Assessing the Effect of Damages to Capital and Total

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 Master’s 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 Dietz’s 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 – The Dynamic Integrated Climate-Economy model. Numbers referring to the year of

the version of the model

GDP – Gross Domestic Product

IAM – Integrated Assessment Model

TFP – Total factor productivity

Abatement of emissions – actions to take away or reducing emissions

Adaptation to climate change – measures that decrease the impacts of climate change

Business as usual – refers to a scenario where no mitigation is taken to prevent climate change

Carbon price – the price of carbon that reflects the marginal cost of climate change.

Greenhouse gases – gases like carbon dioxide that causes climate change

Mitigation – 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 “dangerous anthropogenic

interference with the climate system” (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 – 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 models’ 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 “tolerable

temperature”. 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 – when no mitigation is

implemented to prevent climate change – 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-García (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.

𝑌𝑡 = 𝐴𝑒𝑥𝑜,𝑡𝐿𝑡(1−𝛼)

𝐾𝑡𝛼 (1)

𝐾𝑡 = 𝐾𝑡−1(1 − 𝑑𝑘) + 𝐼𝑡 (2)

𝑠𝑡 =𝐼𝑡

0.00001+𝑌𝑡 (3)

Production creates emissions, Et, of greenhouse gases proportionate to the level of output in

equation (4). Mitigation, μt 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, σt 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.

𝐸𝑡 = 𝜎𝑡(1 − 𝜇𝑡)𝑌𝑡 + 𝑜𝑡ℎ𝑒𝑟𝑡 (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 τt 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 Ωt. 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 Ωt

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, Λt. 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 θ1,t and θ2.


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𝐺𝐷𝑡 = 𝜋1𝜏𝑡 + 𝜋2𝜏𝑡𝜋3 (5)

𝑤ℎ𝑒𝑟𝑒 𝜋1 = 0.00315, 𝜋2 = 0.000656, 𝜋3 = 3.63

𝑅𝐷𝑡 =𝐺𝐷𝑡

1+𝑃𝑡 (6)

𝑃𝑡 = 𝑃(𝑓𝑎𝑑𝑡 , 𝑠𝑎𝑑𝑡) (7)

𝑠𝑎𝑑𝑡+1 = 𝑠𝑎𝑑(𝑖𝑎𝑡 , 𝑠𝑎𝑑𝑡) (8)

𝛺𝑡 = 1 −1

1+𝑖𝑎𝑡+𝑓𝑎𝑑𝑡+𝑅𝐷𝑡 (9)

𝛬𝑡 = 𝜃1,𝑡𝜇𝑡𝜃2 (10)

𝑌𝑛𝑒𝑡𝑡 = 𝑌𝑡(1 − 𝛬𝑡)(1 − 𝛺𝑌,𝑡) (11)

𝑤ℎ𝑒𝑟𝑒 𝛺𝑌,𝑡 = 𝛺𝑡

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

periods’ 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 ρ to make the future less

important. The marginal utility of consumption is decreasing with its elasticity η, making higher

consumption levels relatively less important in equation (13).

𝑇𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡𝑒𝑑 𝑢𝑡𝑖𝑙𝑖𝑡𝑦 = ∑𝑈𝑡

𝑟𝑡

𝑇𝑡=1 (12)

𝑈𝑡 = (𝑐𝑡

1−𝜂−1

1−𝜂) 𝐿𝑡 (13)

𝑟𝑡 = (1 + 𝜌)𝑡−1 (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 β from the total stock of

capital where β=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.

𝑌𝑒𝑛𝑑1,𝑡 = 𝐴𝑒𝑛𝑑1,𝑡𝐿𝑡(1−𝛼)

𝐾𝑡(𝛼+𝛽)

(1.End1)

𝑠𝑡 = 0.23

The damages from climate change, Ωt are partitioned between GDP and either capital or TFP

by a fraction fi in the following manner:

𝛺𝑖,𝑡 = 𝑓𝑖(1 − 𝛺𝑡) , 𝑖 = 𝐾, 𝑇𝐹𝑃 (13)

𝛺𝑌,𝑡 = 1 −(1−𝛺𝑡)

(1−𝛺𝑖,𝑡) (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).

𝐾𝑡+1 = 𝐾𝑡(1 − 𝑑𝑘)(1 − 𝛺𝐾,𝑡) + 𝐼𝑡 (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 γ1 and γ2 are calibrated to match output for the DICE model in absence

of climate damages and da is exogenous depreciation of TFP.

