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Wesleyan University
The Honors College
Exhaustible resource consumption and lessons for
greenhouse gas limitations—a three-country, threeperiod model of iterative decision-making
by
Eunju Rho
Class of 2012
A thesis submitted to the
faculty of Wesleyan University
in partial fulfillment of the requirements for the
Degree of Bachelor of Arts
with Departmental Honors in Economics
Middletown, Connecticut
April, 2012
Contents
Acknowledgement……………………………………………………………………..…… 3
Abstract…………………………………………………………………………………………. 4
Introduction……………………………………………………………………………...……. 5
CHAPTER 1: Literature Review………………………………………………….…… 10
CHAPTER 2: Model Overview and the Baseline Simulation………….…… 23
CHAPTER 3: More Simulations…………………………………………………..…… 29
Conclusion…………………………………………………………………………………..… 42
Postscript……………………………………………………………………………………… 47
Reference……………………………………………………………………………………… 49
APPENDIX 1: Figures and Tables
I. Figures…………………………………………………………………………….. 52
II. Tables…………………………………………………………………………….. 67
APPENDIX 2: Technical Summary
I. Technical Details for Chapter 2……………………………………..…… 77
II. Technical Details for Chapter 3………………………………………… 84
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Acknowledgement
Foremost, I would like to thank my thesis advisor, Prof. Gary Yohe, who has
provided me with much guidance and encouragement to continue this iterative
process of thesis writing. I also thank my thesis tutor, Alex Wilkinson, who
faithfully helped me edit my writing and make it readable.
Then, I thank all of my friends in Wesleyan with whom I’ve spent four years of
my youth. Without you, I wouldn’t have had the same college life.
Last but not least, I thank my families in South Korea; I always feel connected to
you, and this feeling enables me to continue my career.
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Abstract
In this paper, I present an iterative decision-making model in which three
countries choose their consumptions of exhaustible resources across three
periods. With this model, I investigate the significance of changing climate
information and countries’ interactions in the context of global climate policy.
Since climate change depends on cumulative greenhouse gas emissions,
permissible emissions can be regarded as exhaustible resource consumption
under an effective climate policy. Through comparative static analysis and
simulations, I show that the likelihoods of countries’ participation in limiting
emissions, their past decisions, and changing information have a significant
influence on their near-term climate decisions. Moreover, my results
demonstrate the value of early participation—in particular, an early and
adequate response to new information. The insights from this study will be used
for deciphering the results from my future research, which will engage one or
more integrated assessment models.
[Keywords] Cumulative emissions, Climate change, Iterative risk management,
Uncertainty, Decision-making process
4
Introduction
Using an iterative decision-making framework, this paper will investigate the
significance of evolving information and interactions among the actors in the context
of global climate policy. Rise in the global mean temperature has a strong
association with the increasing concentration of greenhouse gas (GHG) in the
atmosphere (Allen et al., 2009; Meinshausen et al., 2009; App.1: Figure 1-1).
Because of its long residence time, the GHG atmospheric concentration can hardly
be reduced (Solomon et al., 2009; Matthews and Caldeira, 2008), so inflow of
emissions keep accumulating in the atmosphere. Therefore, I characterize climate
change as a cumulative emission problem.
I also recognize that a climate decision-making process should be iterative. In
an iterative decision-making framework, the decision-makers consistently evaluate
and adjust their prior decisions with relevant information (ACC, 2010b; App.1:
Figure 1-2). Because the framework admits inherent uncertainty in available
information, an iterative decision-making framework serves as a particularly
valuable tool for complex problems that are subject to multiple uncertainties, such
as climate change (IPCC, 2007b). Since decision-makers have to rely on imperfect
information, the evolving nature of information would impact an iterative climate
decision-making process.
A large number of studies have explored this possibility using an iterative
decision-making framework to investigate the effect of uncertainty and learning on
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near-term climate policy. For convenience, I will roughly define learning as a
“process of acquiring knowledge” (Parson and Karwat, 2011), which is expected to
reduce uncertainty. 1 While earlier works claim that learning has either positive or
negative influence on the severity of near-term policy (Arrow and Fisher, 1974;
Henry, 1974; Pindyck, 2000), more recent works find that the influence can run in
both directions depending on the specifics of model design (Lange and Treich, 2008;
Webster, 2002). There are other studies that use empirical models to examine
implications of uncertainty and learning (Webster, 2002; Richels et al., 2009), hence
providing more comprehensive results compared to those using theoretical models
(Ingham et al., 2007). However, most of them do not treat changing information and
subsequent adaptations in their models.
