Self Enforcing International Environmental Agreements

Barrett 1994Oxford Economic Papers

Question

• Can collective action be sustained?• Specifically, can countries devise multilateral

environmental agreements that– include all affected members– maximize collective welfare– are “Self-enforcing?”

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

Model

• i=1,…,N identical countries• Country i’s net benefits (π) depend on current

own (qi) and total (Q) abatement:

πi = b[aQ-Q2/2]-cqi2/2 (1)-(2)

– where Q= Σj=1Nqj =global abatement

– a,b,c are positive parameters– Define Π = Σj=1πj as global welfare

Cooperative Solution

• Choose {qj}j=1,…,n to maximize Π

• Denote cooperative abatement levels as qc, Qc

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

Compare

• Qo is clearly less than Qc provided N>1

• Each country is ignoring the benefits to the other N-1 countries from its own abatement .

Gains from Cooperation• Πc-Πo=difference 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 won’t 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 Πc-Πo are large

Self-Enforcing IEAs

• Suppose only a fraction, α, of countries sign/ratify the IEA– Nα signatories– N[1-α] non-signatories– Let qn, Qn denote abatement from non-signatories

• Qn=[1-α]Nqn

– qs, Qs … from signatories

Non-signatories

• Have Nash reaction functions:– choose qi to maximize πi subject to Nash

conjectures about all other abatement efforts

Signatories

• Signatories solvemaxqs αNπs s.t. equation 5

…

A Self-Enforcing IEA• An agreement with αN signatories and [1-α]N

nonsignatories is self-enforcing if no signatories want to become non-signatories and no non-signatories want to become signatories

Mathematically

signatory i‘s payoff if it abides by the IEA

signatory i‘s payoff if it rejects the agreement (and all other signatories continue to abide by the IEA)

non-signatory k‘s payoff if it starts abiding by the IEA (and all incumbent signatories continue to abide by the IEA

non-signatory k‘s 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 defector’s own costs.

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

Mechanism: although other signatories increase their abatement in response, the recruit’s costs rise even faster than its benefits

Digression

• Barrett’s (1994) definition of Self-Enforcement isn’t 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.

Using Barrett’s Self-Enforcement Criterion

Numerical example: N=10, a=100, b=1, c=1/4For any α>.4, a signatory would do better by defecting and earning πN(α-.1); for any α <.4, a non-signatory would do better by acceding and earning πS(α+.1)

• Barrett provides a set of simulations• Observes the following:

– the number of coalition members is decreasing in γ=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 doesn’t lead to much additional abatement (since noncooperative abatement is also high), so the gains from cooperation aren’t very high

– if instead γ is large, then few join

Gloomy PictureProposition 1For 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 γ 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.

Silver Lining?

• When N is small, it’s 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

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 you’ve ever abated less than the cooperative level in the past---aren’t necessarily renegotiation proof

• and if countries can renegotiate the punishments, then it’s hard to prevent defections in the first place

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 env’l problem dealt with by the Montreal

Protocol was quite different from climate change• everyone knew that phasing out CFCs was going to be pretty

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