assessing the effect of damages to capital and total
TRANSCRIPT
Assessing the Effect of Damages to Capital and Total Factor Productivity
Damage Mechanisms in Integrated Assessment Models of Climate Change
Ida Nordin
Student
Semester 2015
Master thesis 2, 15 ECTS Masterβs program in Economics
Assessing the Effect of Damages to Capital and Total Factor Productivity, Master Thesis Ida Nordin 2015
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Abstract
Direct damages on capital and on total factor productivity (TFP) have started to get attention in
the field of improving the understanding and the modeling of how climate change impacts the
economy. To understand what the contribution of these damages are, the effects introducing
them are examined in this thesis, modeled in the integrated assessment model AD-DICE. I find,
among other things; negative effects of these extensions on the economy, but smaller effects
than earlier results; that the choice of how to model economic growth have large impacts on the
effects of capital and TFP damages; that damages to TFP has more possibilities to impact the
economy than damages to capital and; that the optimal choice of adaptation versus mitigation
levels are affected. Instead of looking at the sum of effects, the sources of the effects are
revealed, making a better base for discussion.
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Table of contents
Abstract .................................................................................................................................... 1
Table of contents ...................................................................................................................... 2
Abbreviation and word list....................................................................................................... 4
1 Introduction ..................................................................................................................... 5
1.1 Aim of the thesis ...................................................................................................... 5
1.2 Integrated assessment models .................................................................................. 6
1.3 Critique to IAMs ...................................................................................................... 6
1.4 Climate damages ...................................................................................................... 7
1.4.1 Damages to capital and total factor productivity .............................................. 8
1.4.2 Damage functions ............................................................................................. 9
1.5 Literature review ...................................................................................................... 9
1.6 Organization of the thesis ...................................................................................... 11
2 Methodology ................................................................................................................. 12
2.1 The DICE and the AD-DICE model ...................................................................... 12
2.2 Dietz and Stern's extensions................................................................................... 14
2.3 Modifications to the model .................................................................................... 16
2.3.1 Replication of models ..................................................................................... 17
2.3.2 Endogenous TFP growth ................................................................................ 17
2.3.3 Further modifications ..................................................................................... 18
2.4 Table of models ...................................................................................................... 19
3 Results ........................................................................................................................... 20
3.1 Comparison to Dietz and Stern results ................................................................... 20
3.2 Effect of choice of growth model .......................................................................... 21
3.2.1 Growth models ............................................................................................... 22
3.2.2 Capital model .................................................................................................. 22
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3.2.3 TFP model ...................................................................................................... 23
3.3 Stern and Dietzβs extensions - capital model ......................................................... 24
3.3.1 Economic impact ............................................................................................ 24
3.3.2 Mitigation ....................................................................................................... 25
3.3.3 Carbon prices .................................................................................................. 26
3.4 Stern and Dietz Extensions- TFP model ................................................................ 26
3.4.1 Economic impact ............................................................................................ 27
3.4.2 Mitigation ....................................................................................................... 27
3.4.3 Carbon prices .................................................................................................. 28
3.5 Choice of savings rate ............................................................................................ 29
3.5.1 Capital and TFP model ................................................................................... 29
3.6 Effect of fraction size ............................................................................................. 30
3.6.1 Capital model .................................................................................................. 30
3.6.2 TFP model ...................................................................................................... 31
3.7 Only residual damages affecting capital and TFP ................................................. 32
3.7.1 Capital and TFP model ................................................................................... 32
3.8 Adaptation costs as fraction of climate costs ......................................................... 32
3.8.1 Capital model .................................................................................................. 33
3.8.2 TFP model ...................................................................................................... 34
4 Conclusion ..................................................................................................................... 35
4.1 Future research ....................................................................................................... 36
5 References ..................................................................................................................... 37
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Abbreviation and word list
DICE β The Dynamic Integrated Climate-Economy model. Numbers referring to the year of
the version of the model
GDP β Gross Domestic Product
IAM β Integrated Assessment Model
TFP β Total factor productivity
Abatement of emissions β actions to take away or reducing emissions
Adaptation to climate change β measures that decrease the impacts of climate change
Business as usual β refers to a scenario where no mitigation is taken to prevent climate change
Carbon price β the price of carbon that reflects the marginal cost of climate change.
Greenhouse gases β gases like carbon dioxide that causes climate change
Mitigation β refers to the policy variable of how much abatement should be done.
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1 Introduction
Climate change has become known as a big threat to the world that needs to be taken action
against. It has various impacts, among other things; more droughts, agricultural losses and sea
level rise. The Intergovernmental Panel on Climate Change, IPCC, states that there are several
key risks arising with coming climate change that can be seen as βdangerous anthropogenic
interference with the climate systemβ (IPCC, 2014). Facing this, what would the economically
best policy response be, one could ask? How much harm will it do to us, and how is this
translated into economic terms?
To examine optimal policies and the effects of different climate change policies, integrated
assessment models (IAMs) are powerful tools. One important component of an IAM is the
damage function β i.e. how climate change is expected to impact the economy. In IAMs up to
now, impacts have been modeled solely as temperature increases reducing GDP by a
percentage. Dietz and Stern (2015) extends an IAM called DICE, to include a novel damage
specification. In this specification one important extensions is that not only is GDP damaged
by climate change, but also capital and total factor productivity (TFP) can be directly impacted.
This begins to bring in more dynamics in the model and can be important extensions. The paper
has been very influential in policy circles, but the underlying assumptions on which the results
are based have not been examined or presented sufficiently in Dietz and Stern (2015), which
will be the focus of this thesis.
1.1 Aim of the thesis
As the IAMs are complex systems with forces working in different directions, it is important to
not only extend the models to be more realistic, but also investigate the interaction and
individual effects of the extensions. Dietz and Stern (2015) not only introduce damages to
capital and TFP in the DICE model, but also endogenous growth, convex damages (i.e. damages
that increases faster than the standard damages at high, unexperienced temperatures) and
uncertainties about the climate sensitivity parameter. They present their results in a way
implying that including capital or TFP damages means that damages will be disastrously higher.
Is this really true? They do not give much insights to which assumptions and mechanisms that
are creating these results. The focus of this thesis will be on unravelling the underlying
assumptions and effects of their model to see what we can actually learn from it. This will be
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done by modelling assumptions step by step and comparing results with and without these
assumptions.
1.2 Integrated assessment models
Integrated assessment models capture the whole cause and effects chain of climate change,
translating economic activity into emissions, into climate change (using geophysical equations)
and climate change into impacts on the economy. They try to assess what the optimal path of
emissions should be to optimize intergenerational utility in the economy, alternatively looking
at the welfare effects of a policy intervention. The models weigh costs of climate change
(mitigation and possibly adaptation) against benefits of policies (reduced climate change
damages) to arrive at the socially optimal outcome. Some look at different regions, others at the
global scale, some distinguishes between sectors, other aggregates them, and there are different
assumptions of parameter values, dynamics etc., and also different extensions to these models
(Bonen, Semmler and Klasen, 2014).
