American Economic Review 2015, 105(4): 1339–1370
http://dx.doi.org/10.1257/aer.15000001
1339
Climate Clubs: Overcoming Free-riding in
International Climate Policy
†
By W N *
Notwithstanding great progress in scientic and economic under-
standing of climate change, it has proven difcult to forge inter-
national agreements because of free-riding, as seen in the defunct
Kyoto Protocol. This study examines the club as a model for interna-
tional climate policy. Based on economic theory and empirical mod-
eling, it nds that without sanctions against non-participants there
are no stable coalitions other than those with minimal abatement. By
contrast, a regime with small trade penalties on non-participants, a
Climate Club, can induce a large stable coalition with high levels of
abatement. (JEL Q54, Q58, K32, K33)
I. Bargaining and Climate Coalitions
A. Free-riding and the Westphalian System
Subject to many deep uncertainties, scientists and economists have developed an
extensive understanding of the science, technologies, and policies involved in climate
change and reducing emissions. Much analysis of the impact of national policies such
as cap-and-trade or carbon taxes, along with regulatory options, has been undertaken.
Notwithstanding this progress, it has up to now proven difcult to induce coun-
tries to join in an international agreement with signicant reductions in emis-
sions. The fundamental reason is the strong incentives for free-riding in current
international climate agreements. Free-riding occurs when a party receives the
benets of a public good without contributing to the costs. In the case of the inter-
national climate-change policy, countries have an incentive to rely on the emissions
reductions of others without taking proportionate domestic abatement. To this is
added temporal free-riding when the present generation benets from enjoying
the consumption benets of high carbon emissions, while future generations pay
for those emissions in lower consumption or a degraded environment. The result
* Sterling Professor of Economics, Yale University (e-mail: [email protected]). I would like to thank
the many scholars whose research has contributed to the analysis underlying this study as well as people who have
commented on early drafts and presentations. Paul Sztorc of the Yale Department of Economics contributed to
the modeling, particularly of the international trade module. The research has been supported by the US National
Science Foundation and the US Department of Energy. The author declares no relevant conicts of interest.
†
Presidential Address delivered at the one hundred twenty-seventh meeting of the American Economic
Association, January 4, 2015, Boston, MA. Go to http://dx.doi.org/10.1257/aer.15000001 to visit the article page
for additional materials and author disclosure statement.
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of free-riding is the failure of the only signicant international climate treaty, the
Kyoto Protocol, and the difculties of forging effective follow-up regimes.
While free-riding is pervasive, it is particularly difcult to overcome for global pub-
lic goods. Global public goods differ from national market failures because no mecha-
nisms—either market or governmental—can deal with them effectively. Arrangements
to secure an international climate treaty are hampered by the Westphalian dilemma.
The 1648 Treaty of Westphalia established the central principles of modern interna-
tional law. First, nations are sovereign and have the fundamental right of political
self-determination; second, states are legally equal; and third, states are free to manage
their internal affairs without the intervention of other states. The current Westphalian
system requires that countries consent to joining international agreements, and all
agreements are therefore essentially voluntary (Treaty of Vienna 1969, article 34).
B. Clubs as a Mechanism to Overcome Free-riding
Notwithstanding the Westphalian dilemma, nations have overcome many trans-
national conicts and spillovers through international agreements. There are over
200,000 UN-registered treaties and actions, which are presumptive attempts to
improve the participants’ welfare. Countries enter into agreements because joint
action can take into account the spillover effects among the participants.
How have countries overcome the tendency toward free-riding associated with
the Westphalian system? Consider the many important international agreements in
international trade and nance as well as alliances that have reduced the lethality of
interstate military conicts. These have often been accomplished through the mech-
anism of “clubs.” A club is a voluntary group deriving mutual benets from sharing
the costs of producing an activity that has public-good characteristics. The gains
from a successful club are sufciently large that members will pay dues and adhere
to club rules in order to gain the benets of membership.
The theory of clubs is a little-known but important corner of the social sciences.
(For an early analysis, see Buchanan 1965, while for a ne survey, see Sandler and
Tschirhart 1980.) The major conditions for a successful club include the following:
(i) that there is a public-good-type resource that can be shared (whether the benets
from a military alliance or the enjoyment of a golf course); (ii) that the cooperative
arrangement, including the dues, is benecial for each of the members; (iii) that non-
members can be excluded or penalized at relatively low cost to members; and (iv) that
the membership is stable in the sense that no one wants to leave. For the current inter-
national-trade system, the advantages are the access to other countries’ markets with
low trade barriers. For military alliances, the benets are peace and survival. In all
cases, countries must contribute dues—these being low trade barriers for trade or bur-
den sharing in defense treaties. If we look at successful international clubs, we might
see the seeds of an effective international system to deal with climate change.
The organization of this paper is as follows. After a sketch of the proposal, I begin
with a discussion of the issues of free-riding and previous analyses of potential solu-
tions. I examine potential approaches to internalizing the transnational spillovers
and conclude that a Climate Club with penalties for nonmembers is the most fruitful
mechanism. The following sections develop a model of coalition formation with
climate economics (the Coalition-DICE or C-DICE model) and show the results of
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illustrative calculations. The bottom line—that clubs with penalties or sanctions on
nonparticipants can support a strong international climate agreement—is summa-
rized at the end of the paper.
C. A Sketch of the Climate Club
The idea of a Climate Club should be viewed as an idealized solution of the
free-riding problem that prevents the efcient provision of global public goods. Like
free trade or physics in a vacuum, it will never exist in its pure form. Rather, it is a
blueprint that can be used to understand the basic forces at work and sketch a system
that can overcome free-riding.
Here is a brief description of the proposed Climate Club: the club is an agreement by
participating countries to undertake harmonized emissions reductions. The agreement
envisioned here centers on an “international target carbon price” that is the focal provi-
sion of an international agreement. For example, countries might agree that each coun-
try will implement policies that produce a minimum domestic carbon price of $25 per
ton of carbon dioxide (CO
2
). Countries could meet the international target price require-
ment using whatever mechanism they choose—carbon tax, cap-and-trade, or a hybrid.
A key part of the club mechanism (and the major difference from all current pro-
posals) is that nonparticipants are penalized. The penalty analyzed here is uniform
percentage tariffs on the imports of nonparticipants into the club region. Calculations
suggest that a relatively low tariff rate will induce high participation as long as the
international target carbon price is up to $50 per ton.
An important aspect of the club is that it creates a strategic situation in which
countries acting in their self-interest will choose to enter the club and undertake high
levels of emissions reductions because of the structure of the incentives. The balance
of this study examines the club structure more carefully and provides an empirical
model to calculate its effectiveness.
II. Background on International Agreements on Climate Change
A. Basic Free-riding Equilibrium
There is a large literature on the strategic aspects of international environmental
agreements, including those focused on climate change. One important strand is the
analytical work on global public goods. The clear message is that without special
features the outcome will be a prisoners’ dilemma or tragedy of the commons in
which there is too little abatement. This point is illustrated with a simple model that
will form the backbone of the empirical model below.
I begin by analyzing the costs and benets of national climate policies in a
noncooperative (NC) framework (Nash 1950). In the NC framework, countries act
individually and are neither rewarded nor penalized by other countries for their pol-
icies. The analysis assumes that countries maximize their national economic wel-
fare and ignores partisan, ideological, myopic, and other nonoptimizing behaviors.
While history is full of wooden-headed actions of countries and their leaders, as
well as policies that are farsighted and attend to global welfare, attempting to incor-
porate these features is beyond the scope of this study of climate regimes.
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B. Noncooperative Equilibrium in a One-shot Decision
Begin by assuming that countries choose their policies once and for all in a single
decision. I take a highly stylized structure, but the most complex models extant have
virtually identical results.
For this example, I assume that the emissions-intensities (σ) and the damage-output
ratios are identical for all countries and that countries only differ in their sizes.
In what follows, W = total economic welfare, A = abatement cost, D = damages,
Q = output, E = actual emissions,
_
E = uncontrolled emissions, and μ = emissions
control rate [ = (
_
E − E) /
_
E ]. A key variable is the social cost of carbon (SCC),
which is the marginal damage from a unit of emissions. The global SCC is denoted
by γ, while θ is the country share of world output and other variables. This rst
analysis excludes trade.
The basic identity for country i is that welfare equals output minus abatement
cost minus damages. Abatement costs are assumed to be quadratic in the emissions
reduction rate, A
i
= α μ
i
2
Q
i
= α μ
i
2
θ
i
Q
w
, where α is the identical abatement-cost
parameter and Q
w
is world output. Damages are proportional to global emissions.
All these imply for region i:
(1) W
i
= Q
i
− A
i
− D
i
= θ
i
Q
w
− α μ
i
2
θ
i
Q
w
− γ θ
i
( E
i
+ ∑
j≠i
E
j
).
The potential for free riding occurs because most of the damages originate outside
the country. This is captured in the last term of equation (1), which in practice means
that for all countries the preponderance of damages originate outside, while the
preponderance of damages caused by a country’s emissions falls on other countries.
