Environmental Economics
Sareh Vosooghi
Department of Economics, KU Leuven
Climate Change
1/60
Earth’s annual mean energy balance
IPCC AR4, Working Group 1, Main Report
2/60
CO2 emissions and global warming
Source: IPCC 6AR, 2021
There is a near-linear relationship between cumulative CO2 emissions and the increase in
global surface temperature.
3/60
History of global temperature change
Source: IPCC 6AR, 2021
Human influence has warmed the climate at a rate that is unprecedented.
4/60
Global CO2 emissions
Source: Nordhaus (2021, Markus Academy Webinar)
5/60
Multi-model averages and assessed ranges for surface warming
Source: IPCC 6AR, 2021
Human activities affect all the major climate system components, with some responding
over decades and others over centuries. Alarming variables include: global surface
temperature; Arctic sea ice area; global ocean surface pH; global mean sea level change.
6/60
Impacts of Climate Change
from no risk (white) to
irreversible risk (purple)
Source: IPCC 6AR, 2021
7/60
Safe Carbon Budget and Mitigation Options Available
Safe carbon budget is about 400-500 GtCO2 to stay below 1.5 degrees Celsius:
less than 12 years at current use of fossil fuel use left.
Clock is ticking fast!
There are two ways to move towards a goal of reducing the rate of growth of
atmospheric greenhouse-gas concentrations:
• Increase the capacity of sinks that sequester carbon dioxide and other
greenhouse gases from the atmosphere.
• Decrease emissions of greenhouse gases below business as usual (thereby
reducing GHG inflows to the atmosphere).
8/60
The costs of attaining mitigation targets
1. The cost of achieving any given target increases as the magnitude of the
emissions or concentration target declines.
2. Other things being equal, the cost of achieving any given target increases the
higher are baseline (i.e. uncontrolled) emissions over the time period in
question.
3. The cost of achieving any given target varies with the date at which targets are
to be met, but does so in quite complex ways.
4. Abatement costs will be lower, the more cost-efficiently that abatement is
obtained.
5. Climate-change decision-making is essentially a sequential process under
uncertainty.
9/60
Integrated Assessment Models
of Climate Change
10/60
Structure of IAMs
DICE: Economic Components
DICE: Geophysical Model
DICE Criticism
Stern Review
Weitzman: Damage Function, Uncertainty and Extreme Events
Post-Weitzman Perspectives on Damage Function
Environmental goods and IAMs
Structure of the Integrated Assessment Models (IAMs)
IAMs comprise:
• A simple climate model
• A simple economic model
• An emission abatement cost, by which economic decisions affect the climate.
• A damage function, by which the climate affects the economy.
• Optimisation under either Business-as-usual or socially-optimal scenario
11/60
Conceptual
Structure
Conceptual
Structure
of IAMof IAM
Land use
Emissions
Climate Cycle
Fossil Stocks
Abatement
Fossil Fuel Use
Production
Investment
General Capital
Technology
Labour
Consumption
12/60
An Example: Dynamic Integrated Climate Economy (DICE), Nordhaus
(2014)
• Simple economic & simple geophysical models. Linked via:
• Emission abatement cost
• ‘Damage function’
• Evaluate outcomes using social welfare function
• Choose optimal path, starting at i = 0, for
• savings rate
• GHG emissions
I’ll use notation which matches Faulwasser et al. (2018) and so matches the Matlab
code.
13/60
Economic Components
Social welfare is Wi
W=
T
X
U(C(i), L(i))
(1 + ρ)i−1
i=1
where i is the time period, C(i) and L(i) are total consumption and population in
period i, and ρ is the pure rate of time preference.
The utility function is “morally”
L(i)
where c(i) is per-capita consumption
c(i)1−α
1−α
C(i)
L(i) .
In the Matlab code it’s given by
U(C(i), L(i)) = L(i)
1−α
( 1000C(i)
L(i) )
1−α
In real modelling environments you sometimes need factors of 1000 as your units
aren’t as consistent as they should have been.
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Population
Population growth is exogenous
L(i + 1) = L(i)(
La lg
)
Li
This is a neat trick to have a functional form which works a bit like exponential
growth, but with the growth rate declining as L(i) gets bigger, tending towards a
maximum value of 10.5 billion. It’s calibrated to match UN projections.
