The political economy of global carbon emissions reductions

1. ANALYSIS
The political economy of global carbon emissions reductions
Stephen J. DeCanio
UCSB Washington Program, 1608 Rhode Island Avenue, NW, Washington, DC 20036, United States
A R T I C L E D A T A A B S T R A C T
Article history:
Received 11 September 2008
Received in revised form
7 October 2008
Accepted 13 October 2008
Available online 21 November 2008
The discussion about what reductions in greenhouse gas emissions are required and how
the emissions rights might be distributed globally has fostered the belief that there is a
fundamental conflict between the rich nations of the “North” and the poor but populous
nations of the “South.” The argument is that grandfathering the rights will only reinforce
existing global inequalities, while per capita distribution of the rights would lead to such
huge transfers of wealth to the South as to be unacceptable to the North. However, a very
simple general equilibrium model highlighting key elements of the global economy shows
that this perception is incorrect under a plausible interpretation of the goal of the United
Nations Framework Convention on Climate Change to “avoid dangerous anthropogenic
interference with the climate system.” Instead of using an economic damage function to
determine the optimal level of emissions reductions, the model's utility functions are
calibrated to reflect scientific understanding of what would be required to stabilize the
atmosphere at safe concentrations of greenhouse gases. Among policy options that would
accomplish this, the United States has a preference for grandfathering the allocation of
emissions rights over a per capita allocation, but this preference is not strong and could be
offset by other geopolitical considerations.
© 2008 Elsevier B.V. All rights reserved.
Keywords:
Climate change
Global environmental policy
Allocation of emissions rights
Distribution
Fossil fuels
International negotiations
Political economy
1. Background
The debate on how to avert dangerous anthropogenic climate
change has mainly been centered on two themes: (a) what is
the economically optimal reduction in emissions, based on
comparison of the costs and benefits of mitigating climate
change, and (b) how can the cost of the emissions reductions
be distributed to facilitate achievement of a global regulatory
agreement. This approach has failed so far to produce a clear
path forward. The cost-benefit calculations have not been
conclusive, and suffer from very large uncertainties on both
the cost and benefit sides. In the United States the alleged
“cost to the economy” has proven to be a serious barrier to
action. At the same time, no formula has been worked out for
how to distribute across nations the obligations that surely
must accompany significant climate action.
The Kyoto Protocol reflects these tensions. Acknowledging
“common but differentiated responsibilities” of countries at
various states of economic development, Kyoto established a
regulatory regime that called for modest first-step reductions
by the Annex I nations (roughly speaking, the rich countries)
but no binding reduction schedule by the rest of the world
(UNFCCC, 1998). In addition, Kyoto fell very short of the large-
scale global emissions reductions that will be necessary to
stabilize the atmosphere, and left to further rounds of
negotiations (which are now taking place) how to strengthen
E C O L O G I C A L E C O N O M I C S 6 8 ( 2 0 0 9 ) 9 1 5 – 9 2 4
E-mail address: decanio@econ.ucsb.edu.
URL: http://www.stephendecanio.com.
0921-8009/$ – see front matter © 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.ecolecon.2008.10.003
available at www.sciencedirect.com
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2. the target as well as bring about the participation of the
developing countries.1
Measures such as the Clean Develop-
ment Mechanism (CDM) to enable some rich-country emis-
sions reductions to be bought by financing projects in
developing countries have been adopted under Kyoto, but
the success of the CDM in reducing global emissions and in
transferring new technologies to the developing countries has
been modest at best, and the CDM has spawned scandalous
examples of gaming the system (Wara, 2006, 2007).
It is an unexamined presumption, not a known fact, that
economics can determine the proper level of regulatory
stringency for greenhouse gas emissions. Standard integrated
assessment models (IAMs) calculate “optimal” emissions
reductions by attaching an economic damage function to a
physical climate model. But the damage function is not
something that can be known to any degree of precision.
First of all, any economic analysis comes up against the reality
that climate policy's costs and benefits will fall unevenly on
different generations, so no policy prescription can avoid
some kind of treatment (even if it is implicit) of the issue of
intergenerational equity. Even if this problem is subsumed in
the conventional expected discounted utility approach, Weitz-
man (2007, 2008) has shown that very deep analytical
problems arise because of irresolvable uncertainty about
potentially catastrophic and irreversible planetary changes
associated with warming.2
Second, the problem of distributing the burdens of action
across nations is one of equity and politics, raising issues that
reach beyond economics. Economically efficient emissions
reductions are bound to involve creation of new property
rights (or the disposition of new tax revenues), but economics
alone cannot specify how these rights or tax revenues should
be assigned. Many different Pareto-optimal outcomes (with
different wealth and income distributions for each) are
possible depending on how the emissions rights are
allocated.3
The distributional variations can matter more for
politics than the pure economic efficiency of the outcome.
These considerations suggest the need for an alternative
approach. Instead of trying to squeeze optimal policy prescrip-
tions out of IAMs, economics can be usefully employed in a
different way. Scientific insights about what might constitute
“dangerous anthropogenic interference in the climate system”
can be used to calibrate the utility functions in an economic
model so that the optimal solution corresponds to the scientific
guidelines. Then alternative ways of handling the burden-
sharing can be compared to see which approach or approaches
would be preferred, and by whom. In this way, the science
becomes the foundation of policy-making and economics offers
insight into how the political problems might be solved.