Maximizing each country’s welfare in a one-shot game, assuming no cooperation
or strategic interactions, yields (as shown in the online Appendix) the noncoopera-
tive emissions-control rate and domestic carbon price
( τ
i
NC
):
(2) μ
i
NC
= θ
i
[γσ/2α]
(3) τ
i
NC
= θ
i
γ .
The most intuitive result shown in (3) is that a country’s noncooperative car-
bon price is equal to the country share of output times the global social cost of
carbon. A less intuitive result in (2
) is that a country’s noncooperative control rate
( μ
i
NC
) is proportional to the country share of world output, to the global SCC, to
the emissions-output ratio, and inverse to the abatement-cost parameter. Equation
(3) survives alternative specications of the abatement-cost function, while (2) is
sensitive to parameters such as the exponent in the cost function.
Under the simplied assumptions, calculate the global average NC control rate
and carbon price as functions of the cooperative levels
( μ
̅
C
and τ
̅
C
) ;
(4) μ
̅
NC
= ∑
i
θ
i
μ
i
= ∑
i
θ
i
2
[γ σ/ 2 α]
= (γ σ/ 2α)H(θ) = μ
̅
C
H(θ)
(5) τ
̅
NC
= ∑
i
θ
i
τ
i
= ∑
i
γ θ
i
2
= γ H(θ) = τ
̅
C
H(θ) .
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In these equations, H(θ)=
∑
i
θ
i
2
is the Herndahl index of country size.
Equations (4) and (5) show the basic free-riding equilibrium for a global public
good with the simplied structure. The globally averaged noncooperative carbon price
and control rate are equal to the Herndahl index times the cooperative values. For
example, if there are ten equally sized countries, the Herndahl index is 10 percent, and
the global carbon tax and emissions-control rates are 10 percent of the efcient levels.
The Herndahl index for country gross domestic products (GDPs) is about 12per-
cent, indicating that (when emissions-intensities and damage ratios are equal for
each country) the noncooperative control rate and carbon price are about 12 percent
of the cooperative values. This gure is close to calculations that have been made
in more complete models (see Nordhaus and Yang 1996; Nordhaus 2010; Bosetti et
al. 2012). For example in the multiperiod RICE-2010 model with 12 regions, the
noncooperative price is estimated to be is 11 percent of the efcient price (Nordhaus
2010, supplemental materials).
C. Outcomes with Repeated Decisions
A more complete treatment of country interactions in climate-change policy
views interactions in a dynamic framework with decisions over time. The standard
analysis uses the framework of a repeated prisoners’ dilemma (RPD) game. For
simplicity, assume that the structure above is repeated every few years with identical
parameters. One equilibrium of a RPD is just the iterated inefcient one-shot equi-
librium with minimal abatement as described above. However, because players can
reward and punish other players for good and bad behavior, RPD games generally
have multiple equilibria; these might include more efcient outcomes if country
discount rates are low (these being the generalized results of various folk theorems).
The efcient RPD equilibrium with large numbers of countries will be hampered by
free-riding and inability to construct renegotiation-proof strategies in situations with
large number of agents.
The strategic signicance of the analysis of NC behavior is threefold. First, the
overall level of abatement in the noncooperative equilibrium will be much lower
than in the efcient (cooperative) strategy. A second and less evident point is that
countries will have strong incentives to free-ride by not participating in strong
climate-change agreements. Finally, the difculty of escaping from a low-level,
noncooperative equilibrium is amplied by the intertemporal trade-off because
the current generation pays for the abatement while future generations are the
beneciaries of lower damages. But to a rst approximation, the noncooperative
analysis in this section describes international climate policy as of 2015.
III. Climate Coalitions and International Environmental Treaties
A. Key Denitions on Sanctions and Coalitions
Might coalitions of countries form cooperative arrangements or treaties that
improve on noncooperative arrangements? Questions involving the formation,
value, and stability of coalitions have a long history in game theory, oligopoly
theory, as well as in environmental economics. In this section, I analyze coalitions
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without external penalties, that is, ones that have self-contained payoffs and cannot
be enforced by third parties or be linked to other arrangements.
Begin with some denitions. The formal difference between “external” and “inter-
nal” penalties is the following. If countries are playing a repeated game, then inter-
nal penalties maintain the payoff structure of the game, but countries can penalize or
reward others by selecting different combinations of strategies. Tit-for-tat is a game
with internal penalties because it has a reward structure given by the payoffs of the
stage games. In the end, however, the rewards must be some combination of the payoffs
of the original game. By contrast, external penalties change the payoff structure of the
game. A standard external penalty comes when a player imposes a sanction that derives
from a trading relationship that is unconnected to the payoffs of the original game. For
example, in a treaty to preserve whales, a player might punish an uncooperative party
by imposing a duty on the imports of related products. The tariffs are unrelated to the
public-goods nature of the decline of the whale population and are therefore external.
Before turning to the analysis of coalitions, it will be useful to distinguish between
“bottom-up” and “top-down” coalitions. The standard approach in environmental
economics, reviewed in the next section, focuses on a bottom-up approach in which
coalitions optimize their own self-interest and evolve into larger or smaller coali-
tions. Regional trade agreements are examples of this approach.
The Climate Club approach is instead a top-down approach. Here, the regime is
optimized to attract large numbers of participants and attain high levels of abate-
ment, and then countries decide whether or not to join. The Bretton Woods institu-
tions such as the International Monetary Fund or the World Trade Organization are
examples of the top-down model.
B. Bottom-up Coalitions and the Small Coalition Paradox
In the context of climate change, coalitions of countries can form treaties that
potentially improve the welfare of their members by taking concerted action. If sev-
eral countries maximize their joint welfare, the optimized level of abatement will rise
relative to the noncooperative equilibrium because more countries will benet. In
the algebraic example described above, the coalition’s optimal control rate shown in
equation (2) will equal the global optimum times the coalition’s share of world out-
put. As the coalition increases to include all countries, the global level of abatement
will tend toward the efcient rate. This result might form the basis for hopes that
arrangements like the Kyoto Protocol will lead to deep emissions reductions.
In fact, theoretical and empirical studies indicate that bottom-up coalitions for cartels
and global public goods tend to be small, fragile, and unstable. Work on coalition sta-
bility by Hart and Kurz (1983) found that coalitions are generally not stable, and their
structure will depend upon the structure of the payoffs and the stability concept. Studies
of the structure of cartels in oligopoly theory (see, e.g., D’Aspremont et al. 1983 and
Donsimoni, Economides, and Polemarchakis 1986) found that cartels are likely to be
small, unstable, or of vanishingly small importance as the number of rms grows.
Studies in environmental economics and climate change nd virtually univer-
sally that coalitions tend to be either small or shallow, a result I will call the “small
coalition paradox.” The paradigm for understanding the small coalition paradox is
well discussed in Barrett’s (2003) book on international environmental agreements.
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His analysis emphasizes credible or “self-enforcing” treaties (Barrett 1994). These
are ones that combine individual rationality (for each player individually) and col-
lective rationality (for all players together). This concept is weaker than the concept
of coalition stability discussed later, which adds rationality for each subset of the
players. Barrett emphasizes the difculties of reaching agreements on global public
goods with large numbers of participants because of free-riding. Similar to the results
for cartels, Barrett and others nd that stable climate coalitions tend to have few
members; therefore, as the number of countries rises, the fraction of global emissions
covered by the agreement declines. He further argues, based on a comprehensive
review of existing treaties, that there are very few treaties for global public goods that
succeed in inducing countries to increase their investments signicantly above the
noncooperative levels. Moreover, the ones that do succeed include external penalties.
How can we understand the small coalition paradox? Here is the intuition for
climate change: clearly, two countries can improve their welfare by combining and
raising their carbon price to the level that equals the sum of their SCCs. Either coun-
try is worse off by dropping out. The 2014 agreement between China and the United
States to join forces in climate policy might be interpreted as an example of a small
bottom-up coalition.
Does it follow that, by increasing the number of countries in the treaty, this process
would accumulate into a grand coalition of all countries with efcient abatement? That
conclusion is generally wrong. The problem arises because, as more countries join, the
cooperative carbon price becomes ever higher, and ever further from the NC price. The
discrepancy gives incentives for individual countries to defect. When a country defects
from an agreement with m countries, the remainder coalition (of m − 1 countries)
would reoptimize its levels of abatement. The revised levels of abatement would still
be well above the NC levels for the remainder coalition, while the defector free-rides
on the abatement of the remainder coalition. The exact size of the coalitions would
depend upon the cost and damage structure as well as the number of countries.
