INVESTIGATION INTO THE
IMPACTS OF UN
POPULATION PROJECTIONS
ON THE COSTS OF CLIMATE
CHANGE
Word count: 1785
Ryan Truesdale
r.truesdale@student.rug.nl
1. Introduction
The
earth’s
population
has
grown
exponentially in the last few hundred years,
owing to various developments in agriculture,
medicine and technology as a whole.
Development of fertiliser led to increased food
availability and advances in modern medicine,
such as anti-biotics, resulted in declining
mortality rates. The industrial revolution may
be seen as the kick-start of the high growth
rates that bring us to the enormous population
of today [Bavel, 2013].
At the same time, population growth and
climate change are unquestionably linked.
World population and atmospheric CO2
concentration (which is responsible for rising
temperatures) display virtually identical curves
over time [Onozaki, 2009]. The key difference
between the two, however, is that whilst
population growth shows signs of slowing
down, rising CO2 levels do not, as other factors
come into play increasing the emissions per
capita. Nonetheless, it has been suggested that
the most effective way of reducing one’s long
term carbon emissions is to have one fewer
child [Wynes and Nicholas, 2017]. This is due to
the lifetime of emissions associated with every
new person brought into the world.
In this study, the range of possibilities arising
from the UN’s probabilistic future population
estimates are investigated. The study looks at
the effects of different levels of population
growth on climate change associated
economic losses of different economic groups.
The study will also consider how differences in
population growth estimates affect the point
at which 2 degrees warming is expected to be
exceeded if significant changes are not made.
1. Methodology
This study uses a simple Integrated Assessment
Model (IAM) to determine the economic
impacts of climate change, based on United
Nations (UN) probabilistic population
predictions. An IAM combines data and
knowledge from multiple sources and
disciplines to show the effects of human
behaviour on the natural world, in addition to
the effects of the natural world on our
economic systems.
IAMs are of particular use in answering “whatif?” questions, due to the linkages between
different sections of the model. These linkages
mean that changing any one aspect affects all
other sections, without having to collect
additional data, allowing the full impacts of a
decision to be considered. This quality is also
useful for exploring trade-offs between
aspects, and giving a full account of sideeffects that may otherwise be missed.
The IAM used in this study is adapted from that
described in Richard Tol’s textbook “Climate
Economics: Economic Analysis of Climate,
Climate Change, and Climate Policy” [Tol,
2014]. It consists of six interlinking parts: The
Carbon Cycle, Climate, Growth (Solow),
Emissions (Kaya), Abatement, and Impact. Of
particular interest in this study are the Growth
and Impact, which contain the input
population variable and the output costs and
temperature respectively.
For population data from 1960 until 2018, data
was collected from the World Bank and split
based on the World Bank income groups.
“Rich” relates to the High income countries,
“Middle” to Upper-middle income countries,
and “Poor” to Lower-middle and Low income
countries combined. For the years following,
the UN’s quinquennial probabilistic population
estimates up to 2100 were used, together with
the existing data, in order to perform a 6th
order polynomial regression. The resulting
equation was used to populate the post-2018
population in the Solow growth model. As the
data is based on a line of fitting, it does not fully
match the input population estimates, but
does provide a value for every year up until
2100. The UN provide five population
estimates, for the median and the upper and
lower 80% and 95% prediction intervals of the
probabilistic projections. This study uses the
Median and the Upper and Lower 95.
Predicted values take into account the past
experiences of each country, and use that to
predict the future experiences of countries
with similar conditions, including potential
uncertainty [UN, 2019].
1.1. Carbon Cycle
This section calculates atmospheric CO2
concentration (Equation 1) as the sum of
the amount of CO2 in each of five boxes, i,
at a given time, t (Equation 2). αi is the CO2
retained in a box until the next time
period, γi is the share of emissions entering
a box, β is a unit conversion factor for
billion tonnes of C to CO2 ppm, and M*t-1 is
the total emissions in the previous year. αi
and γi differ between boxes. Future
emissions are received from the
abatement module.
𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 1.
5
𝐶𝑡 = ∑ 𝐶𝑖,𝑡
1
𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 2.
∗
𝐶𝑖,𝑡 = (1 − 𝛼𝑖 )𝐶𝑖,𝑡−1 + 𝛾𝑖 𝛽𝑀𝑡−1
1.2. Climate
This module calculates the cumulative
increase in mean surface air temperature
since pre-industrial times in a given year,
TtA (Equation 3). λ1 and λ2 model the effects
of radiative forcing on temperature, and λ3
and λ4 represent exchange of heat
between the oceans and the atmosphere.
TtO represents the temperature of the
oceans (Equation 4). Radiative forcing is
determined
by
atmospheric
CO2
concentration from the Carbon Cycle
module.
𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 3.
𝐴
𝐴 )
𝑇𝑡𝐴 = 𝑇𝑡−1
+ 𝜆1 (𝜆2 𝐹𝑡 − 𝑇𝑡−1
𝑂
𝐴
+ 𝜆3 (𝑇𝑡−1
− 𝑇𝑡−1
)
𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 4.
𝑂
𝐴
𝑂
𝑇𝑡𝑂 = 𝑇𝑡−1
+ 𝜆4 (𝑇𝑡−1
− 𝑇𝑡−1
)
1.3. Growth
The growth module follows the Solow
model, which calculates economic output
in a specific year and region (or in this case
income group), Yr,t* (Equation 5),
depending on available capital, Kr,tα
(Equation 6), population, Lr,t1-α, and the
total factor productivity, Ar,t [Solow, 1956].
α is the “capital share”, δ is the
deprecation rate of capital, Ir,t (Equation 7)
is investment, and s is the saving rate.
𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 5.
𝛼
∗
𝑌𝑟,𝑡
= 𝐴𝑟,𝑡 × 𝐾𝑟,𝑡
× 𝐿1−𝛼
𝑟,𝑡
𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 6.
𝐾𝑟,𝑡 = (1 − 𝛿)𝐾𝑟,𝑡−1 + 𝐼𝑡,𝑡−1
𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 7.
𝐼𝑟,𝑡 = 𝑠𝑌𝑟,𝑡
1.4. Emissions
The emission module is based on the Kaya
identity (Equation 8). Mr,t* are the
emissions in a region (or income group) at
a given time, Lr,t is the population (from the
Solow model), and Yr,t is the economic
output (also from the Solow model).
𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 8.
∗
𝑀𝑟,𝑡
= 𝐿𝑟,𝑡 ×
∗
𝑌𝑟,𝑡 𝑀𝑟,𝑡
×
𝐿𝑟,𝑡 𝑌𝑟,𝑡
1.5. Abatement
The abatement module includes the costs,
Br,t*, of lowering the emissions calculated
in the emissions module (Equations 9, 10,
11, and 12). β is a coefficient for cost based
on the emission control rate, Rr,t, and Br,t is
the economic burden of abatement.
𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 9.
∗
𝑀𝑟,𝑡
− 𝑀𝑟,𝑡 2 ∗
∗
𝐵𝑟,𝑡
= 𝛽(
) 𝑌𝑟,𝑡
∗
𝑀𝑟,𝑡
𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 10.
∗
𝑀𝑟,𝑡 = (1 − 𝑅𝑟,𝑡 )𝑀𝑟,𝑡
𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 11.
2
𝐵𝑟,𝑡 = 𝛽𝑅𝑟,𝑡
𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 12.
∗
𝑌𝑟,𝑡 = (1 − 𝐵𝑟,𝑡 )𝑌𝑟,𝑡
1.6. Impact
The impact module gives the economic
losses (or gains) resulting from rising
temperature, based on parameters ψ1, ψ2,
and ψ6. 𝐷𝑡 gives the economic impact as a
percentage of annual output (Equation
13). 𝑇𝑡 is the increase in global average
temperature since the pre-industrial era.
𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 13.
