- Oslo Centre of Research on Environmentally friendly Energy
The Trade-off between Intraand Intergenerational Equity in
Climate Policy
Snorre Kverndokk
Eric Nævdal
Linda Nøstbakken
Stiftelsen Frischsenteret for samfunnsøkonomisk forskning
Ragnar Frisch Centre for Economic Research
www.frisch.uio.no
1. Equity aspects of climate policy
• Even if everybody agreed on the natural science
background, feedbacks to the economy, future
emissions scenarios and the costs of abating (no
uncertainties), it is still hard to agree on the optimal
GHG reductions.
• The reason is equity aspects
• Intragenerational equity: How should we distribute
the burden within a generation (present or future)?
– Who would suffer from inaction (climate change)
– Who would suffer from action (mitigation)
• Intergenerational equity: How should we distribute
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the burdens across generations?
1. Equity aspects of climate policy (cont.)
• The distribution problems are often assumed
autonomous, but choices that affect the
intergenerational distribution also have impacts on
the intragenerational distribution and vice versa:
– A high discount rate reduces action and increases damage.
The poor regions will suffer more than the rich in the
future: higher intragenerational inequality
– Lowering global income inequality may induce higher
economic growth in LDCs. This may again give higher GHG
emissions
• This paper aims to close this gap: What is the optimal
climate policy when both equity aspects are taken into
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account?
2. Framing a social contract: The basics
of the model
• Two regions: North and South. Population set equal
to 1 in both regions
• Welfare of a representative consumer (Fehr-Schmidt),
U r ,t  u  cr ,t , St    max  ck ,t  cr ,t , 0    max  cr ,t  ck ,t , 0  , r , k  n, s, r  k
α ≥ β ≥ 0:
u  c , S 
lim

cu=
consumption
c
,
S


c
U (c , S )
S = global environmental quality
0
c S
is increasing and concave in c and S , and has the
property:
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We assume that consumption and environmental
r ,t
r ,t
t
cr ,t  0
t
r ,t
r ,t
r ,t
t
t
2. Framing a social contract: The basics
of the model (cont.)
• Production of macro good:
Yr ,t ( K r ,c ,t , K r , d ,t )  Yr ,c ,t ( K r ,c ,t )  Yr , d ,t ( K r , d ,t ), r  n, s
Investments:K  1    K  I , r  n, s, j  c, d ,
• Initially North has more capital of both types:
j  c, d
K
 K , for
Yr ,t  cr ,t  I r ,c ,t  I r ,d ,t , r  n, s
• Resource constraint:
This means there are no direct transfers. Consider
transfers later.
1  0
  S use
 1  of
   Kcapital:
 S dirty
• Pollution followsSfrom
r , j ,t 1
n , j ,0
j
r , j ,t
r , j ,t
s , j ,0
t 1
t
r , d ,t
r
– Quality of the climate:
,
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3. What comes out of the contract?
• Optimization problem:
max



t

  u  cr ,t , St    max  cn,t  cs,t , 0   max  cs,t  cn,t , 0
cnt ,cst , Knct 1 , Ksct 1 , Kndt 1 , K sdt 1 , St 1 t 0


r
given the production functions, resource constraints
and the dynamics of the environmental quality.
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3. What comes out of the contract?
c c
• First order conditions include
(for
n ,t
u (cn ,t , St )
cn ,t
   n ,t
cn,t  cs ,t 
cn,t  cs ,t 
s ,t
u(cs ,t , St )
cs ,t
u(cs ,t , St )
cs ,t
):
   s ,t
     0
   s ,t
 Yr ,t 1  K r ,c ,t 1 , K r ,d ,t 1 

 1   d   t 1   1r ,t , r  n, s
r ,t 1 
K r ,d ,t 1


 Yr ,t 1  K r ,c ,t 1 , K r ,d ,t 1 

 1   c    1r ,t , r  n, s
r ,t 1 
K r ,c ,t 1



r
u (cr ,t 1 , St 1 )
St 1
  1t  1    t 1
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3. What comes out of the contract?
• Some characteristics of the contract:
– In the long run, the socially optimal consumption levels and
capital stocks of the two regions will converge independently
ofinequality
 , t
aversion.
–
: The shadow price of the resource constraint is higher
in
than in the North along the optimal path. The
K the
 K South
, t
difference decreases over time.
– c  c , t: The North carries most of the climate burden by
holding more clean capital than the South.
–
: The consumption level of the South never exceeds that
of the North, independently of inequality aversion.
n ,t
s ,t
n , c ,t
n ,t
s , c ,t
s ,t
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4. How inequality aversion affects the
social contract
• North affects the South through consumption and
impacts on the environment.
• Stronger inequality aversion will generally increase
consumption in the South and reduce consumption
in the North compared to the case with less or no
c
S 
1  
inequality
aversion.
1
u



c
S 
1  


s ,t
n ,t


n ,t
u
cc
n ,t
 

 1  uncs,t
t
 

s ,t
uscc,t  
cs
s ,t
t
 
• Trade-off between inequality now and later. Stronger
inequality aversion may increase consumption
inequality in some periods.
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4. How inequality aversion affects the
social contract (cont.)
Figure 1. Consumption paths in North and South
under different degrees of inequality aversion
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4. How inequality aversion affects the
social contract (cont.)
• How does this affect investments?
– A change in consumption today means a change in
investments
– The only way to achieve equity in the long run is by
shifting investments toward more clean capital in the
North, and more dirty capital in the South: Dirty capital is
more productive.
– This gives higher productivity in the South and lower in
the North.
– Also, the North affects South positively by investing in the
environment.
– However, this will give higher pollution in the South and
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lower pollution in the North.
4. How inequality aversion affects the
social contract (cont.)
• Figure 2. Time paths of clean and dirty capital
under different degrees of inequality aversion
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4. How inequality aversion affects the
social contract (cont.)
• But how does inequality aversion affect the climate?
–
*
*
K

