Download Self Enforcing International Environmental Agreements

Self Enforcing International
Environmental Agreements
Barrett 1994
Oxford 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 QcQo 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 solve
maxqs 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
Re signatories: no one who
has signed the IEA wants to
renege:
signatory i‘s payoff if it
rejects the agreement
(and all other
signatories continue to
abide by the IEA)
signatory i‘s
payoff if it
abides by the
IEA
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 Non-signatories: No one who has
failed to ratify wants to join
non-signatory k‘s
payoff if remains
a non-signatory
non-signatory k‘s payoff
if it starts abiding by the
IEA (and all incumbent
signatories continue to
abide by the IEA
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=1/4
For 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 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 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 selfenforcing 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 oneshot 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
cheap