The online Appendix provides a simple analysis of the bottom-up coalition equi-
librium for identical countries with the cost and damage structure shown in equations
(1)–(5). The only stable coalitions have two or three countries. (For simplicity,
assume the lower number holds in the case of ties.) The size of the stable coalition is
independent of the number of countries, the social cost of carbon, output, emissions,
and the emissions intensity. If there are ten identical countries, there will be ve
coalitions of two countries each. The global average carbon price is twice that of the
NC equilibrium. This result is clear because each country-pair has a joint SCC that
is the sum of the two countries’ SCCs. The globally averaged carbon price will be
one-fth of the efcient level. With countries of different sizes but equal intensities,
countries will group together in stable coalitions of size two, with the countries of
similar sizes grouped together in pairs (i.e., largest with second-largest, and so on).
The key result is that bottom-up coalitions perform only slightly better than the
noncooperative equilibrium.
C. Modeling Results for Bottom-up Coalitions
The coalition theories described above generally use highly stylized structures
and assumptions, so it is useful to examine empirical models of climate-policy
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coalitions with more realistic assumptions. Several empirical studies have examined
the structure of coalitions or international agreements using a variety of alternative
cooperative structures and coalition assumptions. A brief description of key studies
is contained in the online Appendix.
The central results of existing studies reproduce the nding of the small coalition
paradox. Without penalties on nonparticipants, stable coalitions tend to be small and
have emissions reductions that are close to the noncooperative level. In addition,
many studies nd that coalitions tend to be unstable, particularly if transfers among
regions are included.
IV. Sanctions on Nonparticipants to Promote an Effective Climate Club
As noted above, the syndrome of free-riding along with the international norm
of voluntary participation appears to doom international climate agreements like the
Kyoto Protocol. The suggestion in this paper is that a club structure—where external
sanctions are imposed on nonmembers—will be necessary to induce effective agree-
ments. I analyze in depth a specic model of sanctions (tariffs on nonparticipants),
but the model illustrates the more general point that external sanctions are necessary
to promote participation in effective agreements to provide global public goods.
A. Stable Coalitions
While it is easy to design potential international climate agreements, the reality
is that it is difcult to construct ones that are effective and stable. Effective means
abatement approaching the global optimum. The concept of stability used here is
denoted as a coalition Nash equilibrium. Under this denition, a coalition is stable
if no group (sub-coalition) among the countries can improve its welfare by changing
its status. That is, it combines individual rationality (for each player individually),
collective rationality (for all players together), and coalition rationality (for each
subset of the players). This is a natural extension of a Nash equilibrium, which
applies to single countries. The concept is widely used in different elds and was
originally called strong equilibrium in Aumann (1959); also see Bernheim, Peleg,
and Whinston (1987). The term coalition Nash is more intuitive and is used here.
The small coalition paradox motivates the current approach. The goal here is
to nd a structure that is stable and effective for a wide variety of country prefer-
ences, technologies, and strategies. The most appealing structure is one that does
not depend on sophisticated and fragile repeated-game strategies and instead has
an efcient equilibrium for every period (in the stage games) in a repeated game.
I therefore focus on one-shot games that have efcient and unique equilibria. If
these are then turned into a repeated game, each of the one-shot games will be a
sub-game-perfect coalition Nash equilibrium, and the repeated game will have an
efcient coalition-Nash equilibrium.
B. Transfers Undermine Coalition Stability
The present study assumes that there is no sharing of the gains from cooperation
among members of the coalition. In some cases, particularly those with asymmetric
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regions, allowing transfers may allow a more efcient treaty (see Barrett 2003,
ch. 13). However, allowing transfers also increases the dimensionality of the strat-
egy space and may increase the potential for coalition instability.
Before discussing the strategic issues, a practical exception must be made for
poor countries. We can hardly expect low-income countries struggling to provide
clean water or engaged in civil conict to make the same commitment as rich coun-
tries. So there might be a threshold for participation in terms of per capita income.
But once countries graduate into the middle-income group, they would assume the
obligations of club membership.
What happens if surplus-sharing is included as part of country strategies? If there
are no sharing constraints, then coalition instability is inevitable in what might be
called the stab-in-the-back syndrome. This can be seen in the case of three regions.
Suppose that a cooperative agreement of the three regions has a surplus of 300 units,
and agreements require a majority of countries. A rst agreement might divide the
surplus equally among the three regions as proposal A = (100, 100, 100). However,
a coalition of the rst two countries could propose another allocation as proposal
B = (110, 110, 80), which would lead the rst two countries to defect from proposal
A to B. A little reection will show that there is no stable coalition if the surplus can
be divided arbitrarily. (For examples of how different sharing and voting rules lead
to instability, see Meyerson 1991, ch. 9.)
One difculty with the use of differentiated emissions targets in the Kyoto Protocol
was its stab-in-the-back instability. The initial allocation of permits across countries
is a zero-sum distribution. It can generate the same instability as the example of
the negotiation over the division of the surplus. One of the attractive features of a
regime that focuses on carbon prices is that it can operate as a
single-dimensional
choice and thereby avoid stab-in-the-back instability.
1
A study of climate regimes
by Weikard, Finus, and Altamirano-Cabrera (2006) conrms the potential for insta-
bility in climate agreements with transfers (see the online Appendix).
C. Introducing Sanctions on Nonparticipants
Both theory and history suggest that some form of sanctions on nonparticipants is
required to induce countries to participate in agreements with high levels of abate-
ment. It will be useful to dene “sanctions” or “penalties” carefully. In their land-
mark study of sanctions, Hufbauer, Schott, and Elliot (1990) dene sanctions as
governmental withdrawal, or threat of withdrawal, of customary trade or nancial
relationships. A key aspect of the sanctions analyzed here is that they benet senders
and harm receivers. This pattern contrasts with most cases analyzed by Hufbauer,
Schott, and Elliot, whose studies show that sanctions usually impose costs on send-
ers as well as receivers and thereby raise issues of incentive-compatibility.
The major potential instrument is sanctions on international trade. Whether and
how to use international trade in connection with a climate treaty involves many
issues—economic, environmental, legal, and diplomatic. I will emphasize the
1
This point has been emphasized in Weitzman (2014), who shows that a single carbon price provides a more
robust negotiating device than a cap-and-trade regime with country-differentiated permit allocations. The point is
made less formally in Nordhaus (2013, ch. 21).
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economic and strategic aspects and leave other aspects to specialists in those areas
(see Bordoff 2009 and Brainard and Sorkin 2009).
Two approaches to trade sanctions might be considered. A rst approach, called
carbon duties, would put tariffs on imports of nonparticipants in relation to the car-
bon content of imports. A second approach, called uniform penalty tariffs, would
apply uniform percentage tariffs to all imports from nonparticipating countries. I
discuss each of these in turn.
The central question addressed in this analysis is whether a club design which
incorporates penalty tariffs on nonparticipants can produce a stable equilibrium or
coalition that signicantly improves on the noncooperative equilibrium.
D. Carbon Duties
A rst approach called carbon duties—commonly proposed among scholars who
have advocated penalties—would put tariffs on goods imported from nonparticipants
in relation to the goods’ carbon content. (These are also known as countervailing
duties, but I will use the more descriptive term here.) Under this approach, imports
from nonparticipants into a country would be taxed at the border by an amount that
would be equal to the domestic price of carbon (or perhaps by an agreed-upon inter-
national target carbon price) times the carbon content of the import. Alternatively,
under a cap-and-trade regime, the requirement might be that importers purchase
emissions allowances to cover the carbon content of imports.
The technique of carbon duties is commonly used when countries violate their trade
agreements, and is also included in several international environmental agreements
(see Barrett 2003 for an extensive history). The purposes of carbon duties are to reduce
leakage, to level the competitive playing eld, and to reduce emissions. Increased
participation—which is emphasized here—is usually not included as a goal of the
sanctions. See Frankel (2009) for a review of proposals and their relation to trade law.
Studies of carbon duties indicate they are complicated to design, have limited cov-
erage, and do little to induce participation. As an example, consider CO
2
emissions
from US coal-red electricity generation, which is a major source of emissions. Since
the United States exports less than 1 percent of its electricity generation, the effect
of carbon duties here would be negligible. Modeling studies conrm the intuition
about the limited effect of the carbon-duties mechanism. For example, McKibbin
and Wilcoxen (2009) study the effects of carbon duties for the United States and the
European Union. They nd that the proposal would be complex to implement and
would have little effect on emissions. Estimates of this approach using the C-DICE
model described below also indicate that carbon duties have limited effectiveness in
promoting deep abatement (see the online Appendix for more details).
E. Uniform Tariff Mechanisms
Given the complexity of carbon duties, I propose and analyze an alternative and sim-
pler approach: a uniform percentage tariff. Under this approach, participating countries
would levy a uniform percentage tariff (perhaps 2 percent) on all imports from nonpar-
ticipants. This mechanism has the advantage of simplicity and transparency, although it
does not relate the tariff specically to the carbon content of imports.
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While the uniform tariff appears to be less targeted than carbon duties, it has a
different purpose. It is primarily designed to increase participation, not to reduce
leakage or improve competitiveness. The rationale is that nonparticipants are dam-
aging other countries because of their total emissions of greenhouse gases, not only
from those embodied in traded goods.