Science alone, of course, cannot define “dangerous anthro-
pogenic interference.” The meaning of “dangerous” ultimately
must be decided by society (Pachauri, 2006). Science can
indicate the consequences of alternative emissions pathways
for atmospheric concentrations of greenhouse gases, how-
ever, and the “safe” target is most conveniently expressed in
terms of atmospheric concentrations of GHGs or temperature
increases relative to pre-industrial levels. So, for example, the
European Council in 1996 adopted as a climate target that
'global average temperatures should not exceed 2° above the
pre-industrial level' and reaffirmed this target on subsequent
occasions (Meinshausen, 2006, citing EU Presidency Council
conclusions 2005; see also European Environment Agency,
2008). A number of states, including California, Minnesota,
Massachusetts, and Florida, have announced long-term tar-
gets of reducing emissions by approximately 80% from recent
levels (Pew Center on Global Climate Change, 2008).
Well before Kyoto, Wigley, Richels, and Edmonds (1996)
estimated that to achieve atmospheric stabilization of CO2
concentrations between 350 and 450 ppm, emissions would
have to be reduced to roughly 15–30% of their 2000 levels.4
Baer,
Athanasiou, and Kartha refer to “the recommendations of the
Scientific Expert Group (2007) or the Stern Review (2006), both of
which put 450 ppm CO2-equivalent as their lowest recom-
mended stabilization target. Yet both acknowledge (following
for example Meinshausen, 2006) that 450 ppm CO2-equivalent
has at best even odds of keeping below 2 °C warming, and
something like a 20% likelihood of exceeding 3 °C warming. And
as James Hansen and colleagues (2006, 2007) among others have
warned, thedestabilization of theGreenlandIce Sheetispossible
even before global mean warming reaches the 2 °C level,
potentially causing up to seven meters of sea level rise, over
centuries or, perhaps, much more quickly” (2007, fn. 1, p. 90).
Destabilization of the Greenland ice sheet is only one possible
nightmare scenario — others include warming-induced release
of methane from the tundra or offshoreclathrates(Halland Behl,
2006) and interruption of the ocean circulation patterns that
makes the climate of the lands adjacent to the North Atlantic
temperate (Marotzke, 2000; Lenton et al., 2008). Reducing the risk
of these potential planetary catastrophes is the overriding
reason to keep atmospheric concentrations of GHGs within
safe bounds. Hence, in the modeling that follows the utility
functions will be calibrated so that reduction of emissions to
approximately 20% of current global levels is optimal from a
welfare standpoint.
This leaves the question of how to distribute the cuts and
their costs. A number of proposals have been put forward to
allocate emissions reductions globally on an equitable basis.
Thus, Baer, Athanasiou, and Kartha (2007) recommended
assigning the reductions based on a combination of historical
responsibility and ability to pay. Uzawa (2003) notes that an
1
The actual success of the EU in meeting even the very modest
Kyoto target is doubtful. See EurActiv (2007); Dombrovskis (2008).
2
According to Weitzman, “[f]rom inductive experience alone,
one cannot acquire sufficiently accurate information about the
probabilities of extreme tail disasters to prevent the expected
marginal utility of an extra unit of consumption from becoming
infinite for any utility function with relative risk aversion every-
where bounded above zero” (2008, pp. 3-4; see also Weitzman,
2007). Cline in (1992) showed how even a small probability of
future climate catastrophe could tilt a conventional cost-benefit
analysis strongly in the direction of immediate action to reduce
emissions (pp. 302-305).
3
This is a consequence of the Second Fundamental Theorem of
Welfare Economics, stating that “we can achieve any desired
Pareto-optimal allocation as a market-based equilibrium using an
appropriate lump-sum wealth distribution scheme” (Mas-Colell et
al., 1995, p. 551).
4
The pre-industrial concentration of CO2 was 278 ppm (Mein-
shausen, 2006, p. 266).
916 E C O L O G I C A L E C O N O M I C S 6 8 ( 2 0 0 9 ) 9 1 5 – 9 2 4

3. allocation of carbon emissions permits using Lindahl pricing5
would have the permits distributed across countries in propor-
tion to the national incomes. This would reinforce existing
global inequalities, so he recommends an International Fund for
Atmospheric Stabilization that would redistribute a fraction of
the revenues collected by the individual countries' carbon taxes
to developing countries, to offset both the hardship caused by
globalwarmingand the carbon tax and to “restructureindustrial
organizations and social infrastructure, and to introduce
alternative energy sources and energy-saving technologies”
(2003, p. 258). Chichilnisky and Heal (1994) and Sheeran (2006)
have shown that when atmospheric protection is treated
appropriately as a public good, Pareto optimality does not
require equalization of marginal abatement costs across
countries. Rather, efficiency requires either that rich countries
(with lower marginal utility of consumption than poor coun-
tries) abate more, or that wealth transfers be carried out to
equalize the marginal utility of consumption.