Some of the most known IAMs for climate change are the Dynamic Integrated Climate-
Economy model, DICE, and the Regional Integrated Climate-Economy model, RICE
(Nordhaus and Boyer, 2003), the Climate Framework for Uncertainty, Negotiation and
Distribution, FUND (Anthoff and Tol, 2010), the Policy Analysis of the Greenhouse Effect
model, PAGE (Hope, Anderson and Wenman,1993), the World Induced Technical Change
Hybrid model, WITCH (Bosetti et al., 2006) and the Model for Evaluating the Regional and
Global Effects of GHG Reduction Policies, MERGE (Manne, Mendelsohn and Richels, 1995).
Their aim is to give an answer to what is economically best to do, but there are uncertainties
about how different parts of the models should be formulated, and there is also some critique
as to the usefulness of them. Still they are the only tool to look at the whole cause and effect
chain of climate change, and can give many useful insights about the dynamics handled and
studied in the right way.
1.3 Critique to IAMs
There are some critiques and difficulties with IAMs that can be good to bear in mind when
looking at them. Pindyck (2013) argues that IAMs look very precise as they produce exact
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numbers, which they are really not as they build upon uncertain assumptions, it is easy to get
fooled by looking at their results. The precise numbers might not be the most interesting, but
rather the directions and relative sizes of the effects. The critique is briefly covered here to give
some background. One issue is the choice of discount rate. It is an ethical judgment and some
favors a discount rate that reflects observed behavior and others believe that it should not make
a difference between current and future generations and sets it to a lower level. The choice can
have large effects on the suggested policy (e.g. Heal, 2008). Another critique is that the damage
functions is only calibrated from impacts of temperature increases of at the most 3 degrees, that
in some aspects have been observed before. Some damage estimations based on shorter weather
fluctuations are not certain to hold for persistent climate change. The impact in the long run
could be both lower than observed effects because of adaptation possibilities, and larger as e.g.
ecosystem are stressed for a longer time (Dell, Jones and Olken, 2014). In assessment of climate
damages the unrealistic assumption of optimal adaptation in IAMs also results in damage
projections much lower than we can expect to see in the real world (de Bruin, Dellink and Tol,
2009). Neither do we know effects for temperatures above 3 degrees. In the same field of
problems are tipping points with irreversible and nonlinear, large damages, that occur at
uncertain threshold levels. A difficult part of this question is how to deal with the non-negligible
risks of catastrophic outcomes. It could be the expected value of the catastrophe (Nordhaus,
2008) or a precautionary principle to avoid them (Weitzman, 2013). There is also uncertainty
about how much the climate actually will change from a certain level of carbon dioxide
concentration in the atmosphere, and how much this uncertainty affects the credibility of the
results (Pindyck, 2013). Other questions are what happens with the relative prices as e.g.
environmental goods get scarce (Sterner and Persson, 2008)? Are the exogenous parameters
and assumptions right, as for example the growth path or development of mitigation technology,
assumptions that could change outcomes drastically (Moyer et al., 2014)? There is also a need
to update damage functions to recent data (Dell, Jones and Olken, 2012). And this thesis will
uphold itself at the question of by which mechanisms the climate affects the economy, as until
now only GDP is damaged.
1.4 Climate damages
Even though climate damages generally are modeled as affecting GDP directly, this is not the
only possible way. Fankhauser and Tol (2005) analyses different ways the economy is damaged
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by climate change and examines the size of impact of the capital accumulation effect, savings
effect, and different endogenous growth models. Their analysis suggest that under climate
change, there are market impacts that damages output, and that also will have negative effects
on capital accumulation; the effect of higher mortality could increase the capital-labor ratio;
and the capital stock should also decrease as climate change can cause capital to depreciate
faster. The non-market impacts should not affect economic dynamics. By using different growth
models in DICE, they find that the capital accumulation effect has a negative impact on
economic output. The savings effect is also negative but very small. The effects are larger in
endogenous growth contexts where human capital or productivity can be affected by climate
change. They can also see that the effects are relatively larger for low levels of climate damages,
than for higher levels. This is explained as since a damage to GDP will have less than
proportional damages to investment and thus capital, and that in its turn output is less than linear
in capital, then the large drop in GDP will result in a smaller percentage drop in capital and
capital effect on output.
1.4.1 Damages to capital and total factor productivity
The impact on production that is assumed in most models, can be for example crop losses, but
also costs for implementing adaptation measures, that takes away resources from consumption.
It can also have various effects directly on capital, or on total factor productivity, (TFP). The
same effects can in some aspects be thought of as either a damage to capital or to TFP.
The capital stock can be directly damaged, for example by increased rate of storms damaging
infrastructure. With sea level rises capital in coastal areas has to be abandoned, if not enough
adaptive measures are taken (Dietz and Stern, 2015). The productivity of capital can be affected,
as it is constructed for other climate conditions, e.g. if precipitation change, irrigation system
can become less productive. A less stable climate also creates a need to change, or repair capital
more often. As more resources has to be put on reparation there is also less that can be used for
research and development, decreasing possibilities for increased productivity (Dietz and Stern,
2015 and Moore and Diaz, 2015).
Labor productivity can be affected, as for example the mortality rates increase, health is
decreased and health expenditures increases (Dellink et al., 2014). The productivity of workers
seem to decrease with hotter temperature, even if mainly for outdoor workers (Dell, Jones and
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Olken, 2014). Political instability can also increase with temperature shocks, which in its turn
have negative effects on capital accumulation and productivity growth; among other things
(Dell, Jones and Olken, 2012).
1.4.2 Damage functions
Bonen, Semmler and Klasen (2014) reviews the damage functions and its interactions with
other variables in some of the most common IAMs; FUND, PAGE and DICE. The damage is
generally imposed on GDP as a fraction lost each time period due to climate change, measured
as temperature change relative preindustrial levels. None of these damages impacts utility
directly (there are other IAMs, as the MERGE model that also impacts utility directly (Kopp et
al., 2011)). The DICE modelsβ damage is a quadratic function of global average temperature
increase, with some vintages giving the possibility to include a damage function for sea level
rise. The damages in FUND arises from temperature increases and the level of carbon dioxide
concentration in the atmosphere, with 9 sectors with different damage functions aggregated to
an impact on output. It also has damages to its endogenous population, whereas production is
exogenously given. In PAGE the damages are dependent on the increase over some βtolerable
temperatureβ. Its damages are given by a power function and an additive damage after an
uncertain, stochastic, threshold temperature (Bonen, Semmler and Klasen, 2014).
1.5 Literature review
The knowledge about climate change and its impacts on the economy is still limited and there
is also a lag from new findings about climate change to assessing the economic impacts of it. It
has been difficult to do more comprehensive descriptions of damages with this lack of data. But
new research is providing more data and suggestions for better damage specifications are
coming.
Dell, Jones and Olken, (2012) estimates effects of weather shocks on the economy, both short
run effects with lags and medium run effects, which could improve assessment of climate
damages. They find that one degree higher average temperatures reduces growth in output that
year with about 1.3 percentage points for poor regions, but for rich regions the effects is smaller
and not as significant. They also find that a large part of the damages seem to persist for longer
time periods, suggesting damages on growth itself and not only level effects, with a quite linear
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relationship. Effects are not only on agriculture, the sector often highlighted, but are large also
on industrial output, and they find significant effect on political instability. The estimates are
for short and medium run and effects of long lasting climate change is more uncertain as there
are both possibilities for adaptation and more damages as systems are stressed for longer time
periods.