15/60
Production
In DICE, the damage and abatement functions both act on output. So in each period:
• There’s a production function for the output you would have got
• This is then reduced by the action of damages
• And it’s reduced by what is spent on abatement.
The resulting net output goes into savings and consumption.
Gross output itself is just Cobb-Douglas
Y G (i) = A(i)K(i)γ (
L(i) 1−γ
)
1000
where A(i) is technology, K(i) is capital.
(Note that Faulwasser et al. (2018) unhelpfully notate this as Y .)
16/60
Net Output
Now net output is
Y(i) =
1 − Λ(i) G
Y (i)
1 + Ω(i)
where Λ(i) is emission abatement costs and Ω(i) is economic damages from
climate change. (Faulwasser et al. (2018) don’t give this a letter, they just leave as a
function of their Y ).
DICE 2016R (and so Faulwasser et al., 2018 ) use
Y(i) = [1 − Λ(i) − Ω(i)]Y G (i)
For small Ω, the two damage forms of 1 − Ω and
1
1+Ω
are approximately equal.
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Abatement costs
A fraction µ(i) of emissions are abated, which costs the fraction of output
Λ(i) = θ1 (i)µ(i)θ2
Note that when µ(i) = 1, i.e. emissions have been eliminated, we have Λ(i) = θ1 (i).
So θ1 (i) is the fraction of output we would need to spend to eliminate emissions. So
it represents a “backstop” technology. Its price comes down over time.
The fraction µ(i) is one of our two key “control variables”,
which are chosen in each period to maximise welfare.
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Damages
Damages are determined by atmospheric temperature change TAT above
pre-industrial levels, according to the function
Ω(i) = a2 (TAT )a3
Nordhaus uses a2 = 0.00267 and a3 = 2. This has been standard for a long time
but has become controversial. we don't know what a world with +3°C would be like
Given either specifications of the net output, damages reduce consumption
because there is less output to consume.
This reduction in consumption is supposed to give a compensating variation of all
welfare losses from climate change.
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Technology
Total-factor productivity growth is exogenous in DICE.
A(i + 1) = A(i)(1 + gA (i))
where gA (i) is TFP growth, which declines over time, so that
gA (i) =
gA (i − 1)
1 + δA
with δA being the rate of this decline over time.
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Capital and Savings
Capital stock evolves
K(i + 1) = (1 − δk )K(i) + Y(i)s(i)
where δk is depreciation and s(i) is the savings rate.
s(i) is our other key “control variable” that,
we choose for each time period to maximise welfare.
Output which isn’t saved, is consumed:
C(i) = Y(i)(1 − s(i))
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Emissions
Emissions E(i) = Eland (i) + Eind (i) come from the land and from output. Land-use
emissions are just declining over time:
Eland (i + 1) = Eland0 (1 − δEL )i
Industrial emissions are the carbon intensity of output σ(i), times the unabated
fraction of gross output:
Eind (i) = σ(i)(1 − µ(i))Y G (i)
The carbon intensity of output σ(i) also declines over time.
There is a constraint
Ē ≥
X
Eind (i)
i
on total available industrial emissions.
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Social Cost of Carbon
The social cost of carbon, SCC, in period i is the marginal effect of one more ton of
CO2 in period i, in terms of period-i money.
SCC(i) =
∂W
∂E
− ∂Wi
∂Ci
marginal
This is our marginal external benefit (MEB) of abating GHGs.
The minus sign reflects the fact that the marginal effect of emissions is negative,
but we want to measure a positive cost.
In MPC-DICE, the SCC(i) is multiplied by 1000. The factor of 1000 reflects a units
miss-match.
The numerator is evaluated in the model by comparing the value of the objective
function at the ‘optimum’, with its value when a small impulse of emissions have
been added.
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SCC and Optimal Carbon Tax
As defined on the previous slide, the SCC clearly depends on:
• path of economy, esp savings rate;
• emissions pathway before and after period i.
Recall that an IAM will choose these factors to optimise social welfare.
Particularly important is the SCC when the savings rate and emissions pathway are
both optimised. Some economists refer to this as “the” social cost of carbon.
This is also equal to the optimal carbon tax.
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SCC and Marginal Economic Benefits from GHG emissions
SCC and Marginal Economic Benefits from GHG emissions
However,
we can
think
of the
in any
period
a function
of
However,
we can
alsoalso
think
of the
SCCSCC
in any
one one
period
as aasfunction
of total
total cumulative
emissions
(before
and
after
that period).
cumulative
emissions
(before and
after
that
period).