In this paper, I will present a simple iterative decision-making model, in
which three different types of countries (the developed, the BRIC, and the
developing countries) make decision on their exhaustible resource consumption
through 2015, 2035, and 2050. For modeling purposes, I will represent a process of
making decisions concerning permissible emissions under an effective climate policy
by creating a model in which exhaustible resource consumption is under a binding
resource capacity. While countries choose their emission levels in order to maximize
their economic wealth, an effective climate policy would limit the total amount of
emissions that those countries can produce during a specified period. This is
1
Some studies recognize that learning does not always help reduce uncertainty. New information
acquired from a learning process might turn out to be irrelevant or inaccurate so as to hamper
accurate understanding of the issue (termed as a “negative learning” in the latter case). Refer to
Parson and Karwat (2011) for more explanation.
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equivalent to a problem in which countries decide on their consumption level to
optimize utility under a binding budget constraint (in our model, the resource
capacity). In the following chapters, I will describe my model and results primarily in
terms of exhaustible resource consumption. Via those results, however, I ultimately
aim to tell a story about the climate decisions of countries choosing a permissible
emission level; in the concluding chapter of this paper, I will frame my interpretation
of major results in terms of the emission problem.
With my model, I will collect initial hypotheses from the baseline simulation
results, where countries have perfect information and do not adjust their decisions
over time. Then, in further experiments, I will simulate more dynamic (and more
realistic) scenarios characterized with changing information and interactions among
countries. As well as validating my initial hypotheses, I will explore how these
dynamics would influence countries’ decisions in the short term or long term. First, I
will investigate how a country should choose its immediate climate (or consumption)
policy while considering the likelihoods of future collaboration with other countries.
Despite careful calculation, however, the country might adopt too strong or too
weak of a climate policy. Thus, I will also examine to which direction the deviation in
past policy decision would influence decisions of all countries in short and long term.
Lastly, I will observe how countries should adjust their emission (consumption) level
with respect to a change in their knowledge of an appropriate total emission limit
(resource capacity).
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Although many studies on iterative frameworks have already explored
evolving information and its impact on near-term decision-making, my study
employs a model that has three decision-makers and three periods, while most of
the previous studies use a two-decision-makers, two-period model (Parson and
Karwat, 2011). To examine the significance of strategic interactions, it would be
effective to have more than two decision-makers in a model (Kolstad and Ulph,
2008). Using three time periods allows me to compare the consequences of early
and late adjustment, so I can therefore discern the value of timely adjustment.
Moreover, observations made in this study will be used to decipher results from my
upcoming experiments, which engage an integrated assessment (IA) model. Because
no other study has actually imposed a three-country, three-period iterative
framework on an IA model, the results from further experiments should have rich,
yet complicated implications. I expect that my findings in this study will serve as a
basis for understanding those results.
The rest of this paper is organized as follows. In Chapter 1, I will provide the
background information regarding our topic—climate change as a cumulative
emission problem, uncertainty in climate decision, and an iterative risk management
framework. I will also review previous studies that use an iterative framework to
treat learning and its implication on near-term climate decisions. In Chapter 2, I will
present a simple iterative-decision model and collect initial hypotheses from the
major results of baseline simulation. Then, in Chapter 3, I will simulate more
dynamic scenarios to test the robustness of our hypotheses and examine how the
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changes in relevant information would affect countries’ decision on their near-term
climate policy. To tell a more intuitive story in the main body of paper, I will separate
technical details of simulation results to Appendix 2 and focus on interpreting the
results in the following chapters. For specific details behind our interpretation, refer
to the indicated figures and tables in Appendix 1 or relevant notes in Appendix 2.
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Chapter 1: Literature Review
A. Climate change driven by cumulative emissions and uncertainties
Generated from economic activities and natural processes, emissions of
carbon dioxide (CO2) and other greenhouse gases (GHG) flow into the atmosphere,
build cumulative emissions, and eventually contribute to the increasing global mean
temperature. Although GHG inflow is the source of global warming, simply reducing
flow emissions does not seem to limit the increasing climate temperature. Solomon
et al. (2009) suggests that, due to the increases in atmospheric CO2 concentration,
changes in climate would remain irreversible even 1,000 years after emissions stop.
Matthews and Caldeira (2008), using the results from their Earth system model,
demonstrate that stabilizing climate temperature requires zero emissions—in other
words, reducing cumulative emissions in the air. Thus, it must be cumulative
emissions, rather than flow emissions, that are readily linked to the change in global
mean temperature.
