Comments
on
Charles
Kolstad’s
“Equity,
Heterogeneity
and
IEAs”
Sco>
Barre>
Columbia
University
Charlie’s
paper
1.  In
a
simple
linear
model,
there
are
mulFple
equilibria.
2.  Equilibrium
condiFon
is
the
same
for
any
combinaFon
of
countries,
but
global
welfare
is
maximal
if
parFcipaFon
favors
the
“low
b”
countries.
3.  Why?
Because
each
country
can
abate
just
one
unit,
and
lots
of
these
countries
must
parFcipate
in
order
for
parFcipaFon
to
be
collecFvely
raFonal.
Examples
•  Suppose
b
=
1,
c
=
29.5,
and
N
=
100.
•  Then
k*
=
30.
Signatories
get
a
payoff
of
$.50.
Non‐
signatories
get
a
payoff
of
$30.
Global
payoff
is
$2,115.
•  Full
cooperaFon
yields
global
payoff
of
$7,050.
•  Suppose
b1
=
0.333,
b2
=
7,
c
=29.5,
N1
=
90,
and
N2
=
10.
Then
there
are
two
agreements
consisFng
of
one
type
of
country:
•  “Type
1”
agreement
consists
of
k*
=
89.
Signatories
get
$0.167.
Non‐signatories
get
$29.67
(for
sole
type
1
country)
and
$623
(type
2).
Global
payoff
is
$6,274.53.
•  “Type
2”
agreement
consists
of
k*
=
5.
Signatories
get
$5.50.
Non‐signatories
get
$1.67
(type
1)
and
$35
(type
2).
Global
payoff
is
$352.80.
Commentary
•  Is
Charlie’s
result
intuiFve?
No,
but
the
qi ∈{0,1}
assumpFon
that
is
plainly
wrong.
•  Imagine
that
the
bs
were
proporFonal
to
emissions.
States
with
a
high
b
also
have
high
emissions.
Then
the
above
result
would
dissolve.
An
agreement
with
few
parFes,
each
of
which
abates
a
lot
would
be
equally
beneficial
as
an
agreement
with
many
parFes,
each
of
which
abates
just
a
li>le.
Commentary
(2)
•  Another
problem
with
this
model
is
that
as
c
falls,
the
equilibrium
parFcipaFon
level
falls.
Why?
Because
c
is
a
threshold.
•  Note,
however,
that
constant
marginal
cost
is
appropriate
for
some
technologies
(air
capture).
•  Also,
results
can
be
sensiFve
to
modeling
assumpFons.
For
example,
in
a
repeated
game,
assuming
“weak
collecFve
raFonality,”
parFcipaFon
can
be
varied,
with
greater
“breadth”
coming
at
the
cost
of
lesser
“depth.”
Commentary
(3)
•  Finally,
it
must
be
remembered
that
Charlie
is
showing
what
would
happen
if
equilibrium
selecFon
were
to
favor
maximizaFon
of
the
aggregate
payoff.
•  If
it
were
guided
instead
by
equity
principles
(Berlin
mandate?),
the
result
would
differ.
Why
is
cooperaFon
difficult?
•  UN
process
•  But
different
processes
were
pursued,
and
they
all
failed.
•  The
UN
process
worked
previously
(KP),
and
the
outcome
sFll
failed.
•  Hard
to
reach
agreement
on
obligaFons
–  “Comparability
problem.”
–  Equity
(common
but
differenFated
responsibiliFes).
•  But
this
may
be
due
to
the
approach,
as
there
are
plenty
of
examples
of
success
(e.g.,
UN
financing)
•  Enforcement
of
obligaFons
–  ParFcipaFon
and
compliance.
•  No
remedy
offered.
IEAs:
Summary
of
the
literature
•  IEAs
cannot
help
much
unless
–  N
small
–  Can
leverage
cooperaFon
•  Trade
restricFons
•  Technology
interdependence
•  If
countries
are
slightly
asymmetric,
these
results
carry
through.
•  If
countries
are
extremely
asymmetric,
cooperaFon
may
be
helped.
–  Low
benefit
countries
essenFally
“commi>ed”
not
to
abate.
High
benefit
countries
can
then
cooperate
to
“buy”
their
cooperaFon.
Heterogeneity
can
affect
the
gains
to
cooperaFon
•  Suppose
π i = biQ − cqi where Q = ∑ qi and qi ∈{0,1}
i
•  In
Charlie’s
model,
q
represents
polluFon;
here
it
is
abatement.
•  Nash
equilibrium:
If
countries
are
idenFcal
with
bi < c, then qi = Q * = 0.
•  Full
cooperaFon:
if
countries
are
idenFcal
with
b = ∑ b / N and bN > c > b
i
•  then
FC
i
q
= 1; Q
FC
= N.
Heterogeneity
can
affect
the
gains
to
cooperaFon
(2)
•  Suppose
N1 type 1 countries and N 2 type 2 countries with
b1 N1 + b2 N 2
b2 > c > b1 ,
= b < c, and b1 N1 + b2 N 2 > c.
N1 + N 2
•  Nash
equilibrium:
•  Full
cooperaFon:
Q* = N 2
qiFC = 1; Q FC = N1 + N 2
•  Conclusion:
heterogeneity
may
help
non‐
cooperaFon.
A
different
specificaFon
•  Suppose
c 2
π i = biQ − qi where Q = ∑ qi
2
i
•  Nash
equilibrium
bi
q =
c
*
i
•  The
global
payoff
of
abatement
•  FC
i
q
=
∑b
i
i
c
c
Π = ∑ biQ − ∑ qi2
2 i
i
•
Heterogeneity
and
the
gains
to
cooperaFon
Let
b = ∑ b N
i
i
•  Nash
equilibrium
bi bN
Q =∑ =
c
i c
*
•  Full
cooperaFon
Q FC
b bN 2
=∑ =
c
i c
•  Here,
heterogeneity
does
not
shrink
the
gap
between
the
non‐cooperaFve
and
full
cooperaFve
outcomes.
Heterogeneity
and
the
self‐enforcing
IEA
•  However,
k*
=
3,
for
an
agreement
consisFng
of
only
type
1
or
type
2
countries.
•  In
this
case,
an
agreement
comprising
only
“bigger,
richer”
sustains
more
abatement.
•  It
also
sustains
a
higher
global
net
benefit
than
an
agreement
consisFng
of
3
“smaller,
poorer”
countries.
•  By
Charlie’s
logic,
the
former
agreement
should
be
“selected.”
•  But
the
main
point
is
that,
for
this
specificaFon,
and
for
large
N,
an
agreement
can’t
help
very
much.