One objection to this approach is that a tariff on all imports is a major departure
from the approaches authorized under national and international law. It would appear
to collide with current treaties by imposing tariffs on processes and production methods
(PPMs), or on how goods are domestically produced, but that is of course the purpose
of the penalty tariffs. It also departs from the principle of proportionality in having a
binary “in or out” nature of the sanctions. However, the binary feature is central to hav-
ing countries focus on two possible policies, and including proportionate tariffs would
lead to a different set of equilibria. While there may be ambiguities as to whether some
esoteric exceptions can be used to justify the system of uniform, nonproportionate tar-
iffs, trying to shoe-horn the proposed uniform-tariff mechanism into current law seems
ill advised because it would raise questions of legitimacy and durability.
For these reasons, an important aspect of the proposal will be a set of “climate
amendments” to international-trade law, both internationally and domestically.
The climate amendments would explicitly allow uniform tariffs on nonparticipants
within the connes of a climate treaty; it would also prohibit retaliation against
countries who invoke the mechanism. Requiring such amendments would empha-
size that climate change is an especially grave threat, and that this approach should
not be used for every worthy initiative.
F. Tariffs as Internalization Devices
We can interpret penalty tariffs as devices to internalize transnational exter-
nalities. Nations incur but a small fraction of the damages from climate change
domestically—less than 10 percent of global costs on average. Just as taxes or reg-
ulations are needed to correct externalities within nations, some analogous mecha-
nism is needed for global public goods.
Tariffs on the trade of nonparticipants are a reasonable and realistic tool for inter-
nalizing the transnational externality. How well-targeted are penalty tariffs? Using
the C-DICE model (which is described in the next section), I have examined the
external effects of emissions of each region along with the impacts of the penalty
tariff, and the results are shown in Figure 1.
Here are the calculations. I began with a $25 per ton CO
2
global social cost of
carbon. I then calculate each region’s external SCC. This equals the global SCC
minus the national SCC. In all cases, the external SCC is close to the global SCC.
For example, when the global SCC is $25 per ton, the estimated US external SCC
is $21 per ton. Multiplying the region’s external SCC by the difference between the
cooperative and noncooperative emissions provides the externality, shown as the left
bar in Figure 1. In this example, when the United States decides not to participate, it
increases its annual emissions by about 800 million tons, and this produces $16bil-
lion of additional external damages.
I then calculate the cost from the penalty tariff that a country incurs by not par-
ticipating in the Climate Club. The calculation labeled “Cost of out” shows the cost
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of leaving the club when all other countries are in. For example, the United States
has a welfare loss of $10 billion when it does not participate and the penalty tariff is
2percent. (All gures are per year at 2011 incomes and prices.) This cost is below
the external damages of $16 billion. Additionally, the gure shows the “Benet of
in,” which is the benet of forming a club of 1, when the country is the only member
of the club. For the United States, the benet of in is $23 billion.
For all regions, the sum of the transnational externalities is $124 billion. The
sum of the costs of out (clubs of 14) of all 15 regions is $102 billion, while the sum
of benets of in (clubs of 1) is $98 billion. Online Appendix Table B-7 shows the
results for all regions.
The calculations provide a surprising result. They indicate that a penalty tariff pro-
vides incentives that are reasonably well targeted to the transnational externalities.
The penalty always has the correct sign, and the size of the penalty is the right order
of magnitude with a 2 percent tariff. However, because of different trade and emis-
sions patterns, the externality and the trade penalty are imperfectly aligned. Note
that the tariff effect changes with club size, so the internalization effect is variable.
But on the whole, an appropriate tariff appears to be remarkably well-calibrated to
the CO
2
externality.
G. Tariffs as Sanctions for Global Public Goods
Two simple but critical points concern the role of tariffs as sanctions. To begin
with, they play the role of external penalties. This can be most easily seen in repeated
F 1. C T E I P T R
Notes: The left-hand externality bar shows the transnational spillover for each region for a $25 per ton global social cost
of carbon. The middle benet bar shows the benet of participating in a Climate Club with a penalty tariff of 2 percent
for clubs of 1 (that is, the region is the only participant). The right-hand cost bar shows the cost of not participating in a
Climate Club with a penalty tariff of 2 percent for clubs of 14 (that is, the region is the only nonparticipant).
Externality, regime benefit
(US(2011)$ billions per year)
Japan EU US LatAm SEAsia China
Externality ($25/tCO
2
)
Benefit of in for club of 1 (2% tariff)
Cost of out for club of 15 (2%)
35
30
25
20
15
10
5
0
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prisoners’ dilemma (RPD) games. In RPD games with a large number of agents,
it is difcult to design an incentive-compatible internal sanction against defectors
because the punishments punish the punishers. Like a doomsday device, they are
unattractive, particularly when applied against players who make small contribu-
tions to the public good. Part of the problem is that the penalties are internal to the
game and cannot be linked to some larger set of payoffs. The power of tariffs is that
they are external to the RPD game (i.e., they are part of a different game). Because
participation in the trade system has such large benets to countries, these benets
can be used to induce participation in the climate game.
A second critical feature of tariff-sanctions is that they are incentive-compatible.
Many sanctions have the disadvantage that they penalize the penalizer. For example,
if Europe puts sanctions on Russian energy companies, this is likely to raise energy
prices in Europe, hurt European consumers, and therefore have costs on Europe as
well as Russia. Similarly, other sanctions such as a “grim strategy” (which dissolves
the agreement completely if one country violates it) or analogous punishments in
n-person RPD games can only support a cooperative equilibrium for a few coun-
tries (as is discussed in the section on the small coalition paradox). By contrast, the
tariff-sanction mechanism analyzed here (i) imposes costs on the nonparticipating
country but (ii) benets participants that levy the penalty tariffs. Moreover, because
tariffs apply bilaterally, they can support an efcient equilibrium for global public
goods for a large number of countries as long as the optimal-tariff effect operates.
Figure1 shows numerically how the tariff-sanction imposes costs and conveys ben-
ets in a manner that aligns sanctions with external effects.
H. Prices or Quantities?
The Climate Club discussed here focuses on carbon prices rather than emissions
reductions as the central organizing principle for an international agreement. While
at an abstract level either approach can be used, a review of both theory and history
suggests that use of prices is a more promising approach.
Quantitative targets in the form of tradable emissions limits have failed in the
case of the Kyoto Protocol, have shown excessive price volatility, lose precious
governmental revenues, and have not lived up to their promise of equalizing prices
in different regions. Moreover, as emphasized by Weitzman (2014), prices serve
as a simpler instrument for international negotiations because they have a single
dimension, whereas emissions reductions have the dimensionality of the number of
regions. To the extent that carbon-price targets lead to carbon taxes, the administra-
tive aspects of taxes are better understood around the world than marketable emis-
sions allowances, and they are less prone to corruption. This discussion is clearly
just a sketch, but it provides some of the reasons for preferring price over quantity
targets as part of an international climate regime. (For an extended discussion of the
relative merits of prices and quantities, see Nordhaus 2013.)
I. How to Get Started?
An important question is, how would a top-down Climate Club get started?
Who would dene the regime? Would it begin with a grand Bretton-Woods-type
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conference? Or would it evolve from a small number of countries who see the logic,
dene a regime, and then invite other countries to join?
There are no clear answers to these questions. International organizations evolve in
unpredictable ways. Sometimes, it takes repeated failures before a successful model
is developed. The histories of the gold and dollar standards, cholera conventions, the
WTO, the European Union, and the Internet all emphasize the unpredictability in the
development of international regimes (for some histories, see Cooper et al. 1989). The
destination of a Climate Club is clear, but there are many roads that will get there.
V. Modeling Coalition Formation: The Coalition-DICE (C-DICE) Model
A. Description of the Model and Sources
Economic analysis can describe the basic structure of a Climate Club. However
detailed empirical modeling is necessary to determine the effectiveness of differ-
ent regimes in the context of actual emissions, damages, climate change, and trade
structures. For this purpose, I next describe a climate-economic model that exam-
ines coalition formation: the C-DICE model (Coalition DICE, or Coalition Dynamic
Integrated model of Climate and the Economy). It is a static version of the multire-
gional DICE-RICE model (Nordhaus 2010). While the framework is similar to stan-
dard economic integrated assessment models (IAMs), the purpose is different. The
C-DICE model is designed to determine whether or not countries join a coalition
of high-abatement countries, and to nd stable coalitions, rather than to look for an
optimal choice of climate policies or map out emissions trajectories.
The current version has 15 regions, including the largest countries and aggre-
gates of the balance of the countries. The regions are the US, EU, China, India,
Russian Federation, Japan, Canada, South Africa, Brazil, Mideast and North Africa,
Eurasia, Latin America, tropical Africa, middle-income Asia, and the ROW (rest
of the world). The model includes exogenous output, baseline CO
2
emissions, and
a baseline trade matrix for the 15 regions. Countries produce a single composite
commodity, and CO
2
emissions are a negative externality of production. Regions
can reduce emissions by undertaking costly abatement.