A number of recent studies find a fairly consistent climate response to a
given level of cumulative carbon emissions (NRC, 2011). Allen et al. (2009) finds that
both peak temperature and long-term temperature increases are determined by
cumulative CO2 emissions, not by the timing of emissions or peak emission rate. The
study at 5% confidence level estimates that 3.67 trillion tonnes (Tt) of CO2 emissions,
“about half of which has been emitted since industrialization began,” would most
likely result in a peak warming of 2⁰C above pre-industrial temperature.
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Meinshausen et al. (2009) predicts that limiting cumulative CO2 emissions to 1,000
gigatonnes (Gt) and 1,440 Gt over the 2000-2050 period would, by the probability of
25% and 50% respectively, increase global climate by 2⁰C or more above preindustrial temperatures. Although these studies report the response of climate to
cumulative emissions in probabilistic terms, they nevertheless find that there is a
robust relationship between the two (App.1: Figure 1-1).
Today, the level of atmospheric carbon concentration is roughly 440 parts
per million (ppm) CO2-eq and mainly driven by population growth, economic activity,
and the intensity of energy use (ACC, 2010a). The Energy Modeling Forum Study 22
(EMF 22) suggests that the level might grow up to 800 to 1,500 ppm CO2-eq by 2050,
assuming the absence of climate policy (Clarke et al., 2009). Currently, countries in
the Organisation for Economic Co-operation and Development (OECD) region
account for a major portion of cumulative GHG emissions. However, their share is
projected to decrease over time because some of the low- and middle-income
countries (such as Brazil, India, and China) are rapidly growing and expected to grow
faster than high-income countries. Using three different integrated assessment
models, Clarke (2007) projects that the emissions of fossil fuel and industrial CO2 in
the non-Annex I countries would exceed those of the Annex I countries by 2030 or
earlier.
So far, global efforts have been made through international bodies such as
the United Nations Framework Convention on Climate Change (UNFCCC) to establish
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and assign the efforts in stabilizing GHG concentrations in the atmosphere. On the
one hand, the goal of limiting the increase in global mean temperature to 2⁰C above
pre-industrial levels is well recognized by many policy-makers and embodied at the
Copenhagen Accords, G-8 summit in 2009, and other policy forums. On the other
hand, America’s Climate Choices (ACC) recommends a domestic climate policy of
limiting on cumulative emissions, because the concentration is directly affected by
domestic actions and can be measured accurately. In reference to the IPCC (2007a)
and Meehl and Stocker (2007), ACC (2010a) reports that 450 ppm CO2-eq and 550
ppm CO2-eq GHG concentrations can be associated with an increase in global
temperature by 2⁰C and 3⁰C, respectively.
The policy of limiting cumulative emissions to an efficient emissions budget
might be characterized as an exhaustible resource problem; nations would consume
their natural resources and emit GHGs, while considering their economic interests as
well as the limit on their consumption imposed by the emissions budget. In practice,
setting an effective emissions budget is not a simple task because the process
involves uncertainties and value judgments (ACC, 2010a). ACC (2010a) explains that
these uncertainties affect efforts to derive an emissions budget at three different
levels: (1) the link between the atmospheric GHG concentration and climate change;
(2) the link between the GHG flow emissions and the atmospheric concentration;
and (3) allocation of an appropriate share of the global emissions budget to the
United States (ACC, 2010a).
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First, it is hard to specify a target GHG atmospheric concentration that
would limit the warming to 2⁰C above pre-industrialization. As mentioned earlier,
there have been a number of studies that find a robust link between the cumulative
GHG emissions and the global temperature change. Still, their estimates of GHG
budgets for different policy scenarios are described in probabilistic terms. The
uncertainty around the quantitative relationship between GHG concentration and
climate response is reflected in the concept “climate sensitivity,” which refers to the
change in global mean equilibrium temperature associated with the doubling of CO2
concentration in the atmosphere. IPCC (2007a) reports that the climate sensitivity is:
“likely to be in the range of 2⁰C to 4.5⁰C with a best estimate of about 3⁰C” (ACC,
2010a).
Second, similarly, the increase in atmospheric CO2 concentration in response
to CO2 emissions, called “carbon sensitivity,” incorporates uncertainty, since it is
determined by the capacity of natural sinks (Matthews et al., 2009). Using a model
characterized with climate-carbon interactions, Matthews (2006) shows that carbon
cycle feedbacks have a direct impact on the amount of reduction in human-induced
emissions required to stabilize atmospheric CO2 concentration. In the 550ppmstabilization scenario, the study reports that in the simulation with positive carbon
cycle-climate feedbacks the total CO2 emissions over the 21st century were 20%
lower than those in the equivalent simulation without feedbacks. Furthermore, the
study finds that the total emissions gap between simulations with and without
carbon cycle-climate feedbacks ranges from 190 to 540 Gt depending on the level of
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climate sensitivity for the same policy scenario over a 400-year time period.