Different panel data estimates for effects of climate change on different economic sectors are
summed in Dell, Jones and Olken, (2014). They find that there are many studies that show
negative effects of climate change on agriculture, industry, growth, capital, labor productivity,
political instability and conflict, health, among other things. These give a lot of new facts about
the impacts of climate change, even if not all point in the same direction. They find it important
to update IAMs with the new findings.
Dietz and Stern (2015) finds large damages to the economy when introducing endogenous
growth, capital and total factor productivity damages, convex damages and uncertainty about
the climate sensitivity. The methodology will be further explained in the methodology section.
They find in comparison with the standard model much larger optimal mitigation levels when
the damages are partitioned between GDP and capital or TFP, together with endogenous
growth. The differences are larger when convex damages are introduced, and this effect is even
more pronounced when uncertainty is explored by letting the climate sensitivity be 6 degrees.
These effects are also reflected in their results for business as usual β when no mitigation is
implemented to prevent climate change β per capita consumption. Consumption is increasing
in the standard model and with most of the extensions but is damaged by climate change. With
the higher level of convex damages, or convex damages and climate sensitivity of 6 introduced,
consumption per capita decreases after some point in time and can in some case even fall below
the current level. The differences in consumption per capita are not as large between the
standard case and the extensions as for mitigation levels.
Moore and Diaz (2015) introduces damages to TFP and capital by using estimates from Dell,
Jones and Olken, (2012), attempting to catch up with new research. They construct a two-region
model with a poor and a rich region from the 2010 version of the RICE model. A large part of
damages in the model hits TFP (alternatively capital), and some directly impacts GDP,
constructed to catch the persistent rather than one-time effects on growth that Dell, Jones and
Olken, (2012) observed. Damages are calculated from an effective temperature measure, where
impacts of temperature increases in previous time periods to some extent can be adapted away.
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They find that in their model simulations, quite drastic policy interventions would be preferable
in this setting compared the standard damage specification, with quite equal results for models
with capital and TFP damages. Poor countries growth rates are, under a business as usual
scenario where no action is taken to prevent climate change, 3.2% per year when there are no
damages to TFP, but only 2.6% with these growth damages. The effects are much smaller in
rich countries. The results are robust to changes in many parameters, e.g. the discount rate and
an adaptation rate of 0-20 percent per year. One thing it is not robust to is if poor countries are
modeled to become less sensitive to climate change when they reach a certain income level,
reflecting the possibility that rich countries are less damaged by climate change because they
can adapt better when they are richer. In this case the model suggest much less stringent policy
than their unmodified model.
Moyer et al., (2015) looks at the effect of damaging TFP, in an IAM used for US policy, a
modified version of the DICE model. The damages are modeled as either damages to the level
of TFP, or to the growth rate of TFP that year. They conclude that introducing even a small
fraction of damages to TFP have large effects on economic outcomes. Damaging TFP, growth
can become negative, while damaging the growth rate only can slow growth. This shows that
the way TFP damages are modeled is important, and also that it can be a serious mistake not to
include this.
Tol, Estrada and Gay-GarcΓa (2015) examines how the economy in harmed by shocks from
climate change, and how well this is captured in IAMs, if it can be assumed that these can be
seen as macroeconomic shocks. Effects of macroeconomic shocks to the economy has been
observed to have persisting effects, but in an IAM as DICE, the effect is that the model shows
almost no memory to previous damages. As they introduce persistence of shocks the effect on
economic outcomes have possibilities to be much larger, suggesting that economic dynamics
should be more carefully modeled to capture persistence in shocks.
1.6 Organization of the thesis
After the introduction section comes in section 2, Methodology, which describes the modelling
framework used, the extensions of the model that are analyzed, and in what way it is analyzed.
Section 3, Results, provides the results explaining the effects of the model extensions. Section
4 concludes and discusses these results and possible improvements.
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2 Methodology
Dietz and Stern (2015) uses the DICE model from 2010 in their paper. I will use another version
of the DICE model, the Adaptation in DICE model (AD-DICE) which models adaptation
explicit as a policy variable, but provides the same results (de Bruin, Dellink and Tol, 2009). In
this section, the models structure and its theoretical assumptions will be explained. Thereafter
the extensions that Dietz and Stern (2015) implements are shown in the AD-DICE framework,
and lastly the modifications I make are explained.
2.1 The DICE and the AD-DICE model
DICE, the Dynamic Integrated Climate-Economy model, was developed by Nordhaus (1994)
to investigate optimal policy measures in order to tackle climate change and has been updated
several times since then. The objective of the model is to maximize the total discounted utility
over a time period of 600 years. The model contains equations describing the economy, the
climate system, how emissions are created and how climate change is damaging the economy,
connecting all parts with each other. To optimize utility the best choice of mitigation - reduction
in emissions per unit of output - is chosen. In AD-DICE adaptation is possible to explicitly
choose as a policy option, where adaptation in DICE is implicit and assumed to be optimal. The
more important equation, following the AD-DICE framework is described below.
Production Yt is represented with a Cobb-Douglas function in equation (1) where TFP, Aexo,t, is
exogenously given, growing at a decreasing pace. In equation (2) capital, Kt accumulates
dynamically, increasing with the level of investment It that is decided by an savings rate st that
is optimized in the model by equation (3), and depreciates at a constant level, dk. The population,
Lt, grows exogenously. The time periods are 10 years long.
ππ‘ = π΄ππ₯π,π‘πΏπ‘(1βπΌ)
πΎπ‘πΌ (1)
πΎπ‘ = πΎπ‘β1(1 β ππ) + πΌπ‘ (2)
π π‘ =πΌπ‘
0.00001+ππ‘ (3)
Production creates emissions, Et, of greenhouse gases proportionate to the level of output in
equation (4). Mitigation, ΞΌt is given as a fraction of total emissions and represents the fraction
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of emission reduced, decreasing emissions from production. Exogenous technological change
makes production more energy efficient, Οt by time, i.e. the same level of output creates less
emissions. Emissions build up the stock of carbon dioxide in the atmosphere. There is a smaller
amount, othert, of exogenous natural emissions and emissions of other greenhouse gases, e.g.
from deforestation.
πΈπ‘ = ππ‘(1 β ππ‘)ππ‘ + ππ‘βπππ‘ (4)
The climate system is modeled by geophysical equations to make the concentration of carbon
dioxide in the atmosphere change the climate. The change is represented by the global average
increase in temperature Οt relative preindustrial levels. Even though climate change includes
other changes and regional differences in temperature change, this measure is used to make the
model simpler.
The impact on the economy is represented by a damage function Dt that decreases output by a
fraction Ξ©t. Climate change is in this way creating a negative feedback to output, where higher
output in the same time also decreases net output through the increased damages. Damages are
modeled as a quadratic function of the temperature increase. In the AD-DICE model, which I
will use, the coefficients for the damage function, GDt in equation (5), are different to take into
account explicit adaptation. The damages increase more than linearly with temperature. In the
DICE model damages decrease through adaptation and the costs for this is implicit. AD-DICE
explicitly models adaptation, specifying gross damages, GDt, before adaptation, the fraction of
damages that are adapted to, Pt (protection) in equation (7), by flow and stock adaptation. Flow
refers to reactive adaptation that is used as a reaction to realized climate change (e.g air-
condition when temperatures get higher) and the costs have a flow structure. Stock adaptation,
sadt, refers to proactive measures (e.g. building sea-walls) that is taken to prevent coming
impacts from climate change, building up a capacity to live with climate impacts. Residual
damages, RDt, specified in equation (6), are damages after adaptation is implemented. The costs
for flow adaptation, fadt, and investment in stock adaptation, iat, are included in the fraction Ξ©t
of output lost as a consequence of climate change damages and adaptation costs (equation 9).
