Carbon prices for the next thousand
years
Reyer Gerlagh
Tilburg
Matti Liski
Aalto Helsinki
SURED 2012
CESifo WP 3855
Instruments to curb global warming: recent developments
Paris, 4 Oct 2012
Gerlagh-Liski
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The Problem
• Climate is a persistent asset, bar none:
◦ changes in stocks have effects over centuries or
possibly millennia
• Central feature in climate-economy models (“integrated
assessment models”, IAMs)
• But: IAM’s ignore the far-distant impacts when
discounting respects the shorter-term revealed
preferences
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This paper
Premise 1: shorter-term revealed preferences should be respected
• discounting as revealed by the market
◦ Nordhaus (1994,2007), Schelling (1999)
• shorter-term decisions consistent with historical data
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Premise 2: the evidence that far-distant future is treated
differently should also be respected
• Weitzman (2001) surveyed 2,160 economists for their
“best estimate of the appropriate real discount rate to be
used for evaluating environmental projects over a long time
horizon”
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years
discount rate
immediate future
1−5
4
near future
6 − 25
3
medium future
26 − 75
2
distant future
76 − 300
1
far-distant future
301−
≈0
Table 1: Weitzman’s results
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• Some studies invoke “similarity” (Rubinstein 2003, Karp
2005)
◦ a utility gain after 400 years looks the same as after 450
years
◦ no additional discounting from the added 50 years
◦ but in the near term: 50 years delay commands large
discounting
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This paper
• We reconcile distinct short- and long-term time
preferences in a climate-economy model
⇒ hyperbolic time discounting
• The general equilibrium (IAM) implications unexplored
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• The objective: to assess this mechanism in a detailed
climate-economy model
◦ Nordhaus tradition, following Golosov, Hassler, Krusell,
Tsyvinsky, 2011
◦ climate delays explicit (1000 years will play a role...)
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1. Result: equilibrium carbon prices exceed
the Pigouvian level by multiple factors!
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2. Result: Stern can be reconciled with realistic
macroeconomic outcomes!
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discount rate
short-term
long-term savings
carbon price
“Nordhaus”
.02
.02
.25
8.4
Markov
.027
.001
.25
116.9
“Stern”
.001
.001
.30
152.4
Table 1: Equilibrium carbon prices in EUR/tCO2 year 2010.
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3. Result: enforcing Pigou decreases welfare for all
generations!
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The model
Fossil-fuel use history:
st = (z0 , z1 , ..., zt−2 , zt−1 )
budgets:
ct + kt+1 = ft (kt , lt , zt , st ) + (1 − δ)kt .
welfare of generation t
wt = ut + ρ
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!∞
τ =t+1
θτ −t−1 uτ
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%-1
%,1
%+1
%*1
%)1
%(1
%'1
%&1
%%1
%
&%% '%% (%% )%% *%% +%% ,%% -%% .%% &%%%
'%%,!"
'%&&
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Solution
• we consider the following equilibria
◦ Markov: symmetric savings and climate policy rules
for all generations
◦ Pigouvian: externality pricing imposed on Markov
◦ Advanced (non-stationary) equilibria
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• Markov strategies characterized by a pair of constants
(g, h):
kt+1 = gyt ,
M CPt = h(1 − g)yt
• ct = (1 − g)yt ⇒ M CP t/ct = h, carbon price per
consumption is a constant!
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Savings:
αρ
g=
1 + α(ρ − θ)
Carbon pricing:
∆
h=
"
! !
i
j
y
( 1−αθ
+ ∆u )ρπai bj εj
[1 − θ(1 − δi )][1 − θ(1 − εj )]
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Pigouvian tax equilibrium
• Euler equation:
u#t = γu#t+1 Rt,t+1 =⇒
u#t
ct+1
ct+1 kt+1
g
γ= #
=
=
= .
ut+1 Rt,t+1
ct Rt,t+1
ct αyt+1
α
• with this, we can calculate the Pigouvian tax:
∆
hγ =
"
! !
i
j
y
( 1−αθ
+ ∆u )γπai bj εj
[1 − γ(1 − δi )][1 − γ(1 − εj )]
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Proposition 1 For θ > ρ, the equilibrium carbon price strictly
exceeds (falls short of) the Pigouvian carbon price if climate change
delays are sufficiently long (short).
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First look at numbers:
ID
PF
DF
Carbon price
Pigou
7.61
2.44
.45
8.4
Markov
8.05
5.76
.63
29.4
Table 2: Decomposition of Carbon price, MCP [Euro/tCO2].
ID=immediate costs, P F =persistence factor, DF =delay factor, M CP = ID × P F × DF . Parameter values in the text.
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Immediate damages
∆y
ID = (
+ ∆u )π(1 − g)yt
1 − αθ
persistence factor (P F )
PF =
!
i
ai
[1 − θ(1 − δi )]
Temperature adjustment, the delay factor (DF )
DF =
"
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j
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bj ρεj
1 − θ(1 − εj )
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Welfare
• welfare concept: multi-agent Pareto optimality
• welfare analysis elementary, but powerful!
Planner-equivalence ⇔ Pigouvian pricing ! efficiency
• self-enforcing welfare improvements implying even
further deviation from Pigou!
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Quantitative assessment in detail
• for the economy-climate adjustment path we need to
specify the energy sector
yt = ω(st )ktα [At (ly,t , et )]1−α
At (ly,t , et ) = min{Ay,t ly,t , Ae,t et }
• energy and labor: CES with extremely low elasticity of
substitution; otherwise immediate cuts in emissions
become unrealistically deep. See also Hassler, Krusell,
Olovsson, 2011
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Carbon prices: Pigou, Markov, and ”Advanced” policies
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&%%
.%
-%
,%
+%
*%
)%
(%
'%
&%
%
'%%%
'%'%
'%)%
'%+%
'%-%
'&%%
Figure 1. Carbon prices in 3 scenarios
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Carbon emissions: BAU, Pigou, Markov, and ”Advanced”
#
&%%
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-%
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+%
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Temperature increase:
&'
&%
-
+
)
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%
'%%%
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'+%%
'-%%
(%%%
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Relative income changes: Markov-Pigou, Markov-Advanced
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*%%1
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(%%1
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(%%%
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Concluding remarks
• the market for intergeneration welfare transfers is
missing, once we deviate from consistent preferences
• stand-alone cost-benefit ideas no longer apply:
Pigouvian taxation principle bad for climate and welfare
◦ Gerlagh&Liski, 2011
• holds more generally for public decisions involving
persistent assets
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