Earth 104 Activity: Modeling the Economics of Climate Change

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David F. Bice
David F. Bice

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Earth 104 Activity: Modeling the Economics of Climate Change
The global climate system and the global economic system are intertwined —
warming will entail costs that will burden the economy, there are costs associated
with reducing carbon emissions, and policy decisions about regulating emissions
will affect the climate. These interconnections make for a complicated system — one
that is difficult to predict and understand — thus the need for a model to help us
make sense of how these interconnections might work out. In this activity, we’ll do
some experiments with a model that will help us do a kind of informal cost-benefit
analysis of emissions reductions and climate change.
The economic part of the model we will explore here is based on work by William
Nordhaus of Yale University, who is considered by many to be the leading authority
on the economics of climate change. His model is called DICE, for Dynamic,
Integrated Climate and Economics model. It consists of many different parts and to
fully understand the model and all of the logic within it is well beyond the scope of
this class, but with a bit of background we can carry out some experiments with this
model to explore the consequences of different policy options regarding the
reduction of carbon emissions.
Nordhaus’ economic model has been connected to the global carbon cycle model we
used in Module 8, connected to a simple climate model like the one we used in
Module 4.
The economic components are shown in a highly simplified version of a STELLA
model below:
Credit: David Bice
In this diagram, the gray boxes are reservoirs of carbon that represent in a very
simple fashion the global carbon cycle model from Module 8; the black arrows with
green circles in the middle are the flows between the reservoirs. The brown boxes
are the reservoir components of the economic model, which include Global Capital,
Productivity, Population, and something called Social Utility. The economic sector
and the carbon sector are intertwined — the emission of fossil fuel carbon into the
atmosphere is governed by the Emissions Control part of the economics model, and
the global temperature change part of the carbon cycle model affects the economic
sector via the Climate Damage costs. Let’s now have a look at the economic portions
of the model. You should view this video DICE economic model first, and then study
the text that follows.
The Global Capital Reservoir
In this model, Global Capital is a reservoir that represents all the goods and services
of the global economic system; so this is much more than just money in the bank.
This reservoir increases as a function of investments and decreases due to
depreciation. Depreciation means that value is lost as things age, and the model
assumes a 10% depreciation per year; the 10% value comes from observations of
rates of depreciation across the global economy in the past. The investment part is
calculated as follows:
Investment = Savings Rate x (Gross Output - Abatement Costs – Climate Damages)
The savings rate is 18.5% per year (again based on observations). The Gross Output
is the total economic output for each year, which depends on the global population,
a productivity factor, and Global Capital.
Abatement Costs
The Abatement Costs are the costs of reducing carbon emissions, and are directly
related to the amount by which we try to reduce carbon emissions. If you think back
to the model we worked with that calculated emissions scenarios and energy
consumption, abatement is essentially the same as reducing the fraction of our
energy that comes from fossil fuels — there are costs associated with making those
changes. If we do nothing in terms of reducing our consumption of fossil fuels, the
abatement costs are zero, but as we try to do more and more in terms of emissions
reductions, the abatement costs go up. If we go all out in this department, the
Abatement Costs can rise to be 15% of the Gross Output.
Climate Damages
Climate Damages are the costs associated with rising global temperatures. The way
the model is set up, a 2°C increase in global temperature results in damages equal to
2.4% of Gross Output, but this rises to 9.6% for a temperature increase of 4°C, and
21.6% of Gross Output for a 6°C increase. This relationship between temperature
change and damage involves temperature raised to an exponent that is initially set
at 2, but can be adjusted.
Relative Climate Costs
It will be useful to have a way of comparing the climate costs — the sum of the
Abatement Costs and the Climate Damages — in a relative sense so that we see what
the percentage of these costs is relative to the Gross Output of the economy. The
model includes this relative measure of the climate costs as follows:
Relative Climate Costs = (Abatement Costs + Climate Damages)/Gross Output
Also related to the Global Capital reservoir is a converter called Consumption. A
central premise of most economic models is that consumption is good and more
consumption is great. This sounds shallow, but it makes more sense if you realize
that consumption can mean more than just using things it up; in this context, it can
mean spending money on goods and services, and since services includes things like
education, health care, infrastructure development, and basic research, you can see
how more consumption of this kind can be equated with a better quality of life. So,
perhaps it helps to think of consumption, or better, consumption per capita, as being
one way to measure quality of life in the economic model, which provides a measure
for the total value of consumed goods and services, which is defined as follows:
Consumption = Gross Output – Climate Damages – Abatement Costs – Investment
This is essentially what remains of the Gross Output after accounting for the
damages related to climate change, abatement costs, and investment.