The marginal damages of emissions (social cost of carbon (SCC)) are assumed
to be constant. This is reasonably accurate for small time periods because emissions
are a ow, damages are a function of the stock, and the ow-stock ratio is small. The
fact that the SCC is little affected by abatement levels is shown in Nordhaus (2014,
Table 1), where there is virtually no difference in the SCC between the optimal and
baseline policies.
The damage estimates are drawn from a recent comparison of the social cost of
carbon (Nordhaus 2014). That study found a central estimate for the global SCC of
$24 per ton CO
2
in 2011 US$ for 2020 emissions. However, estimates from other
studies range from $10 to as high as $100 per ton CO
2
for alternative goals and dis-
count rates. I therefore use a range of $12.5–$100 per ton CO
2
for the global SCC.
Estimates of national SCCs have proven difcult to determine because of sparse
evidence outside high-income regions. Online Appendix Table B-1 shows the sub-
stantial differences in national SCCs in three integrated assessment models, the RICE,
FUND, and PAGE models. Note that the conceptual basis of the national SCCs used
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here is the calculations made by nations—using their national values, analyses, and
discount rates. Country estimates may differ from those of modelers using uniform
methods and low discount rates. For the central estimates, it is assumed that national
SCCs are proportional to national GDPs. This assumption is primarily for simplicity
and transparency but also because the national estimates are so poorly determined.
However, sensitivity analyses discussed below and in the online Appendix indicate
that alternative estimates lead to identical results on participation.
The abatement costs combine global estimates from the DICE-2013R model
with detailed regional estimates from an engineering model by McKinsey Company
(2009). Abatement costs are largely determined by the carbon-intensity of a region,
which are relatively reliable data. Aside from carbon-intensity, the differences among
regions are largely technological and sectoral as analyzed by McKinsey’s study.
One major new feature is to include the effects of international trade and tar-
iffs on the economic welfare of each region. For both computational and empirical
reasons, the model employs a reduced-form tariff-impact function. This function
represents the impact of changes in the average tariff rate of each country on each
other country. As an example, the model estimates that if the United States imposes
a uniform additional tariff of 1 percent on Chinese imports, US net national income
rises by 0.100 percent and China’s net national income falls by 0.018 percent.
Estimates from the optimal-tariff literature indicate that countries have net ben-
ets if they impose small uniform tariffs on other countries. Similarly, all countries
suffer economic losses if they are the targets of uniform tariffs levied by other coun-
tries. I assume that the tariff function is quadratic with a maximum at the optimal
tariff rates. The numerical parameters of the reduced-form tariff-impact function are
derived from a model developed and provided by Ralph Ossa (2014). Details are
provided in the online Appendix.
Macroeconomic and emissions data are taken from standard sources. GDP and
population are from the World Bank. CO
2
emissions are from the Carbon Dioxide
Information Action Center (CDIAC 2014). Note that I include all industrial CO
2
emis-
sions but exclude land-use emissions as well as non-CO
2
greenhouse gas emissions or
other sources of climate change. The interregional trade data are based on data from
the United Nations Conference on Trade and Development (UNCTAD 2014).
The model considers only one period, centered on 2011. It can be interpreted
as a game with a single long period or as a repeated game with a constant payoff
structure. As discussed above, the purpose is to nd an efcient solution to the stage
game that will also be an equilibrium of the repeated game.
Countries are assumed to maximize their perceived national self-interests, and the
welfare of the rest of the world is not counted in their interests. Their estimates may
turn out to be right or wrong, but they are the basis of treaty negotiations. To avoid
stab-in-the-back instability, I assume that there are no side payments among coun-
tries. Treaties are assumed to be stable in the sense of being coalition Nash equilib-
ria, which means that they are stable as compared to all alternative sub-coalitions.
B. Gains and Losses from Participation
The noncooperative (NC) equilibrium is the starting point in international rela-
tions. Consider the decision of a single country whether to participate in a Climate
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Club. Participation requires countries to have a domestic carbon price at least as
high as the minimum international target carbon price. The choice of climate poli-
cies is simple. A nonparticipant will choose the low NC carbon price because that
maximizes national welfare for nonparticipants. Similarly, a participant will choose
the higher international target carbon price to meet its obligations because that max-
imizes its economic welfare conditional on participation.
In considering whether or not to participate in the high-abatement cooperative
regime, countries face two sets of costs. The rst cost is the additional abatement
cost (net of reduced damages) of participation. The additional abatement costs are
greater than the reduced damages. This fact shows immediately why countries will
not voluntarily depart from the NC equilibrium without some further inducements
to participate.
The second impact of the decision on participation is due to trade impacts. The
present study analyzes a uniform tariff on all goods and services imposed by partici-
pants on the imports from nonparticipants into the Climate Club. Figure 2 shows the
basic structure of the tariff arrangements. As shown in the two cells on the left, the
Club treaty authorizes penalty tariffs on nonparticipants into the Club region, with no
penalty tariffs on intra-Club trade. The two cells on the right indicate that there are
no tariffs, which assumes no reaction or retaliation of non-Club members to the Club.
VI. Algorithmic Issues
Finding the equilibrium coalition, as well as determining stability and unique-
ness, is computationally demanding. Consider a global Climate Club with n regions.
The payoffs are functions of the parameters of the game, including output, emis-
sions, damages, the trade technology, and the tariff penalty function. In addition, the
payoffs depend up the participation of each of the other players.
In the most general version, discussed above in the section on bottom-up coa-
litions, there may be multiple coalitions (i.e., regional groupings). This outcome
is seen in trade associations and military alliances formed on the basis of costs,
location, and ideologies. In the case of multiple coalitions, there will be on the order
of n! possible coalitions. For our study, with 15 regions and multiple regimes, that
would consist of about 10
12
coalitions and would be computationally infeasible.
However, in the case of global climate change, it is more natural to consider
a situation where countries decide whether to join a single global climate treaty.
Assuming a single coalition has the computational advantage that it limits the num-
ber of potential coalitions to 2
n
(or 32,768) coalitions, which can easily be calculated.
The problem is combinatorial in nature, and its solution is thought to be in the
class of NP-hard problems (Wooldridge and Dunne 2004).There appears to be no
efcient algorithm for calculating stable coalitions (Rahwan 2007). In principle, we
would need to take each of the 2
n
coalitions and determine whether they are stable
against all the other 2
n
− 1 coalitions, which requires about 2
2n
≈ 10
9
comparisons.
While this is computationally feasible, it is unnecessarily burdensome, particularly
for model construction and comparison of regimes.
I therefore settled on an evolutionary algorithm to nd stable coalitions. This is
similar to a genetic algorithm except that it considers mutations of all elements rather
than just local searches. This proceeds in the following steps: (i) Start with an initial
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coalition and calculate the outcomes and net benets. Denote these the initial “base
coalition” and “base outcomes.” (ii) Randomly generate a “change coalition” of a set of
m regions from the n regions. Assume that each of the m regions changes its participa-
tion from out to in or from in to out. (iii) Construct a new test pattern of participations,
substituting the new participation status of the change coalition for its participation in
the base coalition. (iv) Calculate the test net benets of the new test participation for
each region. (v) If the test net benets are Pareto improving for the change coalition,
substitute the test participation pattern and other outcomes for the prior base outcomes
to get new base participation and outcomes. Note that while the results of the test coa-
lition will be Pareto improving for the change coalition in the new outcomes, it may
not improve the welfare for the balance of regions. (vi) Go back and restart from (ii) to
generate a new random change coalition and then go through steps (iii)–(v). (vii) The
procedure stops either when (a) the process cycles (a coalition structure repeats), or
(b) no other coalition is able to overturn the existing base coalition.
Note that the termination in (vii b) cannot be determined with certainty because
of the probabilistic nature of the algorithm. However, because the change coalition
is randomly selected, in the worst case the likelihood of there being an overturning
coalition that has not been found is no more than (1 − 2
−n
)
m
after m iterations.
Experiments indicate that stable coalitions are usually found within 100 iterations.
I examined up to 50,000 iterations and random starting coalitions to test stability.
While this algorithm might potentially be improved with bounding renements, the
exibility of the evolutionary algorithm for nding stable coalitions suggests it is
adequate. Further details are provided in the online Appendix.
VII. Results
A. A First Example
Before diving into the results, it will be useful to present a numerical example.
Assume that the international target carbon price is $25 per ton; that the penalty
tariff rate is 4 percent; that all high-income countries participate; and that the United
States is considering whether to participate. The numbers are shown in Table 1.
Exporting
countries
Participants
Participants
Importing countries
No penalty No penalty
Penalty No penalty
Nonparticipants
Nonparticipants
F 2. P S C C
Notes: The matrix shows the structure of penalties in the Climate Club. For example, the lower left cell indicates
that when exporting countries are nonparticipants and importing countries are participants, the trade of exporters is
penalized. In all other cases, there are no penalties.
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All gures in this study apply to annual output and prices for 2011 in 2011 US$.
