For the module ten summative assessment, we're going to be working with this very large and complicated model, that consists of a number of different parts. You can see down in here this is the global carbon cycle and then that includes the percent or the concentration of CO2 in the atmosphere. That concentration of CO2 in the atmosphere then feeds into a climate model that tells us the temperature. And that temperature then goes into determining the sort of climate damages caused by a global temperature, global warming. Those climate damage costs then affect the amount of money that we have leftover to invest in the economy. So here's global capital - this is the whole kind of the heart of the economic model up in here. So climate damages come into play here. Another important cost that comes into play are the abatement costs. These are the costs related to reducing carbon emissions. And so there's something down here called the emissions control rate that we'll fiddle around with. It represents, essentially, different choices we make about how much we're going to try to limit carbon emissions. That limits how much goes in the atmosphere, it limits the temperature, and so on. But it costs money, so there's a certain abatement cost per gigaton of carbon that you are not emitting into the atmosphere. There are a whole bunch of other parts of this global climate and climate and economic model, including something that keeps track of what Nordhaus calls social utility. The global population here is sort of fixed and these are a bunch of things that just sort of sum up some of these economic components of the model. So this is the big model that's behind the scenes. When you look at the actual model, you'll be seeing something like this - an interface where you're just going to change a few basic things. And& for this summative assessment, we're really just going to change the emissions control rate here, which is a graphical function of time.
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:
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 about the DICE Economic Model [1] first, and then study the text that follows.
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 (GDP - Abatement Costs – Climate Damages)
The savings rate is 18.5% per year (again based on observations). The GDP is the total economic output for each year, which depends on the global population, a productivity factor, and Global Capital.
The Abatement Costs are the costs of reducing carbon emissions and are directly related to the amount by which we reduce carbon emissions. If we take steps to reduce our carbon emissions either by switching to renewable energy or improving efficiency or by direct removal of CO2 from the atmosphere, then there are costs associated with these steps. The model includes something called the abatement cost per GT C — this is the cost in trillions of dollars for each gigaton of carbon removed, and it can be changed over time. The default value is $3 trillion/GT C, which is a lot because it also includes the costs of large battery systems and new electrical transmission lines. But, the good thing about these costs is that once you pay for a GT of C removed, you don’t keep paying for it. If we were to completely cut all carbon emissions (currently around 10 GT C/yr) and do it in one year, it would cost $30 trillion or about 1/3 of the global GDP.
The diagram below shows how the abatement costs each year are figured out.
Climate Damages are the costs associated with rising global temperatures, including the costs of dealing with sea level change along coasts, extreme weather events (hurricanes, flooding, droughts, wildfires, etc.), labor (reduced productivity at higher temps), and increased human mortality (loss of workers hurts the economy). In the model, the climate damages are calculated as a fraction (think of this as a percentage) of the GDP. The fraction is a quadratic equation that looks like this:
damage fraction = slope × ΔT + coefficient × ΔTexponent
The ΔT is the global temperature change in °C. Both the slope and exponent can be adjusted in the model; the coefficient is set at 0.003. The default slope is 0.025 and the exponent is 2, which means that if we have a global temperature change of 4°C, damages equal to 15% of GDP; this rises to a devastating 55% for a temperature increase of 10°C. The diagram below shows what this damage fraction equation looks like, plotted as a function of temperature change in °C.
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 GDP of the economy. The model includes this relative measure of the climate costs (in trillions of dollars) as follows:
Relative Climate Costs = (Abatement Costs + Climate Damages) x GDP/initial GDP
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 include 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 (in trillions of dollars), which is defined as follows:
Consumption = Gross Output – Climate Damages – Abatement Costs – Investment
This is essentially what remains of the GDP 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 GDP. In the model, this is in thousands of dollars per person.
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.
The model assumes that our economic productivity will increase due to technological improvements, but the rate of increase will decrease (but will not go negative), 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 GDP of the global economy and two adjustable parameters, one of which (carbon intensity) sets the emissions per dollar value of the GDP (units are in gigatons of carbon per trillion dollars of GDP) and something called the Emissions Control Rate (ECR). The equation is simply:
Emissions = carbon intensity*(1 -ECR)*GDP ;
Currently, carbon intensity has a value of about 0.118, and the model assumes that this will decrease as time goes on due to improvements in the 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 world!
This is a standard exponential growth equation 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:
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 GDP. Below is a list of the model parameters that we will keep an eye on in the following experiments:
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;
GDP — 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 — annual per capita consumption x (GDP/initial GDP); 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 above— 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 — an annual measure of (abatement costs + climate damages) x (GDP/initial GDP); this combines the costs of reducing emissions with the climate damages, in a form that can be compared across different times; the units are trillions of dollars.
Sum of relative climate costs — sum of the relative climate costs — the final grade on costs related to dealing with emissions reductions (abatement) 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