Self Enforcing International Environmental Agreements

1
Self Enforcing International Environmental
Agreements

• Barrett 1994
• Oxford Economic Papers

2
Question

• Can collective action be sustained?
• Specifically, can countries devise multilateral
  environmental agreements that
• include all affected members
• maximize collective welfare
• are Self-enforcing?

3
Assumptions

• Countries are identical
• Net benefit functions are common knowledge
• Pollution abatement is only choice variable
• Abatement levels instantly and costlessly
  observed
• No accumulation
• Cost functions are independent

4
Model

• i1,,N identical countries
• Country is net benefits (p) depend on current
  own (qi) and total (Q) abatement
• pi baQ-Q2/2-cqi2/2 (1)-(2)
• where Q Sj1Nqj global abatement
• a,b,c are positive parameters
• Define ? Sj1pj as global welfare

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Cooperative Solution

• Choose qjj1,,n to maximize ?
• Denote cooperative abatement levels as qc, Qc

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Non-cooperative (Nash) abatement

• Each country chooses own abatement qo so as to
  maximize own net benefits, taking as given the
  behavior of the other countries

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Compare

• Qo is clearly less than Qc provided Ngt1
• Each country is ignoring the benefits to the
  other N-1 countries from its own abatement .

8
Gains from Cooperation

• ?c-?odifference in global welfare under
  cooperation and non-cooperation
• when N is large (as with climate change), then
• when b is large and c small, countries would
  abate a lot unilaterally and so the net gains
  from cooperation are small
• when b is small and c large, countries wont
  abate much even when there is cooperation
• if c and b are approximately equal but small,
  then even though Qc-Qo is large, the gains from
  cooperation will be small
• if c and b are approximately equal and large,
  then both Qc-Qo and ?c-?o are large

9
Self-Enforcing IEAs

• Suppose only a fraction, a, of countries
  sign/ratify the IEA
• Na signatories
• N1-a non-signatories
• Let qn, Qn denote abatement from non-signatories
• Qn1-aNqn
• qs, Qs from signatories

10
Non-signatories

• Have Nash reaction functions
• choose qi to maximize pi subject to Nash
  conjectures about all other abatement efforts

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Signatories

• Signatories solve
• maxqs aNps s.t. equation 5

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A Self-Enforcing IEA

• An agreement with aN signatories and 1-aN
  nonsignatories is self-enforcing if no
  signatories want to become non-signatories and no
  non-signatories want to become signatories

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Mathematically
Re signatories no one who has signed the IEA
wants to renege
Re Non-signatories No one who has failed to
ratify wants to join
signatory is payoff if it abides by the IEA
signatory is payoff if it rejects the agreement
(and all other signatories continue to abide by
the IEA)
non-signatory ks payoff if it starts abiding by
the IEA (and all incumbent signatories continue
to abide by the IEA
non-signatory ks payoff if remains a
non-signatory
Intuition upside of defecting is that own
abatement costs fall. Downside is that remaining
signatories reduce own abatement too. The first
condition in (8) requires that qs is more
responsive to defection than are the defectors
own costs.
Mechanism although other signatories increase
their abatement in response, the recruits costs
rise even faster than its benefits
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Digression

• Barretts (1994) definition of Self-Enforcement
  isnt the only (or best) measure of stability
• Others have argued that an agreement must stand
  up to defection by a subset of members who might
  want to form their own agreement (and earn higher
  net welfare), possibly in conjunction with some
  non-signatories to the IEA in question
• see, e.g., Heal 1992.

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Using Barretts Self-Enforcement Criterion
Numerical example N10, a100, b1, c1/4 For
any agt.4, a signatory would do better by
defecting and earning pN(a-.1) for any a lt.4,
a non-signatory would do better by acceding and
earning pS(a.1)
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• Barrett provides a set of simulations
• Observes the following
• the number of coalition members is decreasing in
  ?c/b
• thus, the lower the cost to benefit ratio, the
  more countries there will be in the coalition
• but, recall from before that, when b is large,
  cooperation doesnt lead to much additional
  abatement (since noncooperative abatement is also
  high), so the gains from cooperation arent very
  high
• if instead ? is large, then few join

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Gloomy Picture

• Proposition 1
• For global environmental problems characterized
  by equations (1) and (2), the self-enforcing IEA
  will be signed by a lot of countries---each
  undertaking substantial abatement---when ? is
  small, but under these circumstances the IEA
  increases global net benefits by very little
  compared with the noncooperative outcome.
• Cooperation would increase net benefits
  substantially when c and b are both large, but
  under these circumstances the self-enforcing IEA
  cannot sustain a large number of signatories.

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Silver Lining?

• When N is small, its easier to get close(r) to
  the cooperative solution
• does this mean that we could get closer to a
  global solution on climate change if there were
  more regional organizations with law-making power
  (like the EU?)
• problem unless the regional organization has the
  power to punish sub-units, then defection problem
  resurfaces

19
Repeated Game

• Folk theorem any cooperative solution of a
  one-shot game can be sustained as a sub-game
  perfect equilibrium of an infinitely repeated
  (trigger-strategy) game if the discount rate is
  low enough
• Problem grim-trigger strategies---I abate at
  Nash level from now until eternity if youve ever
  abated less than the cooperative level in the
  past---arent necessarily renegotiation proof
• and if countries can renegotiate the punishments,
  then its hard to prevent defections in the first
  place

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Conclusions

• when N is large, is hard to get self-enforcing
  IEAs with more than a few signatories
• this problem---that the equilibrium number of IEA
  signatories is only 2 or 3---persists in IEA
  models today
• Montreal Protocol on Ozone Depleting Substances
  is usually heralded as a success in international
  environmental diplomacy
• but the envl problem dealt with by the Montreal
  Protocol was quite different from climate change
• everyone knew that phasing out CFCs was going to
  be pretty cheap