While these proposals deserve serious consideration in the
debate over how to achieve equity, it is not clear that pure equity
arguments are going to be sufficient to induce concerted global
action. Altruism is not a notable feature of international
relations. The main instance of global cooperation to solve a
planetary environmental problem, the Montreal Protocol on
Substances that Deplete the Ozone Layer, was one in which the
costs of solving the problem were quite modest on an absolute
scale (and extremely small relative to the global benefit of
preserving the ozone layer). Furthermore, the effects of ozone
depletion included a direct and tangible threat to the well-being
of the inhabitants of the rich countries – the projected increase
in fatal and nonfatal skin cancers – that was relatively easy to
quantify (DeCanio, 2003). It can be argued that it was cost-
beneficial for the United States to act unilaterally to eliminate
the ozone-depleting substances (Sunstein, 2007), and there is no
doubt that the main producers of the ODSs were industries
located in the rich countries themselves.
The climate problem is different, not least because current
and projected future GHG emissions originate in comparable
amounts from both the developed and developing countries.
Furthermore, it turned out (after the fact; this was not so obvious
before the fact) that technologies to replace the ODSs could be
diffused to the developing countries at not too great a cost and
without adversely affecting the development prospects of those
countries (Norman et al., 2008). The United States exercised
strong diplomatic leadership in negotiating and implementing
the Montreal Protocol (Benedick, 1998). Reaching an encompass-
ing international agreement to largely replace fossil-fuel energy
with alternatives has proven to be a much more difficult task.
2. Model
It is necessary to state briefly at the outset that the modeling
strategy employed in this paper is “conceptual” rather than
“descriptive” (see DeCanio, 2005 for a discussion of the
distinction). Rather than to try to simulate the global economy
as closely as possible by piling on detail regarding multiple
goods, technologies, preferences, and so forth, the approach
will be to encompass key features of the system in the
simplest possible way. There are many reasons the “descrip-
tive” approach is not desirable for analyzing the economics of
climate change, not least of which is that it makes the drivers
of the results non-transparent. Conceptual modeling, on the
other hand, highlights the essential elements – calibration of
the utility functions according to the science, the role played
by the location of fossil fuel reserves, and whether the
emissions rights are “grandfathered” (that is, distributed in
proportion to existing patterns of asset ownership or emis-
sions) or are allocated on a per capita basis. The mathematical
apparatus is minimized. The most significant departure from
descriptiveness here is the deliberate omission of any treat-
ment of technological change or advances in energy efficiency
that could, by expanding the production-possibilities frontier
or moving producers and consumers closer to the theoretical
frontier, lower the cost of the required emissions reductions
(Ackerman et al., 2008; Laitner et al., 2000; IPCC, 1996,
particularly Chapter 8).
The utility functions of the agents – nations or regions – are
specified as follows:
Ui =
x1u
i 1
1 u
k hGg
ð Þ: ð1Þ
Here xi is nation/region i's consumption of the single
produced consumption good, and G is a measure of global
environmental degradation — indicated by total emissions of
greenhouse gases. All nations have utility functions of the same
form.6
The parameters are chosen so as to make a reduction of
emissionsto ∼20% of current levelsoptimal(seebelow). This isa
standard type of utility function: it exhibits diminishing
marginal utility of consumption with coefficient of relative
risk aversion φ, multiplied by a factor that is polynomial in the
environmental damage G.
The environmental damage constitutes a global external-
ity. The individual countries/regions make their consumption
and production decisions without regard for the effects of
those decisions on G. Specifying that G enters the utility
function directly embodies all the ways greenhouse gas
emissions and concentrations in the atmosphere impinge on
human well-being, including the negative effects of risk and
uncertainty on utility, conformance with the precautionary
principle, and acknowledgment of a duty to protect future
generations.7
The model does not attempt to calculate from
5
Under Lindahl pricing, the amount of a public good (such as
climate protection) actually provided is equal to the amount that
each member of society wishes to have, subject to the individuals’
budget constraints. See the detailed discussion in Uzawa (2003)
and the literature he cites beginning with Lindahl (1919).
6
It would be a simple matter to allow the parameters φ, k, θ,
and γ to vary by country. It is not easy to say exactly how these
parameters might vary across country, although it is likely that
the poorer countries/regions will be more adversely affected by
future climate change as they have been by ecological impacts
from human activities in the past (Srinivasan et al., 2008). The
simplest modeling approach is to assume the utility functions are
identical.
7
A somewhat more complicated utility function incorporating a
public good directly is employed by Brekke et al. (2003) in a model
that also allows agents to regard themselves as socially respon-
sible individuals.
917
E C O L O G I C A L E C O N O M I C S 6 8 ( 2 0 0 9 ) 9 1 5 – 9 2 4

4. first principles the consequences of risk and uncertainty as in,
for example, Weitzman (2007, 2008), Chichilnisky (2000), or
Woodward and Bishop (1997), and it does not attempt to
enumerate all the ways climate change can affect human
health, agricultural productivity, extreme weather events, etc.
Having G enter the utility function directly is tantamount to
assuming that all such effects can be summarized by the
functional dependence of total utility on G, in the style of
“conceptual” modeling. This allows the distributional con-
sequences of alternative schemes for allocation of the
emissions rights to be straightforwardly calculated under the
standard economic assumptions of utility and profit
maximization.