Therefore, we might say that our understanding of the relationships among GHG
emissions, cumulative emissions, and global warming is as of yet incomplete, adding
difficulties in establishing a specific carbon budget.
Lastly, the process of allocating a reasonable share of the global carbon
budget to each country, though informed by scientific knowledge, depends mostly
on ethical and political judgments. For example, it would not be easy to choose
between future-oriented efficiency criteria and past-oriented “fairness” criteria
when allocating carbon budget among countries (ACC, 2010a). Climate change can
be regarded as a common-pool resource issue, so the perspectives of different
countries with heterogeneous economic characteristics should be involved in the
decision-making process. Although some countries might adopt a long-term
perspective and endorse a future-oriented carbon budget, other countries
(especially low- and middle-income countries) might claim that economic growth is
their first agenda and that the current wealth of high-income countries is based on
their heavy emissions level in the past. Due to the conflicting interests among
different countries, it is hard to reach agreements and implement a plan with
enough enforcement via multilateral institutions such as the United Nations (ACC,
2010a).
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B. Iterative risk management
As described in the previous section, the process of establishing effective
climate policy is riddled with uncertainties. Still, policy-makers might be able to
identify a “better” policy from the alternatives by incorporating uncertainties and
risks associated with potential outcomes in their decision-making process (CCSP,
2009). For example, Yohe et al. (2004) demonstrates that, despite uncertainties
concerning climate sensitivity and temperature target, an adequate hedging policy
against different possible outcomes requires less adjustment costs than a “wait-andsee” policy that does nothing until 2035. Using Nordhaus’ DICE-99 model, the study
finds that the near-term policy of $10 carbon tax in 2005 entails robust adjustment
costs, while those costs under the no near-term policy scenario are highly variable in
terms of climate sensitivity and target temperature. Moreover, the adjustment costs
in the near-term policy scenario are in general lower than those in no policy
scenario—by more than $20 billion in half of the cases.
The study mentioned above effectively demonstrates that using the nearterm carbon tax policy as a hedge can be a robust strategy, generating even costs
across different possible outcomes. A recent version of the Synthesis and
Assessment Report by the U.S. Climate Change Science Program (2009)
recommends that for climate policy characterized by “deep uncertainty,” policymakers should employ “resilient” and “adaptive” strategies. Although multiple
definitions are available, a “resilient” policy can be explained as a policy that works
well across different scenarios. An “adaptive” policy is one that evolves over time by
15
adjusting in response to new information (CCSP, 2009). Adaptive risk management,
or iterative risk management, is a decision-making framework consisting of “ongoing
assessment, action, reassessment, and response that will continue decades if not
longer, […] so that each iteration learns from previous iterations” (ACC, 2010b). An
iterative risk management framework can implement robustness in its design by
incorporating uncertainties as a set of potential parameter values or probability
distributions (CCSP, 2009) (App.1: Figure 1-2).
In the Fourth Assessment Report by the IPCC, it is recognized that:
“Responding to climate change involves an iterative risk management process that
includes both adaptation and mitigation, [...]” (IPCC, 2007b). An iterative
management approach acknowledges that eliminating all risks is impossible, and
that the results of every action are subject to uncertainty. Thus an iterative
approach does not require perfect knowledge before making decisions, since having
such knowledge is often impossible for complex problems such as climate change,
where definitions of the problem, objectives, and relevance of the issues are often
unclear (ACC, 2010b). Instead of making binding decisions at a single point in time,
decision-makers in an iterative management framework consistently reassess and
modify their choices over time in response to the changing environment. These
sequential adjustments in climate policy decision are valuable—the effects of near
term policy might not be followed by an immediate response in climate, and the
response is subject to large uncertainties (Parson and Karwat, 2011). Also, since
scientific knowledge, socioeconomic environments, and political values and
16
objectives change over time, the process of making climate policy decisions should
accommodate these changes by adapting over time (ACC, 2010b).
C. Adaptation in an iterative framework
A large number of studies have used an iterative risk management
framework in their analysis on a decision-making process characterized with
uncertainty. By definition, an iterative decision-making framework is a continuing
process of decision, evaluation, and adjustment. Thus, the process of acquiring new
information (or “learning”) and the change in uncertainty concerning key
parameters should have a significant influence on near-term decisions as well as on
subsequent decisions. Parson and Karwat (2011) report that the majority of the
studies on an iterative decision framework have investigated the effects of
uncertainty and learning on near-term climate decisions.