Net damages are the same in DICE and AD-DICE.
To mitigate, emissions has to be abated, which is costly. Abatement, Ξt. is assumed to
exogenously get cheaper with technological progress, so that costs decrease with time, but they
also increase as mitigation level rises, modeled by the parameters ΞΈ1,t and ΞΈ2.
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πΊπ·π‘ = π1ππ‘ + π2ππ‘π3 (5)
π€βπππ π1 = 0.00315, π2 = 0.000656, π3 = 3.63
π π·π‘ =πΊπ·π‘
1+ππ‘ (6)
ππ‘ = π(ππππ‘ , π πππ‘) (7)
π πππ‘+1 = π ππ(πππ‘ , π πππ‘) (8)
πΊπ‘ = 1 β1
1+πππ‘+ππππ‘+π π·π‘ (9)
π¬π‘ = π1,π‘ππ‘π2 (10)
ππππ‘π‘ = ππ‘(1 β π¬π‘)(1 β πΊπ,π‘) (11)
π€βπππ πΊπ,π‘ = πΊπ‘
In the optimization, costs for adaptation and abatement are weighed against benefit of avoided
damages to maximize total discounted utility. This is the sum over time in equation (12) of each
periodsβ utility, Ut, derived from consumption per capita ct for the total population. It is time
discounted with rt, in equation (14) decided by the discount rate Ο to make the future less
important. The marginal utility of consumption is decreasing with its elasticity Ξ·, making higher
consumption levels relatively less important in equation (13).
πππ‘ππ πππ πππ’ππ‘ππ π’π‘ππππ‘π¦ = βππ‘
ππ‘
ππ‘=1 (12)
ππ‘ = (ππ‘
1βπβ1
1βπ) πΏπ‘ (13)
ππ‘ = (1 + π)π‘β1 (14)
2.2 Dietz and Stern's extensions
Dietz and Stern (2015) states that they use the DICE model from 2010 and extends it to take
into account some different aspects that IAMs have been criticized for not including. They
introduce endogenous growth in two different models, by spillover effects from the total capital
stock and investment respectively, the first being combined with damages to capital and the
second with damages to TFP. To recognize that firms will not see any effect of their individual
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investment as it is the total stock of capital or investment that creates the spillover effect, savings
are fixed to the average optimal level in the standard model absent climate damages.
The first, called Endogenous growth model 1, has spillover effects Ξ² from the total stock of
capital where Ξ²=0.3, and the model is calibrated to match output for the DICE model in absence
of climate damages, with an exogenous parameter of Aend1,t.
ππππ1,π‘ = π΄πππ1,π‘πΏπ‘(1βπΌ)
πΎπ‘(πΌ+π½)
(1.End1)
π π‘ = 0.23
The damages from climate change, Ξ©t are partitioned between GDP and either capital or TFP
by a fraction fi in the following manner:
πΊπ,π‘ = ππ(1 β πΊπ‘) , π = πΎ, ππΉπ (13)
πΊπ,π‘ = 1 β(1βπΊπ‘)
(1βπΊπ,π‘) (13.Y)
Including capital damages in the capital accumulation, equation (2.K), together with
Endogenous growth model 1 constitutes the Capital model. Here, the damages to output is
decided by equation (13.Y).
πΎπ‘+1 = πΎπ‘(1 β ππ)(1 β πΊπΎ,π‘) + πΌπ‘ (2.K)
Where the fraction of damages to capital, fK, is set to 0.3, as the authors read Nordhaus and
Boyer (2000) to suggest.
In the other growth model, Endogenous growth model 2, TFP, Aend2, t grows as a function of
investment according to equation (14), trying to catch the same spillover effect as the first
model. The coefficients Ξ³1 and Ξ³2 are calibrated to match output for the DICE model in absence
of climate damages and da is exogenous depreciation of TFP.
π΄πππ2,π‘+1 = π΄πππ2,π‘(1 β ππ) + πΎ1πΌπ‘πΎ2 (14.End2)
ππππ1,π‘ = π΄πππ2,π‘πΏπ‘(1βπΌ)
πΎπ‘πΌ (1.End2)
In the TFP model the TFP damages from equation (13) depreciates the TFP by a fraction, in
Endogenous growth model 2, as described in equation (14.TFP). Dietz and Stern (2015) chose
to let the fraction fTFP be 0.05. As they have not found estimates for this, the level is quite
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arbitrary, but chosen to not be too high.
π΄π‘ππ,π‘+1 = π΄ππΉπ,π‘(1 β ππ)(1 β πΊππΉπ,π‘) + πΎ1πΌπ‘πΎ2 (14.TFP)
Further, convex damages are included by making the damage function steeper for high
temperatures. With the original damage function an increase of the temperature by 4 degrees
still does not make a severe impact on the economy. To reflect that this level of climate change
is predicted to be very harmful, two different damage specifications are used in Dietz and Stern
(2015). One was suggested by Weitzman (2012), making 50% GDP loss at 6 degrees
temperature increase, and the other damages the economy by 50% at 4 degrees temperature
increase. I will only use the Weitzman specification, here presented in equation (15), as it is in
relation to standard DICE damages, Dt. Together with the previous models it creates models
that will be referred to as with convex damages.
π·πΆπππ£ππ₯ = π·π‘ + 5.07 β 10β6ππ‘6.754 (15)
To model uncertainty, the uncertainty about the climate sensitivity parameter S1 in the radiative
forcing equation, S is set to different values. This is done by running the model for the most
probable value 3, but also for 1.5 as the IPCC judges it to be 'likely' β meaning a probability of
anywhere between 66% and 100% - to be between 1.5 and 4.5 degrees. The parameter is also
set to 6, that the parameter is judged to be 'very unlikely' β a probability lower than 10% - to
exceed. Another approach Dietz and Stern (2015) use, that will not be included in this thesis, is
fitting a continuous probability density function to these values and run the model with random
number from this.
2.3 Modifications to the model
To look closer at these model extensions I include the changes in a version of AD-DICE that is
based on the DICE model from 2010. Dietz and Stern (2015) state that they use the DICE model
from 2010 from the homepage of William Nordhaus2. The Excel version provided at the
homepage produces different numbers for optimal mitigation from what they report as
mitigation levels in the standard model. The reasons for this is not clear and I will therefore do
1 The climate sensitivity is a parameter describing how much the average temperature will increase when
carbon concentrations in the atmosphere is doubled relative preindustrial levels 2 http://www.econ.yale.edu/~nordhaus/homepage/RICEmodels.htm
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the analysis according to their extensions, but use the 2010 model of DICE written in Excel
translated to code used in the mathematical programming program GAMS, and implemented
in the AD-DICE model. I apply the aggregated damages (where sea level rise damages are not
modeled explicitly) as is done in Dietz and Stern (2015). Using the AD-DICE model gives the
possibility to look at changes in the amount and cost of adaptation when changing damage
mechanism and apply the useful distinction between residual damages and adaptation costs.