Countries/regions maximize utility subject to their budget
constraints:
pxi = wiRi + sei ð2Þ
where p is the price of the consumption good, wi is the return
to the “productive resources” of the country/region i (these
consist of labor, human capital, tangible capital, land, and
other non-traded resources), Ri is the endowment of “produc-
tive resources” of the country/region, and s is the price of fossil
fuels/CO2 emissions. Fossil fuels and CO2 emissions are
assumed to be interchangeable because the units of the fossil
fuels can be converted into CO2 equivalents according to
standard formulas as described in Table 1 below. The εi are the
endowments of fossil fuels/CO2 emissions of each country/
region.
Production is also represented as simply as possible. Each
country produces the consumption good according to a
constant returns Cobb-Douglas production function using
“productive resources” and CO2 emissions as inputs. The
productive resources are not traded, so the only first-order
condition for profit maximization in each country is
p
Afi Li; Ji
ð Þ
AJi
= s ð3Þ
where fi is country/region i's production function, Li is the
amount of productive resources employed by the country/
region in production, and Ji is the amount of the fossil fuel/CO2
emissions input employed by the country/region in produc-
tion. There is no need to solve the model for the wi, because in
equilibrium (which will determine p, the xi, s, and the Ji), the
value of Li will be set equal to the (untraded) level of productive
resources Ri available to each country/region. In conjunction
with Eq. (3) and the assumption of constant returns in
Table 1 – Basic data
Region Pop
(millions)
GDP
(PPP $)
Per capita GDP
(PPP $)
Coal CO2
reserves (MMT)
Oil and gas CO2
reserves (MMT)
Total CO2
reserves (MMT)
2005 CO2
emissions (MMT)
USA 297 12,376 41,670 458,759 19,767 478,526 5957
EU 492 13,019 26,461 71,817 7565 79,383 4276
Japan 128 3870 30,234 789 58 846 1230
China 1,304 5333 4090 221,673 10,648 232,320 5323
India 1,101 2341 2126 201,657 4281 205,938 1166
Eurostat 321 5507 17,156 174,223 88,321 262,543 2474
SA 366 3078 8410 36,743 55,812 92,555 861
CIS 247 2269 9186 416,420 139,474 555,894 2369
Africa 826 1832 2218 110,343 39,313 149,656 896
Middle East 174 1735 9971 920 382,611 383,532 1248
Asia/Pacific 843 2761 3275 16,404 17,745 34,149 1236
Totals 6,099 54,121 1,709,748 765,595 2,475,342 27,036
Notes to Table 1:
Population and GDP (measured by Purchasing Power Parity dollars) are from World Bank (2008). MMT is millions of metric tonnes.
Coal reserves are from Energy Information Administration (2007a), with coal converted to CO2 equivalent according to the formulas:
1 short ton coal = (4391.73 lb CO2/short ton) × (0.4536 lb/kg) for anthracite and bituminous coal, and
1 short ton coal = (3253.75 lb CO2/short ton) × 0.4536 lb/kg) for sub-bituminous and lignite coal.
The conversion factors for coal to pounds of CO2 are the average of the values for anthracite and bituminous coal and the average for sub-bituminous
and lignite coal given by The Climate Trust (2008).
Oil and natural gas reserves are from Energy Information Administration (2008a), with oil converted to CO2 equivalent according to the formula:
1 billion bbls. oil = 1000 million bbls./billion bbls. × 0.137 tonnes/bbl. × 0.918
× 0.85 tonnes Carbon/tonnes Oil × (44/12) tonnes CO2/tonnes Carbon
where 0.137 tonnes/bbl. is from EPPO (2008), 0.918 (the effective fraction oxidized) and 0.85 (tonnes Carbon/tonnes Oil) are from CDIAC (2008, citing
Marland and Rotty, 1983), and (44/12) converts tonnes Carbon to tonnes CO2 by the atomic weights of oxygen and carbon.
Natural Gas is converted to CO2 equivalent according to:
1 trillion ft3
Natural Gas = 120.593 × 109
lb CO2/1000 ft3
gas × 0.4536 kg/lb.
where the 120.593 conversion factor is from The Climate Trust (2008).
CO2 emissions for 2005 are from Energy Information Administration (2007b).