𝐴𝑒𝑛𝑑2,𝑡+1 = 𝐴𝑒𝑛𝑑2,𝑡(1 − 𝑑𝑎) + 𝛾1𝐼𝑡𝛾2 (14.End2)


𝐾𝑡𝛼 (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


16

arbitrary, but chosen to not be too high.

𝐴𝑡𝑓𝑝,𝑡+1 = 𝐴𝑇𝐹𝑃,𝑡(1 − 𝑑𝑎)(1 − 𝛺𝑇𝐹𝑃,𝑡) + 𝛾1𝐼𝑡𝛾2 (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.

𝐷𝐶𝑜𝑛𝑣𝑒𝑥 = 𝐷𝑡 + 5.07 ∙ 10−6𝜏𝑡6.754 (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' – 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' – 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

http://www.econ.yale.edu/~nordhaus/homepage/RICEmodels.htm


17

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.


18

𝐴𝑒𝑛𝑑3,𝑡+1 = 𝐴𝑒𝑛𝑑3,𝑡(1 − 𝑑𝑎) + 𝛾3𝐼𝑡 + 𝛾4𝐼𝑡𝛾5 (14.End3)


𝐾𝑡𝛼 (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)’s 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).

𝐴𝑒𝑥𝑜,𝑡+1 = 𝐴𝑒𝑥𝑜,𝑡(1 − 𝛺𝑡,𝑇𝐹𝑃)𝑔𝑎𝑡, (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


19

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.

𝛺𝑡,𝑖 = 1 −1

1+𝑓𝑖(𝑅𝐷𝑡) (13.RD)

𝛺𝑡,𝑌 = 1 −1

1+𝑖𝑎𝑡+𝑓𝑎𝑑𝑡+(1−𝑓𝑖)𝑅𝐷𝑡 (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).

𝐴𝑑𝑎𝑝𝑡𝑎𝑖𝑜𝑛 𝑐𝑜𝑠𝑡 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 =𝑖𝑎𝑡+𝑓𝑎𝑑𝑡

𝑖𝑎𝑡+𝑓𝑎𝑑𝑡+𝑅𝐷𝑡+𝛬𝑡(16)

𝐹𝑙𝑜𝑤 𝑎𝑑𝑎𝑝𝑡𝑎𝑖𝑜𝑛 𝑐𝑜𝑠𝑡 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 =𝑓𝑎𝑑𝑡

𝑖𝑎𝑡+𝑓𝑎𝑑𝑡+𝑅𝐷𝑡+𝛬𝑡 (17)

𝑆𝑡𝑜𝑐𝑘 𝑎𝑑𝑎𝑝𝑡𝑎𝑡𝑖𝑜𝑛 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑐𝑜𝑠𝑡 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 =𝑖𝑎𝑡

𝑖𝑎𝑡+𝑓𝑎𝑑𝑡+𝑅𝐷𝑡+𝛬𝑡 (18)

2.4 Table of models

Model name Important equations

Standard model 𝑌𝑡 = 𝐴𝑒𝑥𝑜,𝑡𝐿𝑡(1−𝛼)

𝐾𝑡𝛼 (1)

Endogenous growth model 1 𝑌𝑒𝑛𝑑1,𝑡 = 𝐴𝑒𝑛𝑑1,𝑡𝐿𝑡(1−𝛼)

𝐾𝑡(𝛼+𝛽)

(1.End1)

Endogenous growth model 2 𝐴𝑒𝑛𝑑2,𝑡+1 = 𝐴𝑒𝑛𝑑2,𝑡(1 − 𝑑𝑎) + 𝛾1𝐼𝑡𝛾2 (14.End2)

Endogenous growth model 3 𝐴𝑒𝑛𝑑3,𝑡+1 = 𝐴𝑒𝑛𝑑3,𝑡(1 − 𝑑𝑎) + 𝛾31𝐼𝑡 + 𝛾4𝐼𝑡𝛾5(14.End3)

Capital model (1.End1) and 𝐾𝑡+1 = 𝐾𝑡(1 − 𝑑𝑘)(1 − 𝛺𝑡,𝐾) + 𝐼𝑡 (2.K)