The standard model refers to the DICE model without any changes to it. The optimal scenario
refers to the scenario where the economy is optimized by mitigating to take into account climate
damages. Optimal in absence of climate damages is when there are no impacts of climate
change. Business as usual is when no policy measures are taken to slow climate change, but the
economy is optimized in respect to remaining factors.
2.3.1 Replication of models
The same extensions, with some modifications, are made in this model to look at if I reach any
differences in results. The climate sensitivity parameter S is put to 3 in the standard case, as is
done by Dietz and Stern (2015), (even if the value in the DICE model was 3.2). For convex
damages I only use the Weitzman specification, and for uncertainty I only use the two extra
values for climate sensitivity parameter, as these extensions are not the focus in the thesis.
The savings rate is fixed to the same set of rates that is achieved when the model is optimized
in absence of climate damages, and not st=0.23 as they use. In AD-DICE, residual damages,
flow adaptation costs and adaptation investment constitutes the damage measure in DICE,
therefore assigning of fraction is done according to this. To compare with Dietz and Stern
(2015) results, my results for mitigation, carbon prices and business as usual consumption per
capita will first be compared to the standard DICE model, with exogenous growth. In the further
analysis, the TFP model and the capital model will instead be compared to their respective
endogenous growth model, as this captures the effect of these damages explicitly.
2.3.2 Endogenous TFP growth
The Endogenous growth model 2 is used, but also another type was constructed, Endogenous
growth model 3, as in equation (14.End3), that better matches the exogenous growth models
output levels in absence of climate damages.
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π΄πππ3,π‘+1 = π΄πππ3,π‘(1 β ππ) + πΎ3πΌπ‘ + πΎ4πΌπ‘πΎ5 (14.End3)
ππππ1,π‘ = π΄πππ3,π‘πΏπ‘(1βπΌ)
πΎπ‘πΌ (1.End3)
They both follow the growth path for output well at shorter time period, but after some hundred
years the Dietz and Stern (2015) specification, Endogenous growth model 2, produce much
lower values than the DICE model whereas Endogenous growth model 3 follows the path very
well. As they are quite equal in the near future only Endogenous growth model 2 will be used.
2.3.3 Further modifications
I look at optimal mitigation levels to compare with Dietz and Stern (2015)βs results and get a
picture of how drastic measures different extensions imply. The same is for carbon prices, but
this will also reflect the decreasing cost for mitigation and energy efficiency. Business as usual
consumption per capita results illustrates the damage that the economy can face if nothing is
done to prevent climate change.
To see the effect of endogenous growth, I simply model the endogenous growth models without
any damages to capital or TFP comparing to the exogenous growth. To see the effect and
interactions of capital and TFP damages these are also run in exogenous growth contexts.
Exogenous growth and TFP damages is modeled by making an equation for TFP that grows in
the exogenous growth rate gat as in the standard model, but letting it be endogenously damaged
by climate change, as in equation (14.Exo).
π΄ππ₯π,π‘+1 = π΄ππ₯π,π‘(1 β πΊπ‘,ππΉπ)πππ‘, (14.Exo)
The effect of convex damages and its interactions with other extensions are made by introducing
them in the Endogenous growth models 1 and 2 and the Capital and TFP model.
To look at the effect of different assumptions of how big fraction of damages that hits capital
or TFP, the fraction is simply changed, from 0 to 1.0 with 0.1 or 0.2 steps. For the TFP model,
where the original assumption is that the fraction is 0.05, I in addition try a fraction of 0.01, to
capture effects of a smaller fraction.
As a part of the damages are in fact costs for adaptation measures, and the non-adapted damages
are residual damages, it would be more reasonable that no part of the adaptation cost are counted
as damage to capital or TFP, but only affecting GDP. Therefore, I look at the effects of only
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letting a fraction of residual damages damage capital and TFP respectively, as in equation
(13.RD). The way of partitioning the damages is rewritten from Dietz and Stern (2015), but
provides practically the same results.
πΊπ‘,π = 1 β1
1+ππ(π π·π‘) (13.RD)
πΊπ‘,π = 1 β1
1+πππ‘+ππππ‘+(1βππ)π π·π‘ (13.Y.RD)
To look at how components of climate costs are affected by capital and TFP damages
respectively, and relative the case with only residual damages being damaged, adaptation costs
as a fraction of total climate costs are calculated as in equations (16), (17) and (18).
π΄ππππ‘ππππ πππ π‘ πππππ‘πππ =πππ‘+ππππ‘
πππ‘+ππππ‘+π π·π‘+π¬π‘(16)
πΉπππ€ πππππ‘ππππ πππ π‘ πππππ‘πππ =ππππ‘
πππ‘+ππππ‘+π π·π‘+π¬π‘ (17)
ππ‘πππ πππππ‘ππ‘πππ πππ£ππ π‘ππππ‘ πππ π‘ πππππ‘πππ =πππ‘
πππ‘+ππππ‘+π π·π‘+π¬π‘ (18)
2.4 Table of models
Model name Important equations
Standard model ππ‘ = π΄ππ₯π,π‘πΏπ‘(1βπΌ)
πΎπ‘πΌ (1)
Endogenous growth model 1 ππππ1,π‘ = π΄πππ1,π‘πΏπ‘(1βπΌ)
πΎπ‘(πΌ+π½)
(1.End1)
Endogenous growth model 2 π΄πππ2,π‘+1 = π΄πππ2,π‘(1 β ππ) + πΎ1πΌπ‘πΎ2 (14.End2)
Endogenous growth model 3 π΄πππ3,π‘+1 = π΄πππ3,π‘(1 β ππ) + πΎ31πΌπ‘ + πΎ4πΌπ‘πΎ5(14.End3)
Capital model (1.End1) and πΎπ‘+1 = πΎπ‘(1 β ππ)(1 β πΊπ‘,πΎ) + πΌπ‘ (2.K)
TFP model π΄π‘ππ,π‘+1 = π΄π‘ππ,π‘(1 β ππ)(1 β πΊπ‘,ππΉπ) + πΎ1πΌπ‘πΎ2(14.TFP)
With convex damages π·πΆπππ£ππ₯ = π·π‘ + 5.07 β 10β6ππ‘6.754 (15)
TFP in exogenous growth π΄ππ₯π,π‘+1 = π΄ππ₯π,π‘(1 β πΊπ‘,ππΉπ)πππ‘, (14.Exo)
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3 Results
3.1 Comparison to Dietz and Stern results
First, I look at how well my results fit with the numbers reported in Dietz and Stern (2015),
which should give similar results as they are based on the same extensions. As GAMS and
Excel have some computational differences and since the Excel model includes some starting
values not only for 2005, but also for 2015 β which are omitted in the GAMS code as this year
has not yet happened β the results should be slightly different, but show the same pattern.
Figure 1 shows mitigation levels and compares the results for my model (AD-DICE), the DICE
2010 model (DICE), and Dietz and Stern results (D&S). For better visibility I only look at
standard and capital/TFP models, not convex damages or uncertainty about climate sensitivity.
Looking at the three lower curves, standard AD-DICE replicates DICE with small differences.