918 E C O L O G I C A L E C O N O M I C S 6 8 ( 2 0 0 9 ) 9 1 5 – 9 2 4

5. Table 2 – National consumption, utilities, and utility ranks, alternative allocations of emissions rights
(1) Status quo,
allocations ∝ C02
reserves: oil, gas, coal
(2) Status quo,
allocations ∝ C02
reserves: oil and gas
(3) Status quo,
allocations
∝ CO2 emissions
(4) Status quo,
allocations
∝ Population
(5) Negishi
SWF, weights
from (1)
(6) Negishi
SWF, weights
from (2)
(7) Negishi
SWF, weights
from (3)
(8) Per capita
allocation,
G from (5)
(9) Per capita
allocation,
G from (6)
(10) Per capita
allocation,
G from (7)
Consumption (billions of $ annually)
Global GDP 54,121 54,121 54,121 54,121 47,730 47,807 47,651 47,730 47,807 47,651
USA 12,223 11,498 12,340 11,597 10,780 10,156 10,865 10,227 10,244 10,211
EU 12,116 12,020 12,662 12,327 10,686 10,618 11,149 10,871 10,889 10,853
Japan 3562 3561 3757 3,651 3141 3145 3308 3220 3225 3215
China 5313 4967 5759 5832 4685 4387 5070 5143 5152 5135
India 2514 2178 2340 2935 2217 1924 2061 2589 2593 2584
Eurostat 5526 5566 5463 5294 4873 4917 4810 4669 4677 4661
SA 2994 3147 2970 3092 2640 2780 2615 2726 2731 2722
CIS 3060 2876 2467 2263 2698 2541 2172 1996 1999 1992
Africa 1947 1908 1829 2272 1717 1685 1610 2004 2007 2000
Middle East 2267 3760 1796 1720 1999 3321 1581 1517 1519 1514
Asia/Pacific 2600 2640 2738 3139 2293 2332 2411 2768 2772 2763
CO2 price 0.665 0.665 0.665 0.665 2.823 2.771 2.877 2.823 2.771 2.877
Global CO2 10 10 10 10 2.079 2.121 2.036 2.079 2.121 2.036
Utilities (with Utility Ranks in boldface)
USA 85.209 84.907 85.254 84.950 93.558 93.172 93.621 93.233 93.227 93.239
8 10 7 9 2 6 1 4 5 3
EU 85.167 85.128 85.375 85.249 93.505 93.450 93.773 93.608 93.601 93.615
9 10 7 8 5 6 1 3 4 2
Japan 73.559 73.554 74.414 73.962 78.943 78.956 79.998 79.448 79.467 79.429
9 10 7 8 6 5 1 3 2 4
China 78.977 78.209 79.831 79.959 85.740 84.785 86.806 86.972 86.977 86.966
9 10 8 7 5 6 4 2 1 3
India 66.705 63.112 64.979 70.050 70.346 65.881 68.140 74.541 74.568 74.513
7 10 9 5 4 8 6 2 1 3
Eurostat 79.402 79.479 79.280 78.939 86.273 86.375 86.113 85.692 85.699 85.684
8 7 9 10 2 1 3 5 4 6
SA 70.438 71.394 70.280 71.058 75.029 76.252 74.803 75.806 75.831 75.780
9 7 10 8 5 1 6 3 2 4
CIS 70.861 69.640 66.261 64.120 75.559 74.055 69.752 67.103 67.144 67.062
3 5 9 10 1 2 4 7 6 8
Africa 59.926 59.304 57.981 64.223 61.841 61.113 59.346 67.232 67.272 67.190
7 9 10 4 5 6 8 2 1 3
Middle East 64.169 74.425 57.395 55.947 67.164 80.047 58.609 56.851 56.910 56.790
4 2 6 10 3 1 5 8 7 9
Asia/Pacific 67.475 67.822 68.612 71.342 71.312 71.779 72.707 76.162 76.186 76.137
10 9 8 6 7 5 4 2 1 3
Reverse Borda count 88 99 93 74 51 59 50 31 23 39
919
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6
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(
2
0
0
9
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5
–
9
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6. production, this is sufficient to compute the quantity wiRi for
each country/region.
The 11 regions are: USA, EU (27 countries), Japan, China,
India, OECD-Eurostat (excluding the US, EU, Russia, and Japan —
hereafter Eurostat)8
, South America, CIS, Africa, Middle East
(including Iran), and Asia/Pacific (excluding Australia, China,
India, Iran, Japan, and New Zealand). The regional groupings are
based on the World Bank's classification (2008). The “productive
resources” are endowed to the countries/regions in proportion
to their GDPs.
The parameters of the model are set as follows: The
coefficient of relative risk aversion φ is taken at its “conven-
tional” value of 2; the scaling factors k, θ, and γ for the effect of
climate on utility are 100, 0.1, and 2, respectively; and the
elasticity of output with respect to productive resources in the
production functions is 0.92 (implying that the elasticity of
output with respect to the fossil fuel/CO2 emissions input is
0.08 — roughly the share of energy in GDP). The units of
productive resources are set so that the global total is 100, and
of global emissions so that in the original unregulated market
case G=10. Note that we are free to set these units arbitrarily.
The base values of national income, population, and CO2
endowments for the 11 country/regions are given in Table 1.
The model has 45 unknowns (the 11 xi, 11 Ji, 11 Li, 11 Lagrange
multipliers λi, and the emissions price s) and 45 equations (11
first-order conditions for utility maximization, 11 budget
constraints, 11 first-order conditions for profit maximization,
11 equations setting the productive resources in each nation's
production function equal to its national endowment, and one
equation for the total environmental resource constraint). The
consumption good is the numeraire and its price is set to unity.
With the price of the numeraire equal to one, a price-level
conversion is required to express output and consumption in
numbers comparable to current dollar GDP, and this conversion
is made in reporting the results in Table 2. The system is easily
solved numerically using FindRoot in Mathematica (Wolfram,
2008). There do not appear to be wealth effects strong enough to
produce multiple equilibria.
The model embodies a “realist” perspective of international
relations, in which each nation or region is a rational actor
pursuing its own interests.9
The orientation is most plausible for
the individually named countries (and perhaps for the EU); the
aggregate regionsareincluded to complete the model and to give
some indication of where their collective interests lie. Obviously,
the CIS is dominated by Russia. The model could be extended to
have the agents be the individual countries, but it is not clear
that this extra detail would add much explanatory value.