The model also calculates the per capita consumption by just dividing the
Consumption by the Population, and it also includes a converter called relative per
capita consumption, which is just the per capita consumption divided by the gross
The population in this model is highly constrained — it is not free to vary according
to other parameters in the model. Instead, it starts at 6.5 billion people in the year
2000 and grows according to a net growth rate that steadily declines until it reaches
12 billion, at which point the population stabilizes. The declining rate of growth
means that as time goes on, the rate of growth decreases, so we approach 12 billion
very gradually.
Productivity Factor
The model assumes that our economic productivity will increase due to
technological improvements, but the rate of increase will decrease, just like the rate
of population growth. So the productivity keeps increasing, but it does not
accelerate, which would lead to exponential growth in productivity. This decline in
the rate of technological advances is once again something that is based on
observations from the past.
The model calculates the carbon emissions as a function of the Gross Output of the
global economy and two adjustable parameters, one of which (sigma) sets the
emissions per dollar value of the Gross Output (units are in metric tons of carbon per
trillion dollars of Gross Output) and something called the Emissions Control Rate
(ECR). The equation is simply:
Emissions = sigma*(1 -ECR)*Gross_Output
Currently, sigma has a value of about 0.118, and the model we will use assumes that
this will decrease as time goes on due to improvements in efficiency of our economy
— we will use less carbon to generate a dollar’s worth of goods and services in the
future, reflecting what has happened in the recent past. The ECR can vary from 0 to
1, with 0 reflecting a policy of doing nothing with respect to reducing emissions, and
1 reflecting a policy where we do the maximum possible. Note that when ECR = 1,
then the whole Emissions equation above gives a result of 0 — that is, no human
emissions of carbon to the atmosphere from the burning of fossil fuels. In our
model, the ECR is initially set to 0.005, but it can be altered as a graphical function of
time to represent different policy scenarios. In other words, by changing this graph,
we are effectively making a policy — and everyone follows this policy in our model
Making Comparisons — the Discount Rate
We would like to be able to see whether one policy for reducing emissions of carbon
is economically better than another. Different policies will call for different histories
of reductions, and to compare them, we need to find a way to compare the expected
future damages associated with each policy. A problem comes when we try to
compare 200 million in damages at some time in the future vs. 20 million in
damages today. Economists use something called a discount rate to do this. Here is
an example to help you see how this idea works: imagine you have a pig farm with
100 pigs, and the pigs increase at 5% per year by natural means. If you do nothing
but sit back and watch the pigs do their thing, you’d have 105 pigs next year. So 105
pigs next year can be equated to 100 pigs in the present, with a 5% discount
rate. Thus, the discount rate is kind of like the return on an investment. Now think
about climate damages. If we assume that there is a 4% discount rate, then $1092
million in damages 100 years from now is $20 million in present day terms. Here is
how this works in an equation:
 =  ×  ()
$10926 = $206 ×  (0.04 × 100 )
This is a standard exponential growth equation; e is called Euler’s number and has a
value of about 2.7. Now, let’s say we calculate some cost in the future — 8 million
dollars 200 years from now — we can apply a discount rate to this future cost in
order to put it into today’s context. Here is how that would look:
 = $86 ×  (−0.04×200 ) = $2684
It is important to remember that this assumes our global economy will grow at a 4%
annual rate for the next 200 years. The 4% figure is the estimated long-term market
return on capital, but this may very well grow smaller in the future, as it does in our
model. Although we’re not going to dwell on the discount rate any more in this
exercise, it is good to understand the basic concept.
A simpler way of comparing future costs or benefits with respect to the present is to
express these costs and benefits relative to the size of the economy at any one time
— which our model will calculate. This gets around the kind of shaky assumption
that the economy is going to grow at some fixed rate. These relative economic
measures are easy to do — just divide some parameter from the model, like the per
capita consumption, by the Gross Output. Below is a list of the model parameters
that we will keep an eye on in the following experiments:
Global capital — the size of the global economy in trillions of dollars
Gross Output — the yearly global economic production in trillions of dollars
Per capita consumption — consumption/population; this is a good
indicator of the quality of life — the higher it is, the better off we all
are; units are in thousands of dollars per person
Relative per capita consumption — per capita consumption divided by the
gross output; again, a good indicator of the quality of life, in a form
that enables comparison across different times; units are in thousands
of starting time dollars per person
Sum of relative pc consumption — the sum of the relative per capita
consumption — kind of like the final grade on quality of life. If you take
the ending sum and divide by 200 yrs, it gives the average per capita
consumption for the whole period of the model run
Relative climate costs — (abatement costs + climate damages)/gross output;
this combines the costs of reducing emissions with the climate damages,
in a form that can be compared across different times; the units are $/$,
so this is just a dimensionless fraction — multiply it by 100 and you
have the % of the gross output that goes to abatement and climate
Sum of relative climate costs — sum of the relative climate costs — the final
grade on costs related to dealing with emissions reductions and climate;
this is the sum of a bunch of fractions, so it is still dimensionless.