Though Though
both theboth
SCC and
the SCC
and emission
abatement
will
depend on
trajectorythis
of is a useful
emission
abatement
will really
depend
onreally
the trajectory
ofthe
emissions,
emissions, this is a useful shorthand.
shorthand.
Price
MB
M EC
q⇤
q̄
q
In this way, conceptually the same as we’ve seen before.
In this way, conceptually the same as we’ve seen before.
Clear that the Pigouvian tax is equal to the SCC at the optimum quantity.
Clear that the Pigouvian tax is equal to the SCC at the optimum quantity.
25/60
Structure of IAMs
DICE: Economic Components
DICE: Geophysical Model
DICE Criticism
Stern Review
Weitzman: Damage Function, Uncertainty and Extreme Events
Post-Weitzman Perspectives on Damage Function
Environmental goods and IAMs
Carbon Boxes
There are three “boxes” of carbon, represented by
• MAT (i): carbon in the atmosphere
• MUP (i): carbon in the upper ocean
• MLO (i): carbon in the lower ocean
Emissions flow in the atmosphere. Carbon flows in both directions between the
atmosphere and the upper ocean, and between the upper ocean and the lower
ocean.
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Carbon Cycle
M_AT(i+1) = zeta11*M_AT(i) + zeta12*M_UP(i) + zeta2(F_i)
M_UP(i+1) = zeta21*M_AT(i) + zeta22*M_UP(i) + zeta23*M_LO
M_LO(i+1) = zeta32*M_UP(i) + zeta33*M_UP(i)
The flow from one box to the next is linear. e.g. at point i there is
• ζ21 MAT (i) flowing from the atmosphere to the upper ocean
• ζ12 MUP (i) flowing from the upper ocean to the atmosphere.
So there’s a net flow from atmosphere to ocean of
ζ21 MAT (i) − ζ12 MUP (i)
This means that carbon sink in the upper ocean could become saturated, slowing
down re-absorption until enough has sunk down to the lower ocean.
In fact, it is considered that the DICE carbon cycle absorbs carbon into the ocean
too easily.
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Heat “Boxes”
There are two “boxes” of heat, in the atmosphere temperature (TAT ) and in the lower
ocean temperature (TLO ). Atmospheric forcings warm the upper ocean. Similarly to
the carbon cycle, heat then diffuses down to the lower ocean, cooling the climate.
Again, these parts of the DICE model are criticised by scientists - it’s too easy for the
temperature to come back down again.
These parts of the model are described using matrices by Faulwasser et al. (2018).
If you can’t read matrix equations, go over to Phaneuf and Requate (2016), who
don’t use them.
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Radiative forcing
“Radiative forcings” describe the planet’s energy balance. If the inflow of energy
from the sun is greater than the amount being radiated into space, the planet will
gradually be “forced” to a higher temperature.
In DICE,
F(i) = ηlog2 (
MAT (i)
) + FEX (i)
MAT,1750
Here FEX (i) is forcings from other greenhouse gases, which DICE treats as
exogenous. And MAT,1750 is pre-industrial concentrations of CO2 .
So the first term equals η when atmospheric concentrations have
doubled relative to the pre-industrial level.
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Temperature equations
Now DICE has linear equations for the effect of forcings on temperature
TAT (i + 1) = ϕ11 TAT (i) + ϕ12 TLO (i) + ξ1 F(i)
So temperature is a function of MAT (i).
TLO (i + 1) = ϕ21 TAT (i) + ϕ22 TLO (i)
As with carbon, temperature can flow from the atmosphere to the ocean – but the
net flow will slow down if the ocean is warmer.
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Climate sensitivity
Suppose we double concentrations of CO2 from pre-industrial levels, and hold them
constant, and ignore exogenous forcings. So F(i) = η.
Eventually atmospheric and ocean temperatures will stabilise. Write these as TAT
and TLO . Now find TAT using simultaneous equations: T_AT(i) = T_AT(i+1)
(1 − ϕ11 )TAT = ϕ12 TLO + ξ1 η
(1 − ϕ22 )TLO = ϕ21 TAT
The value of TAT we get out from this is called the “equilibrium climate sensitivity (ECS)”.
Higher climate sensitivity means greater temperature change for the same CO2 content.