The gures are often provided with two or three signicant digits, but this is for
presentational purposes and should be interpreted in the context of the uncertainties
inherent in modeling as well as the results of the sensitivity analyses discussed below.
First consider a Kyoto-type regime, with no sanctions when countries do not
participate, which is the rst line in Table 1. If the United States does not partici-
pate, it expends $0.3 billion per year for abatement and has reduced damages (from
all countries’ abatement relative to zero abatement) of $7.3 billion per year. Net
climate-related benets are $7.0 billion per year. In the no-sanctions regime, if the
USparticipates and sets a domestic carbon price of $25 per ton, it expends $11.9bil-
lion annually in abatement and has reduced damages of $10.7 billion per year, for
net climate-related benets of −$1.2 billion annually. So without sanctions, the best
national strategy is not to participate, with an annual net advantage of $8.2 billion.
However, with a 4 percent penalty tariff on nonparticipants, the numbers change
dramatically. Here, the US has trade impacts of −$15.6 billion per year if it does
not participate. This comes primarily from the terms of trade losses induced by
tariffs on the US imposed by participants. If the US does participate, it has positive
trade impacts of $36.7 billion per year because it levies tariffs on the remaining
nonparticipants.
Taking the sum of climate-related gains and trade benets with the 4 percent
penalty tariff, the US would have a positive impact of $35.5 billion per year as a
participant. By contrast, the US would have an annual impact of −$8.6 billion as a
nonparticipant. The US would have an incentive of a net gain $44.1 billion per year
to join the agreement taking account only of its own national economic benet. In
this example, it is not even a close call on whether to participate.
The point of this simple example is to show that nations acting in their self-interest
would join a high-income club with a 4 percent tariff but would not join such a club
with a zero penalty tariff.
B. Basics of the Simulations
The central analysis undertaken here examines 44 different regimes for the Climate
Club. A regime in the following is dened as a combination of target carbon price
and tariff rate. The regimes analyzed here involve four different international target
carbon prices and 11 different tariff rates. The carbon prices are $12.5, $25, $50, and
$100 per ton of CO
2
. While other values have been used in the literature, this spans
T 1—E P N E
US is participant US is not a participant
Penalty
tariff rate Abatement Damages Trade
Net
benets Abatement Damages Trade
Net
benets
Net effect of
participation
0 percent
−11.9
10.7 0.0
−1.2 −0.3
7.3 0.0 7.0
−8.2
4 percent
−11.9
10.7 36.7 35.5
−0.3
7.3
−15.6 −8.6
44.1
Notes: This table provides an illustration of the economic effects of participation for the US with and without a pen-
alty tariff. The difference between the two lines is the impact of the penalty tariff. With a penalty tariff, the global
externality is effectively internalized, giving incentives for self-interested countries to participate in the Climate
Club. Figures in billions of 2011 US$ from the C-DICE model below for a global SCC of $25 per ton of CO
2
.
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the range of common targets, as discussed above. The tariff rates range from 0percent
(no penalty) to 10 percent in steps of 1percent. The upper end is chosen as one that
would begin to place a serious burden on both the trade and the enforcement systems.
For each of the calculations, I started with a base set of participants and then used
the evolutionary algorithm to nd a stable coalition (if one exists), with multiple
restarts and two different platforms to test stability. The results were sensible in all
cases and will be discussed below. This paper presents the results primarily in graph-
ical form. The numbers underlying the gures are contained in the online Appendix.
C. Results for Stability and Participation
The rst remarkable result is that virtually every regime produces a stable coa-
lition. (There are 6 unstable regimes out of 44. Results for these are averages of
quasi-stable coalitions as explained below.) From a theoretical point of view, there is
no obvious reason why the nonlinearities of participation would not lead to multiple
quasi-stable coalitions. The intuition is that the trade sanctions are powerful enough
to push countries into nonparticipation or participation.
The second question is whether the penalty structure is sufcient to induce par-
ticipation. In other words, how many of the 15 regions participate in the Climate
Club? Figure 3 shows the number of participating regions for different tariff rates
and different target carbon prices. The bars are arrayed from left to right by increas-
ing tariff rates.
The results are straightforward. No country joins the Climate Club without trade
sanctions (i.e., at a zero tariff rate). This key result conrms theory and observation.
For low target carbon prices, all or most countries join even for very low tariff rates.
For target carbon prices of $50 and $100 per ton, high penalty tariffs are required
to induce participation. With a $100 per ton target, full participation is not attained
even with the highest tested tariff rates. The participation rate rises monotonically
with the penalty tariff rate.
D. Results for Actual Carbon Prices and Abatement
The next question is the success of different arrangements in inducing abatement.
Figure 4 shows the level of the globally averaged carbon price for different regimes.
The results here are similar to those for participation but in effect weight the results
by region size.
For target carbon prices of $12.5 and $25, the treaty attains the goal of having the
global carbon price equal the target price (which is equal to the global SCC) even
at low tariff rates. For a $50 target carbon price, the target carbon price is almost
reached with a 5 percent tariff.
For a carbon price target of $100, the regime achieves no gain over a regime with
a target price of $50 until the highest tariff rate. Indeed, at medium tariff rates, we
see a Laffer-curve result as the actual global carbon price is lower with the $100
target than with the $50 target. The reason is that abatement is so costly in the $100
regime that most countries choose to accept the trade penalties. This then leads to
a low participation rate and a low actual penalty on nonparticipants because so few
countries are in the Club.
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While the analysis focuses on carbon prices, it is useful to translate these into
emissions reductions. Assuming 100 percent participation, the emissions reduc-
tions for the four target carbon prices ($12.5, $25, $50, and $100) are 9 percent,
18 percent, 36 percent, and 72 percent of baseline emissions. It is relatively easy to
attain emissions reduction rates of 50 percent with a Climate Club at 2011 levels
Tariff rates in bars:
0% at left to 10% at right
$12.5
14
12
10
8
6
4
2
0
$25 $50 $100
Number participating regions
Target price ($/tCO
2
)
F 3. N P R I T C P T R
Notes: This and the following gures have the following structure. The four sets of bars are the model results for
four different global SCCs, running from left to right as shown on the bottom. The 11 bars within each set are the
penalty tariff rates, running from 0 percent to 10 percent. Note that each set has zero participants for a 0 percent tar-
iff. The vertical scale here is the number of participants, while the following graphs show other important results.
$12.5 $25 $50 $100
60
50
40
30
20
10
0
Global average carbon ($t/CO
2
)
Tariff rates in bars:
0% at left to 10% at right
Target price ($/tCO
2
)
F 4. G A G C P T C P T R
Notes: This graph shows the global (weighted average) carbon price for each regime. Weights are actual 2011
industrial CO
2
emissions. The far left bar for each set is the noncooperative carbon price. For the interpretation of
the graph, see Figure 3.
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of income and emissions. To attain higher reduction rates (such as zero emissions)
would require improvements in technology so that it becomes economical to attain
these higher reduction rates at lower costs.
E. Economic Gains from the Climate Club
What are the economic gains from the Climate Club? The Club is designed to
increase economic welfare by overcoming free-riding. Figure 5 shows the net eco-
nomic gains for different regimes, while Figure 6 shows the regime efciency as
measured by the percentage of the cooperative gains that are realized.
First examining Figure 5, it is clear that the gains to cooperation are substan-
tial. Taking as an example the case of $50 per ton of CO
2
, the income gain from
noncooperative actions is $63 billion per year. The most successful cooperation
regimes have gains of $312 billion per year. (Again, all are scaled to 2011 output
and prices.)
Figure 6 shows the extent to which different regimes succeed in achieving the
potential gains from cooperation. At benchmark levels of $12.5 and $25 per ton,
the regime captures all of the potential gains for tariff rates of 3 percent or more.
Similarly, at the $50 per ton rate, the Club achieves virtually all the potential gains
with tariff rates of 5 percent or more. However, for the highest target carbon price,
the regime gets very little of the potential gains except at the highest tariff rates.
F. Trade Inefciencies
How large are the trade costs relative to the climate gains? Note to begin with
that there are no trade losses with full participation because there are no sanctions.
However, with partial participation, there will be efciency losses because of the tar-
iffs. Consider a regime with a low tariff and a low target carbon price, for example,
a 1percent tariff and a $25 per ton target carbon price. Here, there are six nonpar-
ticipants. The gains from the regime are $34 billion while the trade inefciencies
are $0.4 billion. At the other extreme, consider a $50 target price with a tariff of
6percent. For this regime, there are only two nonparticipants. The gains from the
club are $228 billion, while the trade inefciencies are $0.7 billion. In all cases, the
gains from cooperation far outweigh the trade losses.
G. To Join or Not to Join?
An interesting question is to determine which countries join and which stay out
of the Climate Club. On rst principles, the joiners are those with low abatement
costs, low carbon-intensity, high damages, and high trade shares. Table 2 shows the
percentage of the cases where a specic region participates.