Standard D&S is way below this, which indicates some error in their model or reporting. For
the two highest curves showing the TFP model, there is not much difference between AD-DICE
and D&S, and neither for the two curves in the middle, showing the mitigation for the capital
model, but the levels for D&S is slightly lower. This shows that the model used in this thesis
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Figure 1 Comparison of optimal mitigation levels, TFP and capital model β Results for D&S, DICE and
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replicates quite well, the difference being for the standard cases. In figure 2 optimal carbon
prices are shown, following a similar pattern as mitigation, where more mitigation gives higher
carbon prices. The somewhat larger differences between AD-DICE and D&S capital model for
carbon prices than mitigation can be explained with a slightly lower level of mitigation for D&S
in the beginning.
Figure 2 Comparison of optimal carbon prices, TFP and capital model β Results for D&S, DICE and AD-
DICE
3.2 Effect of choice of growth model
The effects of growth is studied to see how it affect capital and TFP damages. These insights
are good to be able to compare results where the extensions is compared to the endogenous
growth models, and for discussing D&S results. By comparing results for endogenous and
exogenous growth models, with and without capital or TFP damages, we can see how much of
the effect that can be accredited to each change.
With endogenous growth higher effects are expected as of the same GDP damages in the
exogenous growth model. For Endogenous growth model 1, the capital accumulation effect on
production should increase. The production is now more dependent on capital, and the lower
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GDP as a consequence of climate change, will give less room for new investment that could
have increased growth, and the economy will be more damaged. Fankhauser and Tol (2005)
show that the capital accumulation effect was increased with endogenous growth. For
Endogenous growth model 2 and 3 we should also see more effects from climate damages.
Climate damages that decrease GDP give less room for investment that in this model creates
TFP growth. This effect will cumulate in the TFP function, as the lower level of TFP will
persist.
3.2.1 Growth models
Comparing the standard model with exogenous growth with the endogenous growth models,
the former gives the consumption in the business as usual scenario, the difference slowly
increasing to about 2.5% in 2105, but for Endogenous growth model 3 only 1%. In the following
centuries differences are increasing, with most damages to Endogenous growth model 2 and 3.
3.2.2 Capital model
In figure 3 the business as usual consumption per capita for exogenous and endogenous growth
is illustrated, with and without capital damages. Capital damages introduced in the exogenous
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Figure 3 Effect of endogenous growth on capital damage impacts -Business as usual consumption per
capita for exogenous and endogenous growth models with and without capital damages.
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growth model results in higher level of consumption than for the standard case, that is, the
economy is less damaged. For the Capital model with endogenous growth and capital damages,
consumption gets lower than for Endogenous growth model 1. This shows that in an
endogenous growth context, capital damages has a negative effect, but in exogenous growth
context the effect is positive.
3.2.3 TFP model
Figure 4 shows the effects of endogenous growth in the TFP model. For the TFP model with
endogenous growth and TFP damages, the damage on GDP is quite strong compared to the
standard model and Endogenous growth model 2. TFP damages with exogenous growth gives
a somewhat larger negative effect, small in this century but larger in coming centuries.
The effect of capital or TFP damages is impacted by the choice of growth model. It is not only
the size of effects, but for capital, the growth model decides if it has a positive or negative
effect. Endogenous growth drives capital damage effect but not the TFP damage effect.
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Figure 4 Effect of endogenous growth on TFP damage impacts -Business as usual consumption per capita
for exogenous and endogenous growth models with and without TFP damages
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3.3 Stern and Dietzβs extensions - capital model
The results for the Capital model is replicated here. When the capital stock is damaged, this
effect will persist until later periods, as it is the same stock that will be used for future
production. This kind of damage can have cumulative effects, and in this way be more harmful
than damages to GDP that only lasts one period. On the other hand, as the Cobb-Douglas
production function have decreasing returns to factors the decrease in output will be less than
proportional to the damage. If for example capital is decreased by 10 percent, GDP will only
decrease by about 6 % that year when the Endogenous growth model 1 is applied and parameters
are defined as in this setting. In the same time it also creates a need for more savings to build
up capital, which decreases consumption. Another effect is that GDP will have less direct
damages, so for the Capital model to be more harmful, the extra damages from capital must be
more than the change in how much GDP is damaged. If damages are higher, mitigation and
carbon pries can also be expected to be higher.
3.3.1 Economic impact
Figure 5 shows consumption per capita in the business as usual scenario for different extensions
combined with capital damages. The higher curves show that low climate sensitivity will give
the highest levels of consumption, slightly better than the endogenous growth model. With
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Figure 5 Consumption per capita, capital model. Business as usual results for different extensions
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damages to capital, consumption per capita will be lower, in 2105 about 2.6% lower than
Endogenous growth model 1. With convex damages added to this, the effect is that consumption
is about 7.4% lower in 2105, and with convex damages and capital damages the effect is 10%.
The capital damage and convex damages effects do not seem to reinforce each other, but rather
add damages in this time span. The lowest curve showing a climate sensitivity of 6 degrees
introduced, the impacts are much bigger than for the other models, even making consumption
per capita decrease after the middle of the century.
3.3.2 Mitigation
Figure 6 show optimal mitigation for the same extensions as above. Only the Capital model
will give a small difference from Endogenous growth model 1. Both starting at about 23% in
2015, and being about 80% in 2105. With convex damages, the mitigation is somewhat faster,
and looking at a climate sensitivity parameter of 6, full mitigation should be implemented in
2065. If, on the other hand climate sensitivity is 1.5, mitigation can be much lower than in the
other cases, showing a big range for optimal policies if the climate sensitivity is between these
values. The convex damages and climate sensitivity seem to have effects that is of more
importance for policies than only capital damages.
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Figure 6 Optimal mitigation levels, capital model. Results for different extensions
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3.3.3 Carbon prices
The carbon prices, in Figure 7, show a similar pattern as mitigation. Endogenous growth model
1, Capital model and these with convex damages have quite similar initial prices, then rising in
relation to the mitigation levels from almost $100 in 2015 to between almost $700 and $1000
in the end of the century. The price for convex damages and high climate sensitivity calls for
much higher prices, beginning at about $250 in 2015.
Figure 7 Optimal carbon prices, capital model. Results for different extensions
3.4 Stern and Dietz Extensions- TFP model
Damage to TFP will be persistent as TFP builds upon previous years TFP. As the TFP increases
production proportionally to its size, a percentage decrease in TFP should also create a
percentage loss in GDP. With exogenous growth, this damage cannot be repaired. In the
endogenous growth context TFP can be repaired by investing more, but then a larger part of
GDP has to be devoted to investment in capital and less to consumption, decreasing
consumption possibilities. Overall, damages should be larger than without TFP damages. This
implies higher level of mitigation and carbon prices.
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3.4.1 Economic impact
Figure 8 shows impacts on consumption per capita under business as usual, with TFP damages.
The effect of these TFP damages is quite large, and growing over time; the TFP model shows
consumption per capita that is about 9% lower than Endogenous growth model 2 in 2105. The
Endogenous growth models 2 and 3 gives basically the same results with TFP damages for this
century, and thus 3 is omitted here. Endogenous growth model 2 with convex damages gives
about 8% lower consumption, and for the TFP model with convex damages, it is about 16%
lower. The convex damages have quite equal impacts as TFP damages and does not seem to
interact with capital damages, but is looks additive so far. When climate sensitivity is 6 degrees,
consumption per capita actually start to slowly decrease after year 2035. The effects here are
bigger than for capital damages, but as the fraction to TFP was set quite arbitrarily they are not
necessarily comparable. Comparing with Dietz and Stern (2015), they report small differences
between the standard and the TFP model, similar to these results, but not consistent with their
numbers for mitigation.