Global temp change — in °C, from the climate model
Experiment 1: Changing the Emissions Control Rate (ECR)
In the model, the ECR can vary from 0 to 1, and it expresses the degree to which we
take steps to curb emissions; a value of 0 means we do nothing, while a value of 1
means that we essentially bring carbon emissions to a halt. According to Nordhaus,
the most efficient way of implementing this control is through some kind of carbon
tax, in which case a value close to 1 represents a very hefty carbon tax that would
provide strong incentives to develop other forms of energy. In this experiment,
we’ll explore 3 scenarios — in A, we’ll keep ECR at a very low level — this is the “do
nothing” policy scenario, in B we'll ramp it up steadily through time — this is the
“slow and steady” policy scenario, and in C, we’ll ramp it much more quickly,
eventually reaching a value of 1.0 — this is the “get serious” policy scenario. You can
make these changes in the ECR by altering the graphical converter.
In your ANGEL mail, you will be provided with the Form letter (A,B,C,D) for the
assessment document. Details of the ECR for your three scenarios will be related to
this letter. The details consists of a string of 5 numbers that are the ECR values for
5 points in time (corresponding to the five vertical lines in the graph); these times
are years 2000, 2050, 2100, 2150, and 2200. This short video Dice model ECR
explains how to make changes to the model.
Do nothing ECR data
Slow & Steady
Get Serious
Use defaults values (no
need to change anything)
0.005; 0.2; 0.4; 0.6; 0.8
(these are the values of
ECR at each of the 5
vertical lines on the
0.005; 0.5; 1.0; 1.0; 1.0
Use defaults values (no
need to change anything)
0.005; 0.15; 0.3; 0.45; 0.6
0.005; 0.33; 0.66; 1.0; 1.0
For each scenario, run the model, study the model results, and record the results
indicated in the table below and then refer to your results in answering the
questions below. Where possible, fill these out to a one decimal point precision.
ECR scenario
Slow &
1. Global temp change @2200
2. Global [email protected]
3. Per capita
[email protected]
4. Relative per capita
[email protected]
5. Sum of relative pc
[email protected]
6. Relative climate
[email protected]
7. Sum of relative climate
[email protected]
Slow &
1. Which of these 3 scenarios leads to the lowest global temperature change?
a) Do nothing
b) Slow and steady
c) Get serious [answer for practice version]
2. The lowest global temperature change @2200 of the three scenarios =
(±0.2°C) [2.1 for practice version]
3. Which of these 3 scenarios leads to the highest global capital?
a) Do nothing
b) Slow and steady
c) Get serious [answer for practice version]
4. Highest global capital @2200 of the three scenarios =
±10) [1583 for practice version]
5. Which of these 3 scenarios leads to the lowest relative climate costs?
a) Do nothing
b) Slow and steady
c) Get serious [answer for practice version]
6. Lowest relative climate costs @2200 of the three scenarios =
Units displayed in the model are % of the gross output that goes to abatement and
climate damages. [4.4 for practice version]
7. Which of these 3 scenarios leads to the greatest relative per capita
a) Do nothing
b) Slow and steady
c) Get serious [answer for practice version]
8. In terms of both economic costs (lowest relative climate costs) and benefits
(highest relative per capita consumption), which scenario is the best?
Do nothing — best in both costs and benefits
Slow and steady — best in both costs and benefits
Get serious — best in both costs and benefits [answer for practice version]
Do nothing — best in benefits; Get serious — best in costs
Slow and steady — best in benefits; Do nothing — best in costs
Now we step back and consider what we’ve done and learned by responding to the
following questions.
9. You have probably heard people (mainly from the realms of business and
politics) say that we should not do anything about global climate change
because it is too expensive and will hurt our economy. After experimenting
with this model, do you agree with them, or do you think they are missing
something (and if so, what is it they are missing)?
10. Remember that each ECR history reflects a different economic/political
policy. Briefly explain how you came to figure out which policy was the best.
In answering this, you have to think about what “best” means — the least
environmental damage; the greatest economic gain per person; the easiest
policy to implement; or some combination of these?

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