Equity, Heterogeneity and
International Environmental
Agreements
Charles D. Kolstad
University of California, Santa Barbara
and
RfF and NBER
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IEAs
• Groups of countries voluntarily band
together to abate pollution
• No overarching authority to enforce
• With global public good, often better to be
on the outside looking in (better in fringe)
• Some theoretical literature on forming
IEAs
• Some experimental literature on voluntary
coalitions to provide environmental goods
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Typical Questions
• How big will an IEA be (# participants)?
• How much better off is everyone as a result of
IEA (as opposed to no cooperation)?
• How can IEAs be structured to strengthen and
increase welfare?
• Does uncertainty undermine or strengthen IEAs?
• How can lessons be brought to bear on real
IEAs, such as Kyoto/FCCC?
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Motivation for Today’s Talk
• We are gathered here to consider ―Distributional
Aspects of Energy and Climate Policy‖
• Internationally, does the unequal distribution of
benefits and costs of climate policy matter?
• [Homogeneity = equity; heterogeneity = unequal.]
• Do differences among countries (heterogeneity of
countries) promote or retard the formation of
IEAs?
• Does heterogeneity promote global welfare in
presence of IEAs?
• Can theoretical results be brought to bear on real
problems?
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Some prior results
• i=1,…,N countries
• Payoff: Πi = qi – γQ
– Where: qi = emissions (0 or 1); Q = total emissions by all
countries; γ = marginal damage from emissions relative
to abatement costs (costs normalized to 1) (γ < 1)
• Two-stage game: countries play a IEA membership
game followed by an emissions game
• Unique IEA with n*=1/γ members [higher γ 
smaller IEA]
• Aggregate payoff with IEA = - (Nγ - 1)2/γ [higher γ
 lower payoff]
• IEA size and payoff inversely related
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Uncertainty and Heterogeneity
• Hypothesis: if you are a country, not knowing
your γ can facilitate cooperation (Young)
• Three stage game
– Membership game (uncertain about type)
– Uncertainty resolved
– Emissions game (certainty about type)
• Theory: Uncertainty ambiguous – can increase
size of an IEA or can be neutral, depending on
parameter values
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Experiments
(from Burger & Kolstad, 2009)
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Coalition Size
6
5
Coalition (MPCR = 0.6)
Coal. w /uncert. (MPCR = 0.6)
4
Coalition (MPCR = 0.3)
Coal. w /uncert (MPCR = 0.3)
3
2
1
0
0
5
10
Period
15
20
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Experiments
(from Burger & Kolstad, 2009)
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Theory tells us higher
MPCR (γ) leads to
smaller coalitions
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Coalition Size
6
5
Coalition (MPCR = 0.6)
Coal. w /uncert. (MPCR = 0.6)
4
Coalition (MPCR = 0.3)
Coal. w /uncert (MPCR = 0.3)
3
2
1
0
0
5
10
Period
15
20
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Simple Theoretical Model of
Heterogeneity
• Two types of countries, 1 and 2
– γ1 < γ2
– Number of countries: N1, N2 with N=N1+N2
• Coalition: (n1,n2)
• Coalition emission decision:
– Abate: W=-n1[γ1(N-n1-n2)] – n2[γ2(N-n1-n2)] =
-(n1γ1 + n2γ2) (N-n1-n2)
– Pollute: W= (n1+n2) – n1γ1N– n2γ2N
• Abate weakly preferred iff n1γ1 + n2γ2 ≥ 1
•  Stable coalitions where n1γ1 + n2γ2 = 1
• Fringe always pollutes
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Graphically
n1γ1 + n2γ2 = 1 (locus of stable coalitions)
n2
Optimal for coalition to abate
and for individual countries to
defect to fringe.
Optimal for coalition to pollute
n1
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Equilibrium Refinement
• Too many possible coalitions
• Focus on the one which gives the greatest
overall welfare (in aggregate for all
countries)—not a trivial refinement!
• W = - (N-n1-n2) (N1γ1 + N2γ2 - 1)
• Maximize subject to n1γ1 + n2γ2 = 1
•  n1 as large as possible; typically, n2=0
•  n1 = 1/γ1
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Add heterogeneity
• Assume
γ1 = γ – δ/N1
γ2 = γ + δ/N2
• For δ≥0, N1 γ1 + N2 γ2 = N γ
• ie, we can adjust the heterogeneity (δ),
keeping the weighted average γ constant
• Question: what happens as δ is increased
from 0?
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Comparative Statics
• Assume case that coalition is only type 1
countries
• Increase in δ increases size of IEA
• Welfare W = [N-1/(γ - δ/N1)] (Nγ - 1)
• Differentiate W wrt δ and dW/dδ >0
•  increased heterogeneity leads to:
– Increased IEA size
– Increased aggregate welfare for society
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An ―Application‖
• US Govt Proposed Fuel Economy Reg
– Social cost of carbon = $20/ton, global; $1.20
per ton for US
• EPA analyses of GHG legislation is US
Congress yields $13/ton marginal cost of
abatement
•  γ =0.09  n*=11
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Reality doesn’t fit the theory but…
• Think of two sets of countries
– Developed and developing
• Developing countries
– Lower abatement cost
– Lower marginal damage
– γ?
• Suggestion of theory is that we are better off
having two blocs of countries rather than a set of
homogeneous countries with same average γ
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Conclusions
• Heterogeneity does seem to matter to
formation of IEAs
• Heterogeneity appears to favor larger IEAs
and higher welfare
• Further work needs to be done
– Refining theoretical model
– Developing empirical implications
– Testing theory (experimentally?)
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