In fact, the direction of the effects of learning remains largely controversial. It
might be the case that learning motivates decision-makers to adopt a strong
preemptive policy to guard against an uncertain future. Or, the possibility of future
learning might induce a delay in immediate action so as to wait for better
information. To investigate how decision-makers maintain a balance between “toomuch” and “too-little” near-term climate policies, studies have frequently referred
to the two opposing “irreversibility effects.”
On the one hand, one of the irreversibility effects represents the
environmental damage from the GHG accumulation in the air, which in most cases is
17
difficult to remedy. Reducing cumulative GHG emissions is nearly impossible
(Matthews and Caldeira, 2008), and GHG-induced global warming is likely to impose
irreversible effects on the climate system (Solomon et al., 2009). This irreversibility
effect of GHG accumulation alarms many decision-makers, since they are uncertain
about the extent of environmental damage and costs of limiting emission that they
might face in the future. One of their largest concerns would be the possibility of
suffering an extreme environmental damage that cannot be undone. Thus, as a way
to “keep one’s options open,” the decision-makers should follow the “precautionary
principle,” (Arrow and Fisher, 1974; Henry, 1974) which suggests that an
appropriate measure should be immediately enacted to prevent irreversible
damages on the environment.
On the other hand, more recent studies recognize that there is another
irreversibility that runs in the opposite direction. It is possible that, after
implementing a climate policy, policy-makers realize that their response was too
stringent. In other words, the actual cost of policy limiting carbon emission might
have been larger than the environmental benefits from the policy. According to an
iterative framework, the policy-makers would reduce the severity of their policy at
the next decision-point, but some parts of capital investments, or “sunk” costs, are
not recoverable. Pindyck (2000) characterizes the two irreversibility effects as the
economic “sunk” cost of the policy implementation and the environmental benefit
of preemptive action, and explains that these effects together determine the
strength of near-term policy. The study finds that the threshold for policy adoption
18
increases with the rising uncertainty over the potential costs and benefits of the
policy, implying that the irreversibility effect on the “sunk” cost side is stronger than
the effect of opposing irreversibility in the face of greater uncertainty.
Many recent studies have found that learning leads to a higher emissions
level in the near future. These studies suggest that, in the presence of learning, the
significance of the “precautionary principle” is overshadowed by the irreversibility of
the sunk costs of climate policy (Webster, 2002). Ingham et al. (2007) shows that
future learning is more likely to result in a weak near-term action against GHG
emissions, given that both adaptation and mitigation options are available for
climate policy choice. Kolstad and Ulph (2008) construct a theoretical model
characterized with more than two decision-makers and two time periods, and
investigate how these decision-makers strategically interact with one another in the
process of uncertainty and learning. They report that the level of global welfare from
forming an international environmental agreement (IEA) decreases as the chance of
learning increases. The authors attribute the negative value of information to
strategic interactions among decision-makers. In the following study, Kolstad and
Ulph (2011) modify their original model to allow decision-makers to have
heterogeneous damage functions. Their study confirms the previous finding in the
2008 article: the possibility of partial learning reduces the global welfare value from
forming an IEA.
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Instead of arguing for a particular direction, some recent works claim that
the effects of learning on near-term climate policy can be in either direction, stricter
or weaker, depending on the formulation of theoretical models and parameter
values. Lange and Treich (2008) suggest that, while the information available before
a decision always has a positive value, the value of information after the decision
has been made can be either positive or negative. Moreover, the decision-makers’
expectation on the availability of future information affects not only future decisions
but might also influence current decisions. Based on these facts, the authors reason
that there is no clear-cut effect of uncertainty and learning on near-term climate
policy, and demonstrate their argument with their iterative-decision model.
Webster (2002), using another iterative decision model, shows that the direction of
learning effects on climate policy is determined by the shape of the probability
distribution over the potential costs of limiting emissions and environmental
damage costs.
Using a simple theoretical framework, just as the aforementioned studies do,
may effectively deliver insights into the climate decision-making process. In addition,
engaging an empirical model can render a broad picture that accounts for the
interactions between humans and the climate system (Ingham et al., 2007).
Extending from theoretical discussion, Webster (2002) uses a modified version of
the MIT Integrated Global System Model and shows that the optimal level of nearterm emissions is determined by the perceived costs and benefits of limiting
emissions. Richels et al. (2009), using an integrated assessment model called MERGE,
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demonstrates that the anticipation of the developing countries’ future participation
in a global climate policy reduces the GDP losses of all participating countries. In
particular, the model shows that the developed countries with the anticipation
would not make a drastic reduction in the near future. However, most of these
studies engaging an integrated assessment model do not adequately treat the
iterative nature of climate decision process; in those models, the entire time path of
decisions are determined by intertemporal optimization, and no mid-course
adjustment is allowed (Parson and Karwat, 2011).