So ECS depends on the ϕ parameters, η and ξ1 . But MPC-DICE allows you to start by
setting ECS – it’s the parameter called “t2xco2” – and will reset the ϕ values to
account for this.
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Results for a range of scenarios
Results for a range of scenarios
Global temperature change
AtmosphericTemperature (degC above preindustrial)
7
6
5
Base
Opt
Lim2t
Stern
SternCalib
Copen
4
3
2
1
0
2000
2020
2040
2060
2080
2100
Year
2120
2140
2160
2180
2200
Global temperature increase ( C from 1900) under alternative policies,
Global temperature increase (◦ C from 1900) under alternative policies, DICE-2013R
DICE-2013R model. Source: Nordhaus and Sztorc (2013)
model. Source: Nordhaus and Sztorc (2013)
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Major Results from DICE
• Efficient emissions reductions follow a “policy ramp” in which policies involve
modest rates of emissions reductions in the near term, followed by sharp
reductions in the medium and long terms.
• For the efficient climate-change policy, the net present-value global benefit of
the optimal policy is $3 trillion relative to no controls. This total involves $2
trillion of abatement costs and $5 trillion of reduced climatic damages.
• The economically optimal carbon price or carbon tax would be $27 per metric
ton in 2005 in 2005 prices. The optimal carbon price would rise steadily over
time, at a rate between 2 and 3 percent per year in real terms, to reflect the
rising damages from climate change.
• The upper limit on the carbon price is determined by the price at which all uses
of fossil fuels can be economically replaced by other technologies. This is cost
of the backstop technology. DICE estimates this to be around $1,000 per ton of
carbon over the next half century or so, falling thereafter at an unknown rate.
33/60
Structure of IAMs
DICE: Economic Components
DICE: Geophysical Model
DICE Criticism
Stern Review
Weitzman: Damage Function, Uncertainty and Extreme Events
Post-Weitzman Perspectives on Damage Function
Environmental goods and IAMs
What is the economic impact of climate change, and what are the
costs and benefits of taking action now?
The Stern Review (2006):
• Commissioned by the UK government to evaluate a proactive response to
climate change.
• Collaboration between renowned scientists and philosophers.
• Countered the popular view (led by figures like Nordhaus) advocating for a
permissible temperature rise of 3-3.5°C by 2100.
• Central finding: Stabilizing CO2 levels between 500-550ppm would cost about
1% of global GDP, given immediate decisive action. Aiming for 450ppm CO2
would be challenging and more expensive.
• A pivotal distinction from DICE was in the choice of the discount rate.
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Nordhaus
Stern
35/60
Discounting in DICE vs Stern
William Nordhaus (Yale University) vs Nicholas Stern (LSE).
Stern chose a much lower discount rate than is standard in the literature (e.g. any of
the versions of DICE).
... and just choosing different discount rates has huge consequences in IAMs.
36/60
Global temperature of DICE results under different scenarios
Source: Nordhaus and Sztorc (2013)
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Output of DICE under different scenarios
Source: Nordhaus and Sztorc (2013)
38/60
Output of DICE under different scenarios
• Economic growth remains consistent across all model scenarios.
• Minimal variance observed between climate change impacts and mitigation.
• Use of a low discount rate magnifies differences.
• The Stern run initially lags behind the Lim2t, but surpasses in later years. WHY?
low discount rate induces a higher savings rate.
• Marginal difference observed between Lim2t and DICE’s optimal run.
• Question to ponder: If the impact on welfare is this minimal, why is climate
change such a big deal?
39/60
Structure of IAMs
DICE: Economic Components
DICE: Geophysical Model
DICE Criticism
Stern Review
Weitzman: Damage Function, Uncertainty and Extreme Events
Post-Weitzman Perspectives on Damage Function
Environmental goods and IAMs
Weitzman’s Perspective on Stern Review
• Stern Review’s distinct low discount rate sparked debates on optimal emission
policies and the Social Cost of Carbon (SCC). Debate about discounting.
• Marty Weitzman (1942-2019) posited Stern was on track but emphasized
different reasons. Stern was right, but for “the wrong reasons”.
• Weitzman’s stance: urgent climate action is crucial to mitigate the minor risk of
severe future consequences.
• Key elements to Weitzman’s view: the damage function and uncertainty.
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Weitzman’s Analysis of DICE’s Damages
• DICE (2014) quantifies output loss using the function:
Ω(T) =
1
1 + a2 T a3
• Concerns arise regarding the model’s treatment of damages from extreme
temperature changes.