TFP model 𝐴𝑡𝑓𝑝,𝑡+1 = 𝐴𝑡𝑓𝑝,𝑡(1 − 𝑑𝑎)(1 − 𝛺𝑡,𝑇𝐹𝑃) + 𝛾1𝐼𝑡𝛾2(14.TFP)

With convex damages 𝐷𝐶𝑜𝑛𝑣𝑒𝑥 = 𝐷𝑡 + 5.07 ∙ 10−6𝜏𝑡6.754 (15)

TFP in exogenous growth 𝐴𝑒𝑥𝑜,𝑡+1 = 𝐴𝑒𝑥𝑜,𝑡(1 − 𝛺𝑡,𝑇𝐹𝑃)𝑔𝑎𝑡, (14.Exo)


20

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 – which are omitted in the GAMS code as this year

has not yet happened – 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 – Results for D&S, DICE and

AD-DICE


21

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 – 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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Capital damages, exogenous growth Endogenous growth model 1

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.


23

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 Dietz’s 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


25

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 2’s 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.


31

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

37,5

38

38,5

39

39,5

40

40,5

41

41,5

42

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Co

nsu

mpti

on p

er c

apit

a 1000 2

005 U

S $

0

5

10

15

20

25

30

35

40

45

2005 2015 2025 2035 2045 2055 2065 2075 2085 2095 2105

Con

sum

pti

on

per

cap

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%


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 – damages after adaptation measures – 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


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

tati

on

Endogen

ous

gro

wth

model

1, F

low

adap

tati

on

Capit

al

model

Flo

w

adap

tati

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


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

el,

resi

du

al d

amag

es,

tota

l

End

og

enou

s gro

wth

mo

del

2,

Inv

estm

ent

in a

dap

tati

on

TF

P m

od

el,

Inv

estm

ent

in

adap

tati

on

TF

P m

od

el,

resi

du

al d

amag

es,

Inv

estm

ent

in a

dap

tati

on

End

og

enou

s gro

wth

mo

del

2,

Flo

w a

dap

tati

on

TF

P m

od

el,

Flo

w a

dap

tati

on

TF

P m

od

el,

on

ly r

esid

ual

dam

ages

, F

low

adap

tati

on

Fra

ctio

n o

f to

tal cl

imat

e co

sts

2015 2105


35

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 – that is, with

and without their extensions – 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


36

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.


37

5 References

Anthoff David and Tol Richard S.J., (2010) FUND–Climate framework for uncertainty,

negotiation and distribution. University of California, Berkeley, USA

Bonen, Antony, Semmler, Willi, Klasen, Stephan, 2014. Economic Damages from Climate

Change: A Review of Modeling Approaches. SCEPA working paper series. 3. Schwartz Center

for Economic Policy Analysis (SCEPA), The New School.

Bosetti, Valentina, Carraro, Carlo, Galeotti, Marzio, Massetti, Emanuele and Tavoni, Massimo,

2006. WITCH - A World Induced Technical Change Hybrid Model, University Ca' Foscari of

Venice Economic Research Paper No. 46/06. Available at SSRN:

http://ssrn.com/abstract=948382 or http://dx.doi.org/10.2139/ssrn.948382

de Bruin, Kelly C., Dellink, Rob B. and Tol, Richard S.J., (2009). AD-DICE: An

Implementation of Adaptation in the DICE Model. Climatic Change, 95(1-2): 63-81.

Dell, Melissa, Jones, Benjamin and Olken, Benjamin, 2012. Temperature Shocks and Economic

Growth: Evidence from the Last Half Century. American Economic Journal: Macroeconomics.

4(3), 66–95.

Dell, Melissa, Jones, Benjamin and Olken, Benjamin, 2014. What Do We Learn from the

Weather? The New Climate-Economy Literature. Journal of Economic Literature 52(3), 740-

798

Dellink, Rob, Lanzi, Elisa, Château, Jean, Bosello, Francesco, Parrado, Ramiro, de Bruin,

Kelly, C., 2014. Consequences of Climate Change Damages for Economic Growth: A Dynamic

Quantitative Assessment (OECD Economics Department Working Paper No. 1135). OECD

Publishing.

Dietz, Simon and Stern, Nicholas, 2015, Endogenous Growth, Convexity of Damage and

Climate Risk: How Nordhaus' Framework Supports Deep Cuts in Carbon Emissions. The

Economic Journal, 125, 574–620. doi: 10.1111/ecoj.12188

Fankhauser, Samuel, 1995. Valuing Climate Change: The Economics of the Greenhouse.