K
n
,
d
r
,d
In the long run,
, and the environmental quality is
not affected by inequality aversion
– In the short run, the dirty capital stock is lower in the North
and higher in the South → ambiguous impacts on S
• Discounting
• Inequality matters relatively

more for higher
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4. How inequality aversion affects the
social contract (cont.)
• To summarize, we should sometimes let the rich
(poor) region invest more (less) today to temporarily
reduce equality at the cost of more inequality in the
future.
• This is a result of discounting. The less weight we put
on future generations relative to those living today
(high discount rate), the stronger the incentive to
immediately eliminate inequality between people
living today through investment.
• Our analysis may justify the claim made by
developing countries; if we all care about equality,
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we may have to sacrifice environmental quality
in the
5. But what if a contract is not possible?
• Each country perceives that its impact on the
dynamics of global environmental quality is
approximately zero.
• The Lagrangian for region r:
   u(c , S )   max  c  c ,0    max  c  c ,0  
L

r , BAU
t
r ,t
t 0
t
r ,t
k ,t
k ,t
r ,t

r ,t Yr ,t ( Kr ,c,t , Kr ,d ,t )  Kr ,c,t 1  1   c  Kr ,c,t  Kr ,d ,t 1  1   d  Kr ,d ,t  cr ,t 
• From
u '   FOCs:

r ,t  r ,t 1  MPr ,c ,t 1  1   c 
u 'ct   s  s ,t
r ,t  r ,t 1  MPr ,d ,t 1  1   d 
ct
n
n ,t
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5. But what if a contract is not possible?
(cont.)
• Some characteristics of the BAU paths:
– Consumption and capital stocks in the two regions converge
c the
c same
t
to
levels.
–
: The consumption level of the South never exceeds that
of the North, independently of inequality aversion.
– Both capital stocks in the North are higher or equal to the
capital stocks in the South.
– The dirty technology does not have to be more productive
than the clean technology.
n ,t
s ,t
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5. But what if a contract is not possible?
(cont.)
• The effects of inequality aversion:
– Under BAU, the North can no longer affect the marginal
utility of the South, as each country takes the quality of the
environment as given.
– The only possibility is to reduce consumption.
– This would lead to higher capital accumulation of both
types (no point of substitute towards clean capital).
– At some stage the higher capital has to be consumed:
Temporary increase in consumption.
– For South: Opposite effects.
– Thus: Inequality aversion generally increases emissions in
the North and reduces emissions in the South.
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5. But what if a contract is not possible?
(cont.)
• Compare to the social contract, the representative
consumers in BAU do not take into account
– The global environment (S)
– Impacts on the other regions inequality aversion, the
consumption externality,
   n   s 
• Less incentive to reduce consumption in North in
BAU → more dirty production
• Opposing incentives for the South:
– Inequality aversion: Lower incentive for dirty production in
BAU
– Global environment: Higher incentive for dirty production
in BAU
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5. But what if a contract is not possible?
(cont.)
• The stock of dirty capital will be lower under the
social contract in the North, but not necessarily in the
South
• Thus, inequality aversion will lead to a reduction in
emissions in the North under the social contract
compared to business-as-usual, while for the South
the result is ambiguous, and emissions may actually
be higher under the social contract.
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5. Extensions: Direct transfers under the
social contract
International transfers:
• A transfer of τt every period from north to south: τt ≤
M.      ,   0 if binding
n ,t
t
s ,t
t
• If M is not binding (unlimited transfers), we get a a
bang-bang solution
– Equalize differences in consumption at once regardless of
inequality preferences
• If M is binding (limited transfers), we get a transfer of
τt = M in every period (the Most Rapid Approach
Path)
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– Conclusions hold, but effects are weaker as the South does
5. Extensions: Direct transfers under the
social contract (cont.)
International loans:
• Transfers have to be paid back: Intertemporal budget
 0
constraint:

t 0
t
t
 s ,t  n ,t  
 MU
c
s ,t
 MUnc,t   2  
• New FOC:
• This means that consumption never converges:
• Impacts of inequality aversion still holds, but again
effects are weaker. More effect of inequality aversion
in the long run.
• Shorter repayment period gives convergence, but
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more inequality earlier.
6. Extensions: Local pollution under the
social contract
u c , D , S 
• Assume:
 u c , D
utility is falling in D, and
c D
• D  K
• This gives:
r ,t
r ,t
t
2
r ,t
r ,t
r ,t
l
r ,t
r ,t
, St 
0
 2u  cr ,t , Dr ,t , St 
Dr2,t
0
r , d ,t
– An additional cost of using Kd
– Both regions will use less of the dirty capital, North will use
more clean capital initially
– This slows down the speed of which the South catches up.
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7. Final remarks
• Let us compare our results to the Kyoto Protocol
– The division between Annex B and non-annex B is justified:
Poor countries should not necessarily have commitments
– The Protocol has a mechanism that supports capital
transfers from North to South; CDM, but not other direct
transfers
– Direct transfers are no planned in an extensive amount
from 2020: Climate finance
But:
– Debt remittance is not included in the Protocol
– Poor countries should take a larger part of the burden
when they become richer. This is not included in the
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Protocol