• Higher temperatures, e.g., 10◦ C, show only a 19% output loss — a perspective
Weitzman finds unconvincing.
• The DICE model isn’t calibrated for this range, but should be if we consider the
implications of uncertainty and irreversibility.
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Damage functions in most IAMs
Source: McCarthy et al. (2001)
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• After the release of the IPCC’s AR4 report, studies began to emerge highlighting
the more severe damages associated with rising global mean temperatures.
Source: IPCC (2014)
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What do we know about 3 degrees of warming?
Nordhaus and Sztorc (2013):
• The damage function has been calibrated for damage estimates in the range of 0 to 3◦ C.
In reality, estimates of damage functions are virtually non-existent for temperature
increases above 3◦ C [...] The damage function needs to be examined carefully or
re-specified in cases of higher warming or catastrophic damages.
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Understanding Equilibrium Climate Sensitivity (ECS)
• Defined as the temperature change resulting from a doubled CO2
concentration, post-equilibrium, i.e., ∆TAT when we double CO2 concentration,
and let the climate reach equilibrium.
• Precise value of ECS remains uncertain.
• Scientists prefer not to assign a specific probability distribution function (pdf)
to the value. Instead, they provide ‘likely’ and ‘very unlikely’ ranges, backed by
varying confidence levels. Hence, the latest IPCC reports refrain from
specifying a pdf for ECS.
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pdf of ECS
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“Thin Tails” versus “Fat Tails” and Extreme events
Thin-Tails versus Fat-Tail pdfs
The normal distribution is an example of a thin tailed distribution. As we
The ‘normal
distribution’
an example
of a thinoftailed
distribution.
As we move
move away
from theismedian,
probabilities
events
become extremely
away from
small.the median, probabilities of events become extremely small.
The ‘Pareto
distribution’
is fat tailed.
decline decline
for more
The “Pareto
distribution”
is fatProbabilities
tailed. Probabilities
forextreme
more events,
Fat-Tailed
Uncertainty
in the Economics of Catastrophic Climate Change
279
but not
nearly
so
fast.
extreme events, but not nearly so fast.
Table 1 Prob½S # S^$ for fat-tailed Pareto and thin-tailed Normal distributions
S^ ¼
^
ProbP ½S # S $
ProbN ½S # S^ $
3!C
4.5!C
6!C
8!C
10!C
12!C
0.5
0.5
0.15
0.15
0.06
0.02
0.027
0.003
0.014
7 % 10&7
0.008
3 % 10&10
Source: Weitzman (2011)
Source:sensitivity
Weitzmanstudies
(2011)into one overarching probability density function (PDF), and there is much
controversy about how it might be done. But for what it is worth (perhaps very little), the
median upper 5 percent probability level over all 22 climate sensitivity PDFs cited in IPCCAR4 is 6.4!C, which fits with the Pareto PDF in Table 1 above.4
Table 2 presents some values of probabilities of eventual increased global mean surface
47/60
Fat Tails and Expectations
Suppose X is a random variable with pdf f(x), and g is a function of X. Then
expectation of g(g) is calculated as,
Z ∞
“Fat tails” andE(g(g))
Infinite
= Expectations
g(g)f(x)dx
−∞
• If X has a thin-tail distribution (like Normal), any ‘reasonable’ g, gives a finite
expectation.
We have a race between the pdf going down, and the thing whose
• But if Xexpectation
has pdf likewe’re
below,
and ggoing
grows
taking,
up.rapidly, the product of these two does
not have a finite integral necessarily.
probability
density
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Uncertainty and Damage in IAM since Weitzman
Weitzman (2007, and ...) argued that:
• The pdf of ECS (or more generally a bad climate outcome) is fat tailed.
• Climate damage grows rapidly as climate outcomes get worse: the curve is
much steeper than quadratic (as were in DICE 2014).
Thus, from the interaction of these two, you would get an infinite expectation.
Weitzman’s Dismal Theorem: SCC varies very sensitively on the worst possible
outcome. One shoudl cap how bad the ‘worst possible outcome’ can be, and find a
finite expectation subject to that cap, and then show that the SCC → ∞ as the cap
is relaxed.
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Uncertainty and Damage of Weitzman in DICE
• Weitzman’s arguments are made without using a full IAM, and don’t necessarily
take account of the fact that a higher ECS means that it takes longer for the
climate to reach equilibrium.