𝐷𝑡 = 𝜓1 𝑇𝑡 + 𝜓2 𝑇𝑡2 + 𝜓6 𝑇𝑡6
2. Results & Discussion
2.1. Results
In Figure 1, it can be seen that, up to a
certain amount of warming, rising
temperatures provide economic benefits,
particularly for rich countries, as reported
in [Tol, 2010]. However, as emissions
increase
further,
the
economic
consequences become increasingly severe
across all economic groups. It can also be
seen that all of the population predictions
are very similar up until around 2050, with
differences only appearing when the
economic impact begins to decrease and
losses are incurred. Similar divergence in
economic impact is seen across all
economic groups, and all groups see the
higher population estimates resulting in
greater eventual losses. In total, poorer
countries’ economies are affected more by
the rising temperatures, despite their
smaller contributions to climate change,
which aligns with the idea of the tragedy of
the commons in which a few reap the
benefits of degradation, but all bear the
cost [Forster Lloyd, 1833]. Poor countries
are affected to a greater extent for three
reasons, outlined in [Tol, 2014]: Their
economies are largely dependent on
weather-dependent industries, they tend
to be in hotter places less able to
withstand further warming, and they lack
funds and technical know-how to adapt to
changes.
Figure 2 shows a starkly different picture
however. On a per capita basis, rich
countries face far greater costs. Once
again, greater populations result in greater
losses. As the differences between the
impacts of the Rich countries’ losses
appear starker, it may be the case that
higher population growth (and population
to begin with) in poor countries results in a
greater ability to share the economic load.
Figure 3 shows the warming based on each
of the population estimates. Whilst
significant differences are present
between the highest (Upper 95) and
lowest (Lower 95) estimates for
population, with a difference of 0.9 billion
in the 2050 predictions, the model displays
little variation in terms of the point in time
at which global warming will exceed 2
degrees compared to the pre-industrial era
(covering a 2 year range). This suggests
that, whilst population is important in
terms of emissions, other factors may be
coming to the fore in the future.
2.2. Limitations
This IAM considers abatement cost, so
does not truly consider the costs of the
damages of climate change, or the loss of
opportunities it presents. It also ignores
factors like health which deteriorates as
climate change occurs, and the associated
non-warming environmental impacts so
presents a limited scope. As it uses the past
to predict the future, it projects the habits
and trends of today onto future
generations who may behave differently.
As it is based on trends, it ignores event
based influences, both human and natural,
that may have tremendous impacts. As
IAMs are so large, a large amount of time
must be put in collecting data, and large
models often end up as “black boxes”
where it is difficult to understand what is
going on inside. The model assumes that
membership of each income group is fixed,
and does not account for countries
increasing or decreasing their wealth and
entering a different income group, which
would result in changes to their
environmental impacts. In 2019-2020,
seven countries were assigned new
income groups [The World Bank, 2019],
most notably Argentina, which represents
0.6% of the World’s population. It is
important to note that the UN population
predictions do not include adjustment
based on the potential effects of climate
change. In reality population growth is
affected by climate change in a dynamic
feedback loop, as climate change leads to
falling fertility rates and higher mortality
rates than otherwise, for a number of
reasons [Van Bavel, 2013]. As this study
uses population predictions, rather than
predicting
population
itself,
the
relationship in the model is one-way;
growing population leads to rising
temperatures.
3. Conclusion
This study shows that whilst all income groups
receive substantial economic losses from
climate change, poor countries are overall
worst off. However, on a per capita basis, rich
countries pay a far higher price, owing to their
smaller populations. Whilst the UN’s
population estimates show substantial
differences, the timeframe in which the world
will exceed 2 degrees warming will not be
substantially affected by differing growth
scenarios, meaning that no matter the case,
urgent action is needed to avert the climate
crisis. Whilst IAMs have extensive limitations,
they provide a valuable insight into the
relationship between human behaviour and
environmental impacts, due to their ability to
link data from socioeconomic and physical
disciplines.
4. References
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