3.4.2 Mitigation
Figure 9 shows optimal mitigation levels for the TFP model, replication of the Dietz and Stern
(2015) extensions. The difference between Endogenous growth model 2βs mitigation and
mitigation for the TFP model, is quite large here, where the former start at 24% in 2015 and the
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Figure 8 Consumption per capita, TFP model. Business as usual results for different extensions.
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later at 31 %, reaching full mitigation in 2095. Introducing convex damages makes a difference,
but not as much as the TFP damages. The reason for this can be that optimal mitigation levels
are high enough to avoid high temperatures, so the high temperature damages are not close.
Including a climate sensitivity of 6 degrees almost double the speed towards full mitigation,
being full already in 2055. The high temperatures are much easier to reach, causing need for
more mitigation.
Figure 9 Optimal mitigation levels, TFP model. Results for different extensions
3.4.3 Carbon prices
Looking at Figure 10, for the TFP model and TFP model with convex damages carbon prices
are quite equal and higher than Endogenous growth model 2 without these extensions. This
reflects the mitigation levels. Starting at about 150$ in 2015, they reach price of almost $700 to
$1000 in the end of this century. With high climate sensitivity, carbon prices starts at about
$400 and reaches $1100 in the middle of the century, before starting to decrease.
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Figure 10 Optimal carbon prices, TFP model. Results for different extensions
3.5 Choice of savings rate
Fixing the savings rate at the optimal rate given capital or TFP damages, but not endogenous
growth, consumption possibilities can be expected to be higher than if the savings rate is set to
the rate when no capital or TFP damages as this should reflect the behavior of firms in the
presence of the damages better. This as the need for new investment is higher when some capital
is damaged. This would probably result in higher optimal consumption per capita. Fankhauser
and Tol (2005) studies the effect of the choice of savings rate under climate change in the DICE
model, but finds very small effects.
3.5.1 Capital and TFP model
The effect of fixing the savings rate for the capital model is negligible; fixing it at 0.23, fixed
at the optimal levels for the standard model in absence of climate damages, or fixed at the
optimal levels when capital damages are included creates very similar results. If savings are set
free in the endogenous growth models, consumption per capita can increase drastically, but this
is because all the spillover effects can be exploited, that is firms are made to save for the
common good. They could be made to this, but the model is not calibrated to take this into
account. A reason to why we do not see any effect on the results is that climate damages is such
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a small part of the economy, thus other factors in the economy will affect savings much more,
as for example the effect we can see when a spillover effect is included.
The savings effect is less direct for TFP, but as TFP is damaged exogenously, the response
should be some change in behavior. This is, as for the Capital model negligible, only making a
very small effect. Again, if savings are set free, consumption increases, but the model is not
calibrated for this.
3.6 Effect of fraction size
The fraction of damage impacting capital was estimated from Nordhaus and Boyer 2000 to be
around 0.3, and the fraction to TFP was more arbitrarily chosen to 0.05. Results for
consumption per capita in business as usual are estimated for fractions ranging from 0 to 1.0.
The 0 case thus is represented by the endogenous growth models. This will show the importance
of the size of the fractions. The effect should be larger with larger fractions, as damages to
capital and TFP has been shown to cause greater damages.
3.6.1 Capital model
In figure 11 the results are shown for the Capital model, the axis starting at 37 500 US $. When
no capital damages are present this gives the smallest damages on consumption, and when a
large part of damages are on capital the most damages are observed. The difference in 2105
between the no capital damage and the 1.0 case is about 6% less, where the differences are
getting bigger by time, illustrating the compounding effect. There is also more difference for
the lower values of fractions, than for the higher values. The relative difference from only GDP
damages is bigger for small fractions.
The results can be compared to estimated fractions of damages to capital from different sources,
upon which the damage estimates for DICE is built. The estimate for Nordhaus and Boyer
(2000) damages, is a fraction 0.26, for Tol (1995) the fraction is estimated to 0.14, for the FUND
2.9 model 0.11, and for Fankhauser (1995) it is estimated to be 0.10. Following this, the effect
of capital damages should be smaller than reported, and as three studies suggest a fraction of
about 0.1, the effect is about 0.9% lower than Endogenous growth model 1, only almost a third
of the 2.6% effect on consumption per capita that a fraction 0.3 has.
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Figure 11 Effect of size of damage fraction, capital model. Business as usual consumption per capita for damage fraction
varying from 0 to 1.0 in 2105
3.6.2 TFP model
Figure 12 shows the differences in businesses as usual consumption per capita when TFP is
damaged. Some of the fractions are left out to make the graph easier to read. The damage on
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ita 1
000 2
005 U
S $
0 0.01 0.05 0.1 0.2 0.4 0.6 0.8 1.0
Figure 12 Effect of size of damage fraction, TFP model. Business as usual consumption per capita for
damage fraction varying from 0% to 100%
Assessing the Effect of Damages to Capital and Total Factor Productivity, Master Thesis Ida Nordin 2015
32
the economy is smallest at low fractions and larger for higher fractions. The differences are
larger than for capital damages, in 2105, the consumption is about 70% lower when all damages
on TFP, than when it is not damaged at all. The differences are clearly increasing by time.
Looking at the fractions, already when the fraction is 0.4 consumption are going to start
decreasing in the end of this century, showing much more damages than the case when no
damages are on TFP damages and the economy continues to grow. The increase in differences
are smaller for the larger fractions than for the first low fractions.
3.7 Only residual damages affecting capital and TFP
When only a fraction of the residual damages β damages after adaptation measures β are
damaging capital or TFP, capital damages will consequently be smaller than when also
adaptation measures are included. As both capital damages and TFP damages have been shown
to have a negative effect on the economy in the endogenous growth context, the total damages
should now be smaller.
3.7.1 Capital and TFP model
When capital damages are only a fraction of residual damages, consumption in the business as
usual case is about 0.7% larger than for the original Capital model, illustrating a similar effect
as when making the fraction of damages to capital decrease. For the TFP model the story is the
same as with capital damages but the effect is 2.6%; when only residual damage damages TFP,
the impact on the economy is smaller. The best results is still for the endogenous growth models
without capital or TFP damages.
3.8 Adaptation costs as fraction of climate costs
Adaptation costs, costs for flow adaptation and stock adaptation investment, are shown both
together as a fraction of total climate costs, and with their individual shares. The total climate
costs also include residual damages and costs for abatement.
When adaptation costs are only on output, their damaging effect should not be as big as when
it is on capital or TFP too. These extensions have been shown to give larger impacts, thus,
implementing adaptation will be a cheaper choice in this setting as it does not have the dynamic
Assessing the Effect of Damages to Capital and Total Factor Productivity, Master Thesis Ida Nordin 2015
33
effects that residual damages has. At the same time adaptation is also used to reduce residual
damages, which are relatively more harmful as they are on capital and TFP. The original Capital
model compared to Endogenous growth model 1, should give a lower share of adaptation cost,
because of its higher level of optimal mitigation. Mitigation takes a larger part of climate change
policy choices at higher damage levels as it has more effect on higher damages.