Thus, many studies using an iterative framework have significantly
contributed to our understanding of how near-term decisions are influenced by
updated information acquired through the learning process. Parson and Karwat
(2011) report that the majority of those studies using a theoretical framework,
however, have employed a highly simplified iterative framework: a “single unitary
actor” making a “binary or one quantitative choice of mitigation stringency” over
“two decision points.” Kolstad and Ulph (2008) suggest that having three or more
decision-makers in the model would better represent a decision-making process,
especially in the context of an international environmental agreement where
strategic interactions among the decision-makers are crucial. Parson and Karwat
(2011) comment that such strategic interactions should be represented with more
complexity in decision models; there would be interactions not only among the
actors at the current decision-point, but also between the current actors and the
actors in the future.
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My study contributes to the existing literature on iterative climate policy
mainly by modeling a three-country, three-period framework. Because it involves
more than two actors (countries), the model can generate results that provide richer
implications on their interactions. Also, with more than two periods, this study
effectively demonstrates how near-term climate decisions of countries would
influence their decisions made further in the future. Using this theoretical model, I
will examine how countries would make their climate decisions while perceiving
another’s decision (Chapter 2). In further experiments, I will also allow some key
information to change over time and study how countries should respond to the
change (Chapter 3).
22
Chapter 2: Model Overview and the Baseline Simulation
In this chapter, I will give an overview of a simple iterative decision model, in
which three countries make decisions over three periods on their exhaustible
resource consumption and, by analogy, their participation in a global climate policy
limiting emissions. The idea of the analogy is that the climate system depends on
cumulative emissions, so that participation in a global policy of limiting greenhouse
gas (GHG) emissions is equivalent to participation in the consumption of what is, for
all intents and purposes, an exhaustible resource. With this model, I will simulate the
baseline scenario, in which countries are assigned fixed likelihoods of their
participation and are well aware of those likelihoods. At each decision point,
countries solve optimization problems and strictly follow their theoretically defined
optimal consumption levels. Moreover, they have perfect knowledge of the longterm resource capacity from the beginning of their decision-making process; they
have only to worry about what other countries would do. At the end of this chapter,
I will collect a set of hypotheses from the results of the baseline simulation.
To provide the details behind my interpretations, I will refer to the tables and
figures (Appendix 1) that describe the simulation results and other relevant
information. I will also refer to specific parts in the technical summary (Appendix 2)
to explain how I interpreted the numerical results.
23
A. Model overview
In my iterative decision-making model, countries make decisions on their
exhaustible resource consumption through decision points in 2012, 2035, and 2050
(App.1: Figure 2-2). Countries are categorized into three different groups—the
developed, the BRIC (Brazil, Russia, India, China), and the developing countries. On
the one hand, I assume that the group of developed countries is aware of the
scarcity of nonrenewable resources and is willing to cooperate with other groups to
limit GHG emissions. On the other hand, I assume that other country groups are
initially unaware of scarcity, and therefore myopically maximize their immediate
economic benefits in 2015. In 2035, however, the group of BRIC countries decides
whether or not to participate in the joint climate policy with the developed country
group; and in 2050 the group of developing countries considers the same issue. The
structure of the model is fully explained in Appendix 2 (App.2: 2A).
B. Baseline scenario and the simulation results
With the model described in the previous section, I simulate the baseline
scenario, in which the BRIC countries group is more likely to participate in the global
climate policy than the developing countries group. Understanding their significant
role in world economy and their increasing effects on the environment, the BRIC
countries should cooperate with the developed countries to limit GHG emissions
(App.2: 2B-(a)). The results from the baseline simulation—consumption and benefit
trajectories of the three countries over three periods—are presented in Figure 2-3 of
24
the Appendix 1. Since the consumption trajectories look the same as the benefit
trajectories for each country, I will mainly discuss the consumption trajectories.
In the consumption trajectory of Country 1 (App.1: Figure 2-3A), we see that
Country 1 approaches its highest possible level of long-term (2050) consumption if
all three countries participate in the global climate policy by 2050. Given that
Country 3 participates in 2050, Country 1 can achieve its highest possible
consumption in 2050 if Country 2 participates early in 2035 (App.2: 2B-(b)-Note 1).