It is important to realize that realism does not preclude
cooperation among states, particularly if cooperation is the
most effective way to achieve national objectives. The utility
functions as specified imply that a reduction in greenhouse
gas emissions sufficient to stabilize the atmosphere at the
“safe” level of an approximately 80% reduction from current
emissions is in the interest of almost all countries. The crux of
the problem is how to allocate the emissions rights. The
political problem therefore can be thought of as having two
distinct components. The first is arriving at the decision to
“prevent dangerous anthropogenic interference with the
climate system.”10
The second is how to distribute the costs
of meeting that target. In the conceptual model employed
here, the first decision is embodied in the specification of the
individual country/region utility functions. It is the political
economy of the second decision that is at issue.
3. Results
The first step is to estimate status quo market solutions under
alternative specifications of how the carbon emissions rights are
presently distributed. Three ways of expressing current fossil fuel
ownership or use in terms CO2 emissions rights were used: (1)
converting total fossil fuel reserves (oil, gas, and coal) to their CO2
equivalents; (2) converting oil and gas reserves to their CO2
equivalents (and treating coal as a non-traded resource); and (3)
assigning the rights according to current CO2 emissions. A fourth
market “status quo” in which the fossil fuel rights are assigned on
a per capita basis was estimated also for comparison purposes.
Then, for each of the first three cases, the optimal level of global
CO2 emissions was calculated by maximizing the Negishi-
weighted social welfare function (SWF), with the weights
determined from the corresponding market equilibria.11
The
Negishi weights are just the inverses of the Lagrange multipliers
from the first-order conditions of the individual country/region
constrained utility maximizations. The λi can be interpreted as
the marginal values of a unit of income in countryi. Maximization
in this model of a Negishi global social welfare function
N =
X
i
1
ki
Ui ð4Þ
is equivalent to a market solution in which the CO2 allocations are
proportional to the countries' unregulated CO2 endowments, but
8
The countries making up this grouping are: Albania, Australia,
Bosnia and Herzegovina, Canada, Croatia, Iceland, Israel, Korea
Rep., Macedonia FYR, Mexico, Montenegro, New Zealand, Norway,
Serbia, Switzerland, and Turkey.
9
A standard treatment of the realist tradition in the study of
international relations is Donnelly (2000). Of course, different
realist political theorists place different emphases on the pursuit
of power, economic gain, etc., in motivating the actions of states.
10
The UNFCCC (1992) entered into force on 21 March 1994. It had
received 192 instruments of ratification, as of August 2007 (UNFCCC,
2007). There is international consensus on this goal, at least in
principle.
11
Use of the Negishi form of the social welfare function is a common
practice in integrated assessment modeling. Aside from its mathe-
matical convenience, it has been justified as being necessary to
prevent the models’ implying larger-than-observed trade flows
between countries at different levels of development in equilibrium
(Nordhaus and Yang, 1996, 2006; Negishi’s original paper was (1960)).
While this is a desirable property, it should not be overlooked that
using the Negishi weights to construct a global social welfare function
weights the welfare of different countries in inverse proportion to
their marginal utilities of income. There is no ethical basis for such a
weighting; it may reflect the purchasing power of countries as they are
today, but that is all. The Negishi SWF is used in this paper so that the
utility functions can be calibrated to imply that an ∼80% emissions
reduction is optimal. It might be noted that in calculations not
reported in detail here, an egalitarian SWF (with each country/region
weighted equally), does indeed show much larger-than-observed
trade flows, and an optimal emissions level is somewhat higher
(∼26% of current levels) than is estimated with Negishi weights.
920 E C O L O G I C A L E C O N O M I C S 6 8 ( 2 0 0 9 ) 9 1 5 – 9 2 4

7. total emissions are determined by the outcome of the maximiza-
tionoftheSWFwithNegishi weights.Thatis,maximizationofthe
Negishi social welfare function is equivalent to a market solution
in which the CO2 rights are grandfathered in proportion to the
initial unregulated property rights (i.e., according to total fossil
fuel reserves, oil and gas reserves, or CO2 emissions).
Finally, three additional equilibria were computed. In these
equilibria, the total global emissions were set at the optimum
levels found from maximization of the Negishi SWFs, but the
rights were allocated on a per capita basis. Thus, comparison
of the three Negishi solutions to the three per capita allocation
solutions amounts to a comparison of the three ways of
grandfathering the emissions rights to the corresponding per
capita allocations of the rights with the same total global
emissions. The results of the ten equilibrium calculations are
shown in Table 2. The first half of Table 2 shows the values of
global GDP, national consumption, the CO2 price, and global
CO2 emissions (measured so that the original unregulated
total is 10 units). The second half of Table 2 shows the
calculated equilibrium utility values for each country/region
and, more importantly, the utility rank for the country/region
for each specification. It is the utility rank matters rather than
the absolute utility value, because of the elementary fact that
all the market observables (national consumption, CO2 inputs
in production, and the CO2 price) are invariant under mono-
tonic transformations of the individual utility functions.