• Introducing uncertainty in climate sensitivity has a negligible effect on DICE
model outcomes, unless the damage function is modified. WHY?
• Damages rise quadratically with temperature shifts.
• Higher ECS leads to a delayed equilibrium.
Result: SCC in DICE is roughly linear in ECS, making uncertainty’s inclusion
relatively inconsequential. Thus our stance on the damage function also
shapes our perspective on uncertainty.
50/60
Structure of IAMs
DICE: Economic Components
DICE: Geophysical Model
DICE Criticism
Stern Review
Weitzman: Damage Function, Uncertainty and Extreme Events
Post-Weitzman Perspectives on Damage Function
Environmental goods and IAMs
An Alternative Damage Function (Weitzman (2012))
Ω(T) =
1
T a2
1 + a1
+ a3 T a4
with a2 = 2 as in DICE, and a3 , a4 chosen so that damages are 50% of world GDP at
6◦ C and 99% at 12.5◦ C.
Golosov et al. (2014):
Y_,t = exp(C*T_t)*A_t
*K_t^alpha*L_t^beta
*E_t^(1-alpha-beta)
Y: total output
T: global T (°C)
C: cst.
A: total factor productivity
K: kapital
L:
E: composite energy
t: time
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Dietz and Stern (2015) and Capital Stock Damages
• Dietz and Stern (2015) stress the role of capital stock knowledge spillovers in
economic growth, echoing thoughts from Arrow (1962) and Romer (1986).
ENDOGENOUS GROWTH MODELS.
• They theorize that climate change might adversely impact capital stocks,
subsequently hampering growth. ↑ TAT → ↓ K → ↓ Y
• The capital stock damages by climate change include:
Damages due to storms or wildfires; abandoned coastal areas; reduced
productivity of capital; high depreciation of capital due to climate change
damage
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Dietz and Stern (2015)
So they suggest two modifications to DICE-2014:
Y(i) = (1 − Ω(i))(1 − Λ(i))A(i)K(i)γ+β L(i)1−γ
when one firm invests more, there are positive spillovers to the whole economy
(β > 0).
K(i + 1) = (1 − DK (i))(1 − δ K )Kt + It
DK is the climate change damage that directly affects capital.
They deliver results under four scenarios:
• Standard DICE
• Weitzman damage function with 50% damages at 6◦ C
• ‘High damage’ function with 50% damages at 4◦ C
• Weitzman damage function with ECS (‘S’ here) of 6 instead of 3
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Results:
Per Capita Consumption with no climate policy
Dietz and
Stern
(2015)
2015]
GROWTH, CONVEX DAMAGES AND CLIMATE RISK
K Model
100
Consumption Per Capita (US $2005)
90
80
585
Standard
S = 3, Quardratic Damage
S = 3, Weitzman Damage
S = 3, High Damage
S = 6, Weitzman Damage
70
60
50
40
30
20
10
0
2000
Elizabeth Baldwin
2050
2100
Environmental Economics and Climate Change
2150
Hilary Term, 2020
2200
77 / 92
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Weitzman damage, S = 6
High damage
0.432
0.396
Dietz and Stern (2015)
0.584
0.538
0.722
0.663
0.868
0.783
1
0.891
1
0.984
1
1
1
1
1
1
1
1
Table 2
Optimal Carbon Prices (2005 US$/tC), 2015–2105. S = 3 Unless Otherwise Indicated
Standard
2015
44.4
2025
57.0
2035
71.2
2045
87.8
2055
106.2
2065
127.1
2075
150.0
2085
175.8
2095
204.6
2105
236.6
Capital models
Quadratic damage
Weitzman damage
Weitzman damage, S = 6
High damage
76
91
196
178
129
156
337
309
182
226
495
455
245
310
684
617
316
405
895
774
393
506
1097
909
476
609
1074
1017
563
711
1052
1052
656
812
1032
1032
752
912
1012
1012
Productivity models
Quadratic damage
Weitzman damage
Weitzman damage, S = 6
High damage
118
133
271
233
196
222
456
393
272
313
653
559
363
420
888
738
466
541
1121
911
580
670
1097
1066
705
806
1074
1074
840
945
1052
1052
984
1032
1032
1032
1012
1012
1012
1012
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Structure of IAMs
DICE: Economic Components
DICE: Geophysical Model
DICE Criticism
Stern Review
Weitzman: Damage Function, Uncertainty and Extreme Events
Post-Weitzman Perspectives on Damage Function
Environmental goods and IAMs
Sterner and Persson (2008) and Environmental Goods
• Applying insights from Krutilla-Fisher model (using a lower discount rate on
environmental goods) in IAMs.
