influenced
by many factors, which are still subject to great uncertainty,
and the same is true of other greenhouse gases. Rather, I have
tried to demonstrate that integrated assessment models such as
PAGE can perform a useful service by taking the best information
from the detailed scientific and economic research, and revealing
its policy implications. They can also highlight just how much
we still have to learn about the economic implications of climate
change, and enable different views on economic and scientific
parameters, such as discount rates, equity weights and climate
sensitivity, to be rigorously explored.
14 January 2005