Thus, Country 1 should wish for all countries to participate, and particularly prefers
the early participation of Country 2 in 2035 to its late participation in 2050. Then,
Country 1 must have some incentive to encourage other countries’ participation at a
decision point each in 2035 and 2050. However, unanimous participation does not
result in the optimal outcome for the other countries. In fact, their best strategy is
not to participate at any period (App.2: 2B-(b)-Note 1). Therefore, I expect that
Country 1 would provide the other countries with enough incentive to encourage
their participation.
Further observation suggests that Country 1 would encourage Country 2 to
participate early in 2035. If Country 2 does not participate in 2035, for Country 1, not
only would variance in its potential long-term consumptions grow larger, but also
the chance of having the lowest-possible long-term consumption would increase
from 6% to 20% (App.2: 2B-(b)-Note 2). For both Country 2 and Country 3, its worst
outcome is the case in which one country participates but the other does not. Once
25
Country 2 chooses not to participate in 2035, Countries 2 and 3 would become
hesitant to participate in 2050 because each would not know if the other would
participate (App.2: 2B-(b)-Notes 3, 4). Thus, it would be difficult for Country 1 to
encourage other countries’ participation if Country 2 does not participate in 2035.
As for Country 2, its two worst outcomes are the ones in which Country 2
participates in either 2035 or 2050 while Country 3 does not participate at all.
Between those two worst outcomes, however, Country 2 can afford larger long-term
consumption if Country 2 participates in 2035 rather than in 2050. Thus, I conclude
that Country 2 can avoid its worst possible outcome if it participates early in 2035,
under the condition that Country 2 will eventually participate in the global climate
policy at some point (App.2: 2B-(b)-Note 3).
In sum, Country 1 would encourage all countries to participate in the global
climate policy. However, the best strategy for other countries is not to participate at
any period, so Country 1 would need to provide enough encouragement to them.
Even though Country 1 would welcome any participation, Country 1 would
particularly prefer Country 2’s early participation in 2035 to its late participation in
2050. If Country 2 decides not to participate in 2035, then variance in potential longterm consumptions of all countries would grow. As they face greater risk in their
future consumptions, Countries 2 and 3 would become hesitant to participate,
which would make it difficult for Country 1 to encourage their participation in 2050.
Lastly, assuming that Country 2 eventually participates in the climate policy, Country
26
2 would find it the lesser of the two evils to participate in 2035 rather than in 2050.
These observations are summarized in a set of hypotheses in Table 2-5 (App. 1).
C. Robustness test
Before exploring further scenarios, I assessed whether the model can
generate a reliable output at a wide range of parameter values. By running the
model with different values of (a) participation likelihoods, (b) resource capacity
level, and (c) discount rate, I confirmed that the model worked well with a
reasonably wide range of participation likelihoods and discount rates (App.2: 2C-(a),
-(c)). However, the model works with a rather limited range of resource capacity
levels (App.2: 2C-(b)). I take these considerations into the design of further
simulations in Chapter 3.
D. Summary
In this chapter, I introduced my theoretical model, which simulates an
iterative decision-making process of three countries across three periods concerning
their exhaustible resource consumption. As a preliminary step, I explored the
baseline simulation, in which countries had perfect information of key parameters
and took one another’s decisions into account. Based on the results from the
baseline simulation, I constructed three initial hypotheses (App.1: Table 2-5) that
will be tested with further simulations in Chapter 3. Prior to those simulations, I
conducted robustness tests to demonstrate that my model generates a reliable
outcome with a variety of parameter values. It turns out that my model is robust to
27
a wide range of parameter values, but only to a limited range of resource capacity
levels. With these issues in mind, I will run further simulations in the following
chapter to explore how countries would make decisions in the face of uncertainty in
key parameters.
28
Chapter 3: More Simulations
In this chapter, I explore further scenarios that add more dynamics to the
baseline model. Specifically, I experiment with more general scenarios within which
country participation and the true resource capacity level are imprecisely known. I
first examine how Country 1’s decision on its near-term consumption is influenced
by perceived likelihoods of participation by the other countries. Then, I explore the
effects of Country 1’s near-term consumption on the future consumptions across
the other countries. Lastly, I investigate the value of early information on the
ultimate resolution of cumulative resource capacity and suggest appropriate
responses to that information. The idea here is that climate science may evolve so
that what was perceived to be an emissions (consumption in the simulation)
constraint may turn out to be too high (so that long-term emissions, or
consumptions, have to be contracted) or too low (so that long term constraints can
be relaxed). The critical question here is what effect this uncertainty might have on
near-term decisions, taking into account of the decisions of other countries.