First it should be noted that the status quo equilibria are
least preferred by most countries/regions — the utility
rankings of these equilibria are 7,8,9, and 10 for the USA, the
EU, Japan, China, Eurostat, South America, and Asia/Pacific
(except that Asia/Pacific ranks the per capita allocation of the
status quo emissions 6th). The significant exceptions are the
poor but populous regions (India and Africa) and the regions
other than the USA that are richest in fossil reserves (the CIS
and Middle East). The two poorest regions stand to gain
considerably by per capita allocation of the rights under any
scenario, and the two regions other than the USA that are
richest in fossil fuel reserves stand to lose the most by
reduction in the quantity of their resources that can be sold.
The general low preference for status quo emissions is a
reflection of the way the utility functions are calibrated,
specifically, so that maximization of the Negishi SWFs yields
global emissions that are approximately 20% of the original
total.12
Given that the global emissions reduction target was in
effect built into the utility functions, the real question is how
the rights are to be allocated across countries. This is where
conflicts of interest emerge. Consider the comparison between
the three emissions reduction scenarios in which the rights
are grandfathered (columns (5), (6), and (7)) and the three
scenarios in which the emissions rights are allocated on a per
capita basis (columns (8), (9), and (10)). Some of the countries/
regions (the USA, Eurostat, CIS, and Middle East) tend to prefer
some form of grandfathering, although the USA ranks emis-
sions grandfathered according to oil and gas reserves 6th, and
the Middle East ranks emissions grandfathered according to
current emissions 5th. The other regions (EU, Japan, China,
India, South America, Africa, and Asia/Pacific) generally prefer
that the reduced emissions be allocated per capita. Again,
there are exceptions: the first choice of the EU and Japan is
emissions grandfathered according to current emissions
levels, and South America's first choice would be grand-
fathering in proportion to oil and gas reserves.
The bottom row of Table 2 gives the reverse Borda Count for
each option. The reverse Borda Count is calculated by adding
the ranks assigned to each outcome by each individual person.
Hence, it is obtained from the ranks shown in the body of
Table 2 by computing the population-weighted sum for each
column.13
A lower number indicates greater preference for the
outcome. The reverse Borda Count clearly favors the per capita
allocation of the emissions rights, as would be expected given
the general preference of populous regions for a per capita
allocation.
A summarypicture ofthepattern ofnational interests isgiven
in Table 3. This Table shows the average rank of the grand-
fathering options (rounded to the nearest unit), the average rank
of the per capita allocation options, the difference in these two
average ranks, and the difference (in percentage terms relative to
the grandfathering average) between average national consump-
tion under the three grandfathering options versus the three
per capita allocation options. Averages were used because it is
impossible to know what kind of grandfathering might emerge
from the international negotiations. It seems probable that some
mix of grandfathering and per capita allocation might be arrived
at, but focusing on the polar cases shows most vividly where the
underlying interests lie.
12
It was not difficult to find the appropriate parameter values for
the utility functions to yield this result. The functions are very
simple in form, and only a bit of trial and error was needed to
selected values of k, θ and γ to achieve the desired calibration.
13
The properties and advantages of the Borda Count in voting on
lists of ranked alternatives are described by Saari (2001). The
Borda Count is computed in Table 2 to show what the outcome
would be hypothetically if each human being had an equal voice
in voting on the different allocations or CO2 rights, but of course
the global climate negotiations are not going to be settled by a
vote.
Table 3 – Coalitions and salience of grandfathering vs. per
capita allocations
921
E C O L O G I C A L E C O N O M I C S 6 8 ( 2 0 0 9 ) 9 1 5 – 9 2 4

8. The preferences for grandfathering vs. per capita allocation
are indicated by the shaded boxes. The last two columns of
Table 3 exhibit the salience of the difference between grand-
fathering and per capita allocation. Here the picture could not
be clearer: The CIS and the Middle East would experience the
greatest percentage losses in utility rank or consumption from
per capita allocation of the emissions rights relative to
grandfathering, while the poor but populous regions – India,
Africa, and Asia/Pacific – stand to gain the most from per
capita allocation relative to grandfathering.
A global political solution is not going to align the preference
rankings of all nations, at least given the science-based criterion
of reducing total emissions to 20% of current levels. However, the
possibility of reaching a workable global agreement depends
crucially on the United States. While the USA prefers grand-
fathering to per capita allocation, the salience of that preference
(and that of its Eurostat allies)14
is relatively low. A coalition
including the United States, the Eurostat nations, and the nations
that prefer per capita allocation of the emissions rights would
have overwhelming political weight. The CIS and the Middle
Eastern oil and gas producers would be the losers, but there are
strong geopolitical reasons for the United States to prefer an
alliance with the great majority of the nations and peoples of the
world over aligning itself with the CIS and the Middle East on
climate. Also, the United States could seek political concessions in
other areas (e.g., fighting terrorism,resisting nuclear proliferation,
WTO issues) in return for joining with the nations favoring per
capita allocation of the CO2 emissions rights. A coalition that
includes India, China, Africa, and the Asia/Pacific nations rather
than the CIS and Middle East would certainly be preferable on
utilitarian equity grounds, but it is also consistent with a broader
realist perspective on the part of the United States.