Earthscan

http://ssrn.com/abstract=948382

http://dx.doi.org/10.2139/ssrn.948382


38

Fankhauser, Samuel and Tol, Richard S.J., 2005. On Climate Change and Economic Growth.

Resource and Energy Economics. 27(2005), 1-17

Heal, Geoffry, 2008. Climate Economics: A Meta-Review and Some Suggestions (Working

Paper No. 13927). National Bureau of Economic Research.

Hope, Chris, Anderson, John and Wenman, Paul, 1993. Policy analysis of the greenhouse

effect: an application of the PAGE model. Energy Policy 21(3), 327-338.

IPCC (2014) Summary for Policymakers. Climate Change 2014: Impacts, Adaptation and

Vulnerability. Part A: Global and Sectoral Aspects. Contribution of Working Group II to the

Fifth Assessement Report of the Intergovernmental Panel on Climate Change. Field, C.B, V.R.

Barros, D.J. Dokken, K.J. Mach, M.D. Mastrandrea, T.E Bilir, M. Chatterjee, K.L. Ebi, Y.O.

Estrada, R.C. Genova, B. Girma, E.s. Kissel, A.N. Levy, S. MacCracken, P.R. Mastrandrea and

L.S. White (eds.). Cambridge University Press, Cambridge, United Kingdom and New York,

USA, 1-32.

Kopp, Robert E., Golub, Alexander, Keohane, Nathaniel O. and Onda, Chikara, 2012. The

Influence of the Specification of Climate Change Damages on the Social Cost of Carbon.

Economics: The Open-Access, Open-Assessment E-Journal, 6 (2012-13), 1—40.

http://dx.doi.org/10.5018/economics-ejournal.ja.2012-13

Manne, Alan, Mendelsohn, Robert and Richels, Richard, 1995. MERGE: A model for

evaluating regional and global effects of GHG reduction policies. Energy policy 23(1), 17-34.

Moore, Francesca C. and Diaz, Delavane B., 2015.Temperature impacts on economic growth

warrant stringent mitigation policy. Nature Climate Change, 5(2), 127-131,

doi:10.1038/nclimate2481

Moyer, Elisabeth J., Woolley, Mark D., Matteson, Nathan J., Glotter, Michael J. and Weisbach,

David A., 2014. Climate Impacts on Economic Growth as Drivers of Uncertainty in the Social

Cost of Carbon. The Journal of Legal Studies. 43, 401 – 425.

Nordhaus, William, 1994. Managing the Global Commons: The Economics of Climate Change.

Cambridge, MA: MIT Press.

Nordhaus, William, 2008. A Question of Balance: Weighing the Options on Global Warming

http://dx.doi.org/10.1038/nclimate2481


39

Policies. The Challenge of Global Warming, Economic Models and Environmental Policy,

Yale.

Nordhaus, William, Boyer, Joseph, 2003. Warming the World: Economic Models of Global

Warming. MIT Press.

Pindyck, Robert S., 2013. Climate Change Policy: What Do the Models Tell Us? (Working

Paper No. 19244). National Bureau of Economic Research.

Sterner, Thomas, Persson, U. Martin, 2008. An Even Sterner Review: Introducing Relative

Prices into the Discounting Debate. Review of Environmental Economics Policy. 2, 61–76.

doi:10.1093/reep/rem024

Tol, Richard (1995) The Damage Costs of Climate Change -- Towards More Comprehensive

Calculations. Environmental and Resource Economics. 5, 353-374. ISSN 0924-6460

Tol, Richard S.J., Estrada, Francisco and Gay-García, Carlos, 2012. The persistence of shocks

in GDP and the estimation of the potential economic costs of climate change (Working Paper

Series No. 4312). Department of Economics, University of Sussex.

Weitzman Martin, 2012. GHG Targets as Insurance Against Catastrophic Climate Damages.

Journal of Public Economic Theory. 14(2), 221-244.

Weitzman, Martin, 2013. A Precautionary Tale of Uncertain Tail Fattening. Environmental and

Resource Economics 55, 159–173. doi:10.1007/s10640-013-9646-y

http://sro.sussex.ac.uk/22146/

http://sro.sussex.ac.uk/22146/

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