A related question is, who gains and who loses from the Climate Club? The
answer depends upon the regime that is chosen. Figure 7 shows the net gains and
losses for four different sets of parameters for seven major regions. All major
regions gain from the club relative to the noncooperative outcome. In the entire set
of 40regimes and 15 regions, there are 69 (12 percent) cases where countries lose
relative to the noncooperative regime.
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400
350
300
200
250
150
664
100
50
0
Net income gain (billions, 2011$/year)
Target price
(
$
/
tCO
2
)
$12.5 $25 $50 $100
Tariff rates in bars:
0% at left to 10% at right
F 5. N E G D R
Notes: Gains are global total in 2011 US international $. In each case, the gain is relative to
zero abatement. The total includes abatement costs, damages, and trade inefciencies. Note
that the far left bar for each group is the gain in the noncooperative (zero-participation) out-
come. For the interpretation of the graph, see Figure 3. Note that the graph is truncated at $400
billion at the top, with the gure for highest benet regime shown.
F 6. P P G C A D
R
Notes: Bars show the global gain in each regime relative to the noncooperative outcome as a
percent of the difference between the 100 percent cooperative and the noncooperative result.
Gains are as dened in Figure 5. For the interpretation of the graph, see Figure 3.
Target price ($/tCO
2
)
$12.5 $25 $50 $100
Net income gain (% of potential)
100
80
60
40
20
0
Tariff rates in bars:
0% at left to 10% at right
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What explains the pattern of gains and losses? It is primarily determined by the
carbon-intensity of production and trade openness. South Africa and Eurasia are
the only countries showing a high fraction of losses because they have high carbon
intensity. They must either incur expensive abatement costs or pay dearly through
sanctions on their international trade. Countries with high damages (such as India)
show gains in all regimes.
T 2—P R R A 4 × 10 R
P T
Region Percent of regimes where participate
Canada 88
European Union 83
Mideast 75
Japan 73
Latin America 73
Southeast Asia 73
Sub-Saharan Africa 70
United States 70
ROW 70
Russia 63
China 63
Brazil 60
Eurasia 60
India 53
South Africa 45
All regions 68
Net benets (billions, 2011$/year)
30
47
25
20
15
10
5
0
Brazil Japan
EU US Russia India China
Tariff=3%; SCC=$12.5
Tariff=1%; SCC=$25
Tariff=3%; SCC=$25
Tariff=4%; SCC=$50
F 7. W L C C
Notes: Estimates show the gains for regions in four selected regimes. The gains are relative to the noncoopera-
tive regime and are in 2011 US international $ per year. The graph is truncated at $30 billion to magnify the scale.
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H. The Kyoto Protocol as a Failed Regime
One test of the approach used here is to examine the stability of the Kyoto Protocol.
This agreement included at the outset a substantial fraction of global emissions and
would, if it had broadened and deepened, have made a substantial contribution to
slowing the growth of emissions. However, it failed to gain new adherents, and some
of the members with binding commitments, particularly the US, dropped out.
Conceptually, the Kyoto Protocol was a climate club with no sanctions. To test
its coalition stability, I formed an initial club with only the original Annex I Kyoto
Protocol countries having binding emissions commitments with no penalties for
noncompliance (0 percent tariff). Starting with the original Kyoto coalition status, I
tested for coalition stability as described above.
All of the simulations collapsed to the noncooperative equilibrium. (See
Figure B-5 in the online Appendix for the simulations.) This might not be sur-
prising in light of the analysis above. However, recall that the analytical models
assume much more environmental and economic homogeneity than is seen in real-
ity. Perhaps some combination of damages, abatement costs, and carbon intensities
might lead to limited cooperation. However, for the modeling structure used here,
the Kyoto Protocol could not survive.
So the conclusion from this simple test is that the Kyoto Protocol was doomed
from the start. It did not contain sufcient economic glue to hold a cooperative coa-
lition together.
I. Regional Choice among Regimes
The present analysis focuses on the design of a Climate Club and the extent to
which different club designs succeed in inducing efcient participation and abatement.
In reality, treaties do not spring full-grown but emerge from a complicated diplomatic
process. The key steps are negotiation, ratication, implementation, and renegotiation.
The present study focuses on negotiation and assumes that once treaties are nego-
tiated, they are ratied and implemented (so there are no “cheap talk” negotiations).
Negotiations take place in two parts. The rst stage is treaty design, while the second
is the decision whether to participate. For the Kyoto Protocol, the United States was
deeply involved in treaty design but did not ratify the treaty. The last section explains
the US nonparticipation and the eventual collapse of the Kyoto Protocol as the failure
to design a treaty that would lead to widespread participation and renewal.
Turn next to the issue of treaty design. Suppose that climate negotiations consider
the different Climate Club regimes analyzed above. Which of the possible regimes
would be chosen? Consider these questions for a single case where the global SCC
is $25 per ton CO
2
and where the penalty tariff rate is 5 percent. Individual countries
have their own SCCs (say that the US SCC is $4 and India’s is $2), as well as their
national abatement cost functions. If countries are just scaled-up or scaled-down
replicas, all would prefer a $25 per ton target carbon price. In reality, countries
differ, so their preferred target prices will differ. Countries with high damages will
prefer a high target carbon price because they will benet from higher global abate-
ment; countries with high abatement costs will prefer a low target price because that
will reduce their abatement costs. The analog for health clubs is that people who
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desire minimal facilities want low dues, while those who prefer extensive coverage
choose more elaborate facilities with higher dues.
Let’s take an experiment where we ask each country for its preferred international
target carbon price (always keeping the global SCC at $25 and its regional distribu-
tion unchanged). Using the C-DICE model, calculate the equilibrium coalition for
each treaty price between $0 and $200 per ton. Then, examining the welfare effects
for each region, ask which treaty carbon price is optimal for the region. For the
example chosen, the impacts on net regional incomes are roughly quadratic for low
prices because all regions participate. Above $34 per ton, countries begin to drop
out, so the calculations become clouded by the effects of participation.
Figure 8 and Table 3 show the distribution of preferred target carbon prices for
regions where the global SCC is $25. The curves show on the vertical axis the fraction
of regions that would prefer an international target carbon price at or below the target
price on the horizontal axis. The noncooperative regime is shown at the upper left
with the circle marked “NC.” The curve to the left marked “preferred” shows the dis-
tribution of regional preferred rates (the distribution of rst choices). The line marked
“breakeven” shows the distribution of prices at which the country would be indifferent
between the target price and a zero price. The breakeven is close to twice the preferred.
The median preferred international target carbon price using GDP weights is $28
per ton, which is slightly above the global SCC. The median breakeven carbon price is
$48 per ton. An important nding is that all regions prefer a weak regime to the non-
cooperative regime. Even the least enthusiastic region (South Africa) would prefer a
target price of $18 per ton to the $3 per ton NC equilibrium. Where the negotiations
would actually settle is an important question beyond the scope of the present study.
J. Unstable Regimes
Of the 44 regimes, 6 displayed coalitional instability, and these can be easily under-
stood. For example, 3 came with a $50 international target carbon price and low tariff
rates. For example, with a tariff rate of 2 percent, the solution cycled around among a
small number of quasi-stable coalitions with an average of 2.9 participants. The other
instabilities came with the $100 per ton target price and high tariff rates. For example,
with $100 per ton target price and a penalty tariff of 9 percent, the coalitions cycled
with an average number of participations of 3.9 regions.
The instabilities arise because the gains from participation are close to equal in
these different midsized coalitions. Hence, the solution cycles among quasi-stable
coalitions as each outbids the others. None of the regimes degenerates to the
noncooperative equilibrium. Rather, they cycle among similar numbers of partici-
pants and levels of abatement.
Another potential source of instability would arise if the damage function has a cat-
astrophic threshold (which has not been modeled in the C-DICE model framework).
In the limit, assume that if emissions pass some quantity (below the emissions in
the NC equilibrium), then damages for each region are unlimited. There will be
multiple combinations of abatement by different regions that can stay under the cat-
astrophic threshold. It might be stable to a single country leaving, but would not be
stable to multiple countries entering and leaving. This example suggests that highly
nonlinear damages open up a different set of issues for regime design.
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K. Sensitivity Analysis
How sensitive are the results to alternative parameters? The sensitivity analyses are
presented in detail in the online Appendix, and the results are summarized here. I exam-
ine the impact of three different sets of parameters. The rst is alternative estimates of
the regional distribution of the global SCC. There are virtually no impacts of this sen-
sitivity test on the participation rate or on the actual global carbon price for any of the
regimes. The second sensitivity test is for the parameter of the abatement-cost function,
which is varied by a factor of 3. The results showed considerable sensitivity, especially
for global SCC of $50 and $100. The optimal tariff was varied over a range of a factor
of 6. This had virtually no impact on the outcomes. The main variable that affects the
outcome is the global social cost of carbon, as shown in the gures and tables.