Aside from this central point, several other observations can
be made about the model calculations. First, it has already been
emphasized that the reductions in GDP between the reduced-
emissions scenarios and the unregulated emissions scenarios
do not represent declines in well-being, because of the fact that
the climate externality enters the utility functions directly. Even
with this caveat in mind, it should be noted that the GDP
reductions from the status quo shown in Table 2 include no
provision for technological progress. A politically practical path
to the 80% reduction in emissions will take time, and over time
both energy productivity and total factor productivity can be
expected to increase. Fossil fuel intensity can decline even faster
than total factor productivity increases because of technological
change incentivized by the higher carbon price. Such produc-
tivity gains would ameliorate or eliminate the GDP decline
calculated in the model without technological progress. Thus,
the “no technological progress” decline in measured GDP
reflected in Table 2 may be thought of as a strong upper bound
for the decline in consumption of produced goods. The actual
decline inconsumption that would accompanyimplementation
of climate stabilization policies would inevitably be smaller.
Additional calculations not reported here show that the
USA's “CO2 trade deficit” is reasonable given the assump-
tions underlying the scenarios. The status CO2 trade balance
is $ – 878 billion/year if the CO2 rights are assigned for oil and
gas reserves only, somewhat higher than the actual value.15
This estimate is on the high side because of the importance
of coal in the fossil fuel mix, even though not much
coal is traded internationally. The USA's CO2 trade deficit
is $ – 687 billion plus or minus a billion dollars under the per
capita allocations. Only by replacing oil and gas with
renewables, nuclear, and coal with carbon capture and
sequestration can the United States avoid purchasing
significant amounts of CO2 rights from the rest of the
world if a per capita allocation of CO2 rights is enacted. It
should be noted that the CO2/fossil fuel price is about four
times as large under the optimal reduced CO2 emissions
scenario as it is under the status quo.
The story is unchanged if the utility and production
functions differ slightly across the countries. However, further
research would be necessary to examine the consequences of
varying the degree of substitutability between CO2 emissions
and other productive resources (i.e., with CES production
functions), variations in the degree of relative risk aversion in
the utility function(s), and large differences in the utility
functions across countries.
4. Conclusion
No meaningful global carbon emissions reductions are going to
be achieved unless the decision-makers of the great powers
understand that the climate change problem is of real and vital
interest to their nations. Reaching this conclusion will require
guidance from the best available science, as well as acceptance
of moral responsibility for the well-being of future generations.
Economics is not likely to be able to provide either of these
essential inputs. However, if the will to address the climate
issue can be mustered, economic analysis can provide insight
both into the methods that would be effective in reducing
emissions and the consequences of adopting those methods
for the national economies of the world's leading states.
This paper offers an outline of the distributional implica-
tions of reducing emissions to around 20% of their current
values. Given calibration of national utility functions to this
kind of emissions reduction target, the chances for achieving a
global agreement and the specific shape of that agreement
depend critically on the position taken by the United States. If
the United States aligns itself with the nations that are rich in
fossil fuel reserves to insist that the regulatory regime
grandfathers the emissions rights based either on fossil fuel
reserves or current emissions, the negotiating impasse is
likely to continue. If the United States is willing to settle for a
slightly less-preferred agreement that is tilted in the direction
of per capita allocation of the rights, a global coalition that
14
Recall that the Eurostat group includes the USA’s two NAFTA
partners, Canada and Mexico.
15
U.S. net imports of crude oil and petroleum products have
been averaging 11,908 thousand barrels per day from January
through August 2008 (EIA, 2008b). At $120/barrel, this comes to
$522 billion per year. U.S. net imports of natural gas through the
first 6 months of 2008 have been 1,461,517 million cubic feet (EIA,
2008c), so with an average price of $11/thousand ft3
, this would
total $32 billion per year. The sum is $554 billion, somewhat less
than the $700 billion that has been widely advertised by T. Boone
Pickens as the cost of imported oil (Pickens, 2008).
922 E C O L O G I C A L E C O N O M I C S 6 8 ( 2 0 0 9 ) 9 1 5 – 9 2 4

9. includes most nations and the large majority of the world's
population is possible. The economic sacrifice required of the
United States for this outcome would be relatively small, and
could well be offset by other geopolitical gains. The losers from
such a regulatory regime would be the nations endowed with
large reserves of fossil fuels, particularly petroleum and
natural gas. The primary conflict of interest with regard to
climate is not between the rich nations of the OECD and the
large, rapidly developing economies of the “South” such as
China, India, and Brazil. It is only the threat to the wealth of
the oil-and-gas-rich nations that runs counter to strong action
to protect the climate.
How the underlying long-term conflicts of interest revealed
by this analysis might ultimately be resolved is beyond the
scope of this paper. It does seem clear that it is incumbent on
the governments of the fossil fuel exporting nations capitalize
on their temporary advantage in having a rich resource base,
to invest in the non-fossil sectors of their economies so that
when the oil and gas money dries up they will be well-situated
to be competitive in other economic areas.16
Wasting the oil
and gas windfall rather than using it to build infrastructure
and invest in human capital would be a tragedy. Even so, it
would be an even greater tragedy if political short-sightedness
on the part of the United States, combined with the intransi-
gence of a small number of fossil fuel-rich countries having a
small fraction of the human population, were to block the
world from averting irreversible catastrophic climate change.
Acknowledgments
Insights and suggestions from Frank Ackerman, John Harte,
Richard Norgaard, Catherine Norman, Kristen Sheeran, the
Editor and two anonymous referees are gratefully acknowl-
edged. The conclusions and responsibility for any errors are
mine alone.
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