• Assume there are two goods: material consumption C; and environmental
amenities E. Utilities are:
h
(1 − γ)C
σ−1
σ
+ γE
σ−1
σ
σ
σ−1
i1−α
U(C) =
1−α
E and C are imperfect substitutes (0 < ρ < 1). Why? for example: loss of
agricultural output reduces global GDP. So, MRSCE should be diminishing
dramatically.
• Assume temperature affects environmental quality by
E(i) =
E0
(1 + aT(i)2 )
where a is a constant and E0 is level of environmental amenities in year 2005.
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70
Upshot:
Optimal
Emission Paths
Sterner and
Persson
(2008)
T. Sterner and U. M. Persson
rising over time (middle line—labeled Relative price effects). See text for further explanation.
Downloaded from http://reep.oxfordjournals.org a
Figure 1. Optimal carbon dioxide emission paths in amended version of the DICE model, showing how
conclusions
concerning
depend
crucially
on assumptions
regarding
discounting
and relative
‘Relative
price effect’
is abatement
run under
high
discount
rate, but
where
the relative
price of
prices. Note: Emissions paths are shown for three different cases: a high discount rate case (upper line—
the environmental
good rises over time.
labeled Nordhaus discounting), a case utilizing the lower discount rate argued for in the Stern Review (the
Similarlower
to Krutilla-Fisher,
this model
a high
justification
a lower
line—labeled Stern discounting),
and provides
a run with the
discount rate,for
but using
where the
nonmarket
impacts
are
attributed
to
the
consumption
of
a
representative
environmental
good
whose
relative
price is
discount rate on environmental goods.
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References I
[1]
R. Perman, Y. Ma, M. Common, D. Maddison, and J. McGilvray, “Natural
resource and environmental economics,”, 2011.
[2]
N. Stern, “The structure of economic modeling of the potential impacts of
climate change: Grafting gross underestimation of risk onto already narrow
science models,” Journal of Economic Literature, vol. 51, no. 3, pp. 838–859,
2013.
[3]
T. Faulwasser, C. M. Kellett, and S. R. Weller, “Mpc-dice: An open-source
matlab implementation of receding horizon solutions to dice,”
IFAC-PapersOnLine, vol. 51, no. 5, pp. 120–125, 2018.
[4]
S. Dietz and N. Stern, “Endogenous growth, convexity of damage and climate
risk: How nordhaus’ framework supports deep cuts in carbon emissions,” The
Economic Journal, vol. 125, no. 583, pp. 574–620, 2015.
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References II
[5]
J. J. McCarthy, O. Canziani, N. Leary, D. Dokken, and K. White, Climate change
2001: Impacts, adaptation, and vulnerability report of ipcc working group ii,
2003.
[6]
W. Nordhaus and P. Sztorc, “Dice 2013r: Introduction and user’s manual,” Yale
University and the National Bureau of Economic Research, USA, 2013.
[7]
A. Rezai and F. Van Der Ploeg, “Second-best renewable subsidies to
de-carbonize the economy: Commitment and the green paradox,”
Environmental and Resource Economics, vol. 66, no. 3, pp. 409–434, 2017.
[8]
N. H. Stern, The economics of climate change: the Stern review. cambridge
University press, 2007.
[9]
T. Sterner and U. M. Persson, “An even sterner review: Introducing relative
prices into the discounting debate,” Review of Environmental Economics and
Policy, 2008.
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References III
[10]
M. L. Weitzman, “A review of the stern review on the economics of climate
change,” Journal of economic literature, vol. 45, no. 3, pp. 703–724, 2007.
[11]
M. L. Weitzman, “Fat-tailed uncertainty in the economics of catastrophic
climate change,” Review of Environmental Economics and Policy, 2011.
[12]
M. L. Weitzman, “Ghg targets as insurance against catastrophic climate
damages,” Journal of Public Economic Theory, vol. 14, no. 2, pp. 221–244, 2012.
[13]
D. J. Phaneuf and T. Requate, A course in environmental economics: theory,
policy, and practice. Cambridge University Press, 2016.
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