Those familiar with the literature on climate-change economics will wonder what
happened to the discount rate, which is critical in virtually all areas. The answer is
that the discount rate will primarily affect the global and national SCCs, but has
little effect on the outcomes conditional on the SCCs. For example, a lower dis-
count rate will raise the estimated global SCC, perhaps from $12.5 to $25. This will
lead to a higher target carbon price, higher emissions reductions, and lower annual
Breakeven
Preferred
Target price ($/tCO
2
)
0
0
25
50
75
100
NC
20 40 60
Percent of countries preferring prices at or below target price
F 8. R P T C P
Notes: For a regime with a global SCC of $25 and 5 percent penalty tariff, regions will have differing preferences
on the international target carbon price. The lines show the percent of regions (on the left scale) that would be ben-
etted by a given target carbon price (shown on the horizontal scale). The point marked NC at the upper left is the
noncooperative carbon price. The line to the left shows the cumulative distribution of preferred carbon prices; the
line to the right shows the distribution of breakeven carbon prices. Because instabilities arise above $60, I have trun-
cated at that price for the breakeven.
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damages. There will be second-order effects through cost-of-capital factors, GDP,
and other economic variables. But a changed discount rate will affect the outcome
primarily through changes in the SCC.
VIII. Conclusion
The present study analyzes the syndrome of free-riding in climate agreements such
as the Kyoto Protocol and considers potential structures for overcoming free-riding.
This concluding section summarizes the basic approach and conclusions.
A. The Climate Club
The structure of climate change as a global public good makes it particularly
susceptible to free-riding. The costs of abatement are national, while the benets are
T 3—C P I T C P
(For global SCC of $25)
Region
Global target carbon price that
maximizes domestic welfare for SCC
$25/t CO
2
and penalty tariff
of 5 percent
South Africa 9
China 14
Eurasia 14
Southeast Asia 17
Russia 19
ROW 24
United States 28
Brazil 29
Latin America 31
India* 31
Canada* 34
Japan 38
European Union* 38
Sub-Saharan Africa 39
Mideast 40
Memorandum items ($ per ton CO
2
)
Global SCC 25
Average preferred price
GDP weights 28
Population weights 27
Median preferred price
GDP weights 28
Population weights 29
Notes: What international target carbon price would regions prefer when the global SCC is $25
per ton? For example, the US national welfare is highest when the target price is $28 per ton.
Countries with high damages and low abatement costs such as the EU prefer high target prices.
The table shows the optima without trade effects. The optima with trade effects have higher
country-preferred target carbon prices.
* Countries with multiple local optima.
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global and independent of where emissions take place. An additional complication
is that the abatement costs are paid today while most of the benets of abatement
come in the distant future. The present study shows, in a stylized model of costs and
damages, that the global noncooperative carbon price and abatement rate are pro-
portional to the Herndahl index of country size. This implies, given realistic data,
that the global noncooperative carbon price and control rate will be in the order of
one-tenth of the efcient cooperative levels.
Next consider possible mechanisms to combat free-riding and focus on a Climate
Club. It is generally assumed that the most effective approach will be to impose trade
sanctions on nonparticipants, and this is the route followed here. Most trade sanctions
rely on duties on carbon-intensive goods. For strategic, economic, and technical rea-
sons, this paper instead considers penalties that take the form of uniform ad valorem
tariffs levied by club participants on nonparticipants. In the analysis, the tariff rates
vary from 0 percent to 10 percent. It is further assumed that a climate treaty will
amend trade rules so that a penalty tariff conforms with international trade law and
retaliation by nonparticipants is prohibited.
This study assumes that countries adopt an international carbon-price target rather
than a quantity target as the policy instrument. The assumed target price ranges from
$12.5–$100 per ton CO
2
. In the experiments, the international target carbon price is
always set equal to the global social cost of carbon.
Individual countries are assumed to adopt climate policies that maximize their
national economic welfare. Welfare equals standard income less damages less
abatement costs less the costs of trade sanctions. I assume a one-shot static game,
but this can be interpreted as the stage game of a repeated game. The equilibrium,
described as a coalition Nash equilibrium, is a coalition of countries that is stable
against any combination of joiners and defectors. The equilibrium is calculated by
an evolutionary algorithm that tests each coalition against a random collection of
countries that can defect and join.
The study introduces a new approach called the C-DICE model (Coalition
DICE, or Coalition Dynamic Integrated Model of Climate and the Economy). It is
a 15-region model with abatement, damages, international trade, and the economic
impacts of tariffs. Using an evolutionary algorithm, the model can be used to nd
stable coalition Nash equilibria.
B. Qualications
I begin with qualications on the results that relate to the data and structural
parameters. The data on output, CO
2
emissions, and trade are relatively well mea-
sured. The global SCC is uncertain but can be varied as shown in the different
experiments. The national SCCs are also uncertain, but since they are all small
relative to the global SCC, their exact magnitudes are not critical for the ndings.
Other structural uncertainties relate to the abatement cost function and the optimal
tariff rate.
A related question is whether a trade-penalty-plus-carbon-price regime can oper-
ate in the future with the rising carbon prices that are generally associated with an
efcient climate-change program. Answering this question requires a multiperiod
coalition model and is on the agenda for future research.
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These results are presented in the spirit of an extended example used to clarify the
free-riding in international agreements rather than as a specic proposal for a cli-
mate treaty. A Climate Club of the kind analyzed here raises central issues about the
purpose of the global trading system, about the goals for slowing climate change,
about the justice of a system that puts all countries on the same footing, and about
how countries would actually negotiate such a regime. The dangers to the world
trading system of such a proposal are so important that they must be reiterated.
Today’s open trading system is the result of decades of negotiations to combat pro-
tectionism. It has undoubtedly produced large gains to living standards around the
world. A regime that ties a climate-change agreement to the trading system should
be embraced only if the benets to slowing climate change are clear and the dangers
to the trading system are worth the benets.
C. Results
One major result is to conrm that a regime without trade sanctions will dissipate
to the low-abatement, noncooperative (NC) equilibrium. This is true starting from
a random selection of participating countries. More interestingly, starting from the
Kyoto coalition (Annex I countries as dened by the Kyoto treaty) with no sanc-
tions, the coalition always degenerates to the NC structure with minimal abatement.
A surprising result is that the Climate Club structure generates stable coalitions
for virtually all sets of parameters. A few regimes produce quasi-stable coalitions
with similar numbers of participants.
A next set of results concerns the impact of different Climate Club parameters
on the participation structure. The participation rate and the average global carbon
price rise with the tariff rate. For the lowest target carbon prices ($12.5 and $25 per
ton), full participation and efciency are achieved with relatively low tariffs (2 per-
cent or more). However, as the target carbon price rises, it becomes increasingly
difcult to attain the cooperative equilibrium. For a $50 per ton target carbon price,
the Club can attain 90+ percent efciency with a tariff rate of 5 percent or more.
However, for a target carbon price of $100 per ton, it is difcult to induce more than
the noncooperative level of abatement.
Why is it so difcult to attain efcient abatement with high social costs of
carbon even with high penalty tariffs? The reason is that the gap between the
cooperative and the noncooperative equilibrium rises sharply as the global SCC
increases. Take the case of a large country like China or the United States. For
these countries the national SCC might be 10 percent of the global SCC. For a
global SCC and target price of $25 per ton, participation would require increas-
ing the domestic carbon price from $2.5 to $25, while a global SCC of $100
would require increasing from $10 to $100. Because abatement costs are sharply
increasing in the target carbon price, this implies that the costs of cooperation
become much larger as the target carbon price rises. On the other hand, the costs
of trade penalties associated with nonparticipation are independent of the global
SCC. So the national cost-benet trade-off tilts toward nonparticipation as the
international target carbon price rises.
Next examine the patterns of gains and losses. Here, measure the impact rela-
tive to the noncooperative equilibrium. Note as well that these results assume no
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transfers among countries. The benets are widely distributed among countries. The
only regions showing losses across several regimes are Eurasia and South Africa;
however, the losses are small relative to gains for other regions. There are no regimes
with aggregate losses.
Look at the distribution of gains and losses to determine whether a Climate Club
would be attractive to most countries relative to existing arrangements. All regions
would prefer a regime with penalties and modest carbon prices to a regime with
no penalties. Paradoxically, this is the case even for countries that do not partici-
pate. The reason is that the gains from strong mitigation measures of participants
outweigh the losses from the tariffs for nonparticipants as long as the tariff rate is
not too high. This powerful result indicates that a regime with sanctions should be
attractive to most regions.
D. Bottom Line
Here is the bottom line: the present study nds that without sanctions there is
no stable climate coalition other than the noncooperative, low-abatement coalition.
This conclusion is soundly based on public-goods theory, on C-DICE model sim-
ulations, on the history of international agreements, and on the experience of the
Kyoto Protocol.
The analysis shows how an international climate treaty that combines target car-
bon pricing and trade sanctions can induce substantial abatement. The modeling
results indicate that modest trade penalties on nonparticipants can induce a coalition
that approaches the optimal level of abatement as long as the target carbon price is up
to $50 per ton at current income and emission levels. The attractiveness of a Climate
Club must be judged relative to the current approaches, where international climate
treaties are essentially voluntary and have little prospect of slowing climate change.
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