I have collected additional insights from these scenarios mostly from
comparative static analyses, tested the hypotheses from Chapter 2 in a more
uncertain world, and illustrated results from some simulation exercises. The specific
details supporting my interpretations of each set of results are highlighted in tables
(Appendix 1) that demonstrate the comparative statics, but the technical summary
(Appendix 2) is essential to understanding my conclusions about the sign of the
29
change; each interpretation is illustrated in figures (App.1) derived from specific
simulation, and associated sections in the technical summary (App.2) again provide
some insight and context. Thus, the following text conveys a more intuitive narrative
rather than providing all of the details.
A. Sensitivity of Country 1’s near-term (2015) resource consumption to
other countries’ likelihoods of participation
This section proposes to answer the following question: how will the nearterm (2015) resource consumption of Country 1 be influenced by the likelihoods of
participation by the other countries? Using the theoretical model presented in
Chapter 2, I will investigate the sensitivity of the optimal near-term consumption of
Country 1 to the likelihoods of the other countries' participation. It is worth noting
that Country 1 may or may not choose to consume the optimal level in a real-world
scenario. Still, within my model, the country's actual consumption level should be
more or less anchored to the optimal level.
(a) Comparative static analysis
Although it is possible to present the comparative statics in mathematical
expressions, I could not simplify the results into one concise and meaningful
mathematical expression from which sign can be determined. However, the results
from simulations are suggestive, so they are presented to infer the signs and
magnitudes of comparative statics (App.1: Table 3-1). The simulation results suggest
that the near-term consumption of Country 1 increases as Country 2 or Country 3
becomes more likely to participate in the global climate policy (App.2: 3A-(a)-Note
30
1). If Country 2 or Country 3 were more inclined to participate in the next period,
then Country 1 would expect its burden of reducing consumptions to be shared with
the participating countries in the near future; thus, Country 1 would reduce its
participation by increasing its consumption. In other words, the more likely it is that
the other countries would participate in the next period, the smaller Country 1’s
reduction in near-term consumption would be.
This reduction in near-term consumption in response to the likelihood of
participation by another country (say, Country 2) would not be very sensitive if a
second country (say, Country 3) were highly likely to participate in the future. In fact,
the two likelihood parameters have negative cross-partial effects on the near-term
consumption of Country 1 (App.2: 3A-(a)-Note 2). This means that Country 1 would
not be too concerned with another country’s participation as long as Country 1
knows the other country is highly likely to participate and share the burden with
Country 1.
(b) Hypothesis test
Next, I test whether my initial hypotheses (App.1: Table 2-5) are robust in
reference to the different levels of participation likelihoods (App.1: Figures 3-1A, B,
C). First, I investigate whether Country 1 would really seek unanimous participation
regardless of the likelihoods of participation by the other countries. The simulation
results indicate that Country 1 would enjoy the largest long-term (2050)
consumption if all countries were to participate in the global climate policy by 2050
31
(App.2: 3A-(b)-Note 1). On the other hand, participating in either 2035 or 2050 is
not the most advantageous strategy for Countries 2 and 3. As has been previously
stated, the optimal strategy for these two countries is choosing not to participate at
any period, which results in the worst outcome for Country 1. Therefore, Country 1
would encourage all other countries to participate in the plan.
Second, at different levels of participation likelihoods, Country 1 prefers the
early participation of Country 2 in 2035 to its late participation in 2050. Between the
two outcomes in which all three countries are participating by 2050, Country 1 can
enjoy a higher level of long-term consumption in the outcome where Country 2
participates in 2035 than in the other outcome where Country 2 participates only by
2050 (App.2: 3A-(b)-Note 1). Also, for each country, variance in potential long-term
consumptions is small if Country 2 participates in 2035 rather than in 2050 (App.2:
3A-(b)-Note 2). Greater variance in long-term consumptions can be interpreted as a
greater risk in future wealth. If Country 2 decides not to participate in 2035, then all
countries are exposed to a fair amount of risk in their long-term consumptions; the
risk could be smaller if Country 2 participates in 2035. Then, in the viewpoint of
Country 1, Country 2’s decision not to participate in 2035 makes it difficult for
Country 1 to encourage the future participation of Country 2 and Country 3. As a
result, from 2035, Country 1 will actively seek for the early participation of Country 2
rather than sitting back and letting the latter make any decision.
32
Lastly, at all levels of participation likelihoods, Country 2 can avoid its worst
possible outcome by participating in 2035 rather than in 2050 (App.2: 3A-(b)-Note
3). Country 2 would fear the most those outcomes in which it participates in either
year while Country 3 does not participate at all; in those outcomes, Countries 1 and
2 would have to undertake a significant reduction in their consumptions to make up
for the inaction by Country 3. If Country 2 decides to participate only by 2050, it
would have to make a drastic cut in its long-term consumption. If, in contrast,
Country 2