3.8.1 Capital model
In figure 13 the fraction of climate costs consisting of adaptation in 2015 and 2015, for the
Capital model, is shown. In 2105, when only residual damages are damaging capital, the
fraction of costs being adaptation costs is about 12% (2.5 percentage points) larger than for the
Endogenous growth model 1, and about 30% (5.3 percentage points) higher than the original
Capital model. The total share of costs being adaptation costs increases in this century, which
is mostly because of a rising share of flow adaptation costs. This change is most seen for the
case where adaptation is not allowed to impact capital, implying that adaptation has better
possibilities to reduce impacts in these settings. So, capital damages decrease adaptation,
whereas when capital is not damaged by adaptation costs, adaptation increases.
0
0,05
0,1
0,15
0,2
0,25
Endogen
ous
gro
wth
model
1, to
tal
Capit
al
model
tota
l
Capit
al
model
, re
sidual
dam
ages,
tota
l
End
ogen
ous
gro
wth
model
1, In
ves
tmen
t in
adapta
tion
Capit
al
model
, In
ves
tmen
t
in a
dap
tati
on
Capit
al
model
, re
sidual
dam
ages,
Inves
tmen
t in
adap
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on
Endogen
ous
gro
wth
model
1, F
low
adap
tati
on
Capit
al
model
Flo
w
adap
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on
Capit
al
model
, only
res
idual
dam
ages,
Flo
w a
dapta
tionFra
ctio
n o
f to
tal
clim
ate
cost
s
2015 2105
Figure 13 Effect of composition of climate costs when capital is only damaged by residual damages.
Optimal results for adaptation costs as a fraction of total climate costs for the capital model, where the fraction
of damages at total damages and only at residual
Assessing the Effect of Damages to Capital and Total Factor Productivity, Master Thesis Ida Nordin 2015
34
3.8.2 TFP model
In figure 14 the fraction of climate costs consisting of adaptation in 2015 and 2015, for the TFP
model, is shown. Again, the share is much higher for the case when TFP is only damaged by
residual damages. In 2105, when only residual damages are damaging TFP, the fraction of costs
being adaptation costs is about 29% (5.9 percentage points) larger than for the Endogenous
growth model 1, and about 64% (10.3 percentage points) higher than the original TFP model.
The total share of costs being adaptation costs increases in this century, except for the case with
only residual damages on TFP where the fraction of adaptation costs decrease slightly. This is
mostly because of a rising share of flow adaptation costs, but also somewhat lower levels of
adaptation investment costs, implying relatively better possibilities for adaptation. The numbers
should not be compared too much with outcomes for the capital model, as their fractions of
damage are not matched. But, also here TFP damages decrease adaptation, whereas when
adaptation is not included in the TFP damages, adaptation increases.
Figure 14 Effect of composition of climate costs when TFP is only damaged by residual damages.
Optimal results for adaptation costs as a fraction of total climate costs for the capital model, where the fraction of
damages at total damages and only at residual damages.
0
0,05
0,1
0,15
0,2
0,25
0,3
End
og
enou
s gro
wth
mo
del
2,
tota
l
TF
P m
od
el,
tota
l
TF
P m
od
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resi
du
al d
amag
es,
tota
l
End
og
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wth
mo
del
2,
Inv
estm
ent
in a
dap
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on
TF
P m
od
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Inv
estm
ent
in
adap
tati
on
TF
P m
od
el,
resi
du
al d
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Inv
estm
ent
in a
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on
End
og
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wth
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del
2,
Flo
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dap
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on
TF
P m
od
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Flo
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TF
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od
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on
ly r
esid
ual
dam
ages
, F
low
adap
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Fra
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f to
tal cl
imat
e co
sts
2015 2105
Assessing the Effect of Damages to Capital and Total Factor Productivity, Master Thesis Ida Nordin 2015
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4 Conclusion
Assessing the effects of climate change damages on capital and total factor productivity by
following the suggested modelling of Dietz and Stern (2015), some interesting findings were
done. The differences from the result for optimal policies in the standard model β that is, with
and without their extensions β are much smaller than Dietz and Stern (2015) concluded. I could
not find the reason for this in the small disparities from the choice of models, and no answer
was found. Moving on, effects on the economy of introducing capital and TFP damages was
found, even if not in the size earlier suggested. These results hold for comparison to both the
standard AD-DICE (and DICE) results, and to the Endogenous growth models that are part of
the extended models, but less difference in the latter case, showing the explicit effect of capital
or TFP damages in this context.
The growth model chosen was observed to be important for these results, as damages to capital
only have a negative effect of some percentages loss in the endogenous growth context with
spillover effects to capital, but positive effects in the standard exogenous growth model.
Although capital damages increased impacts, their possible impact were shown to be limited in
this model, when even putting all damages to capital. For TFP damages on the other hand, a
large share of damages on TFP were shown to have a potentially very big effect on economic
outcomes, which could decrease GDP. The effects of TFP damages are somewhat larger in an
exogenous growth context, but nevertheless can the cumulative TFP damages have a large
impact also in the endogenous growth model, decreasing possible GDP with several percent.
Changing the savings rate, on the other hand, to take into account capital or TFP damages does
almost not give any differences. The savings rate seems to be more affected by other factors in
the economy. Convex damages were not seen to pronounce the effects of capital and TFP
damages, at the temperature levels reached, but shows an impact larger or in comparison with
capital and TFP damages. Exploring the effects of a high climate sensitivity, effects that are
much larger than capital and TFP damages are found, giving some perspectives on the size of
effects.
Damages on capital and TFP should not include adaptation costs in the same way as damages
to GDP should, as Dietz and Stern (2015) assumed, since the funds for this are taken from GDP.
Changing this showed that the policy choices become different. Residual damages and
adaptation costs are not affecting the economy in the same way anymore and thus the
Assessing the Effect of Damages to Capital and Total Factor Productivity, Master Thesis Ida Nordin 2015
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composition changes. This is leading to larger share of adaptation costs of the total climate costs
than if capital, TFP and output are affected in the same way.
The results illustrates that it is important to explore every change in assumptions that is done,
to find out more, and prevent drawing hasty conclusions from implementing a number of
changes at once. As Pindyck (2013) states, it is easy to believe that IAMs are very precise, but
by clarifying where all results come from it can get easier to get out of that imagination. Keeping
in mind that an assumption is just one of several possible ones, then beginning to understand
what is most important and how they are specified in a most fair and realistic way.
4.1 Future research
This thesis does not cover all various explorations or improvements to these extensions, neither
other similar and realistic extensions that are in line with this, and more sophisticated and
realistic models are needed. A more precise and well-motivated specification of the fraction of
damages going to capital or TFP is needed. The damage functions could look differently for
damages to GDP, capital or TFP as they could possibly have impacts with different functional
forms, beyond costs of adaptation. Instead of trying only one endogenous growth model, the
differences for using other endogenous growth models could have been tried. Rather than fixing
the savings rate so that it was not affected by the fact that we had spillover effects from capital,
it could have been made endogenous to reflect that in optimum society should have recognize
this and make firms act in to save in accordance with this. A specification where both capital
and TFP were damaged at the same time could be analyzed. Another idea for extension would
be to explicitly look at the damage to labor and labor productivity, where for example the
population could stay constant, but labor productivity or fraction of population in the labor force
(due to e.g. diseases) could be decreased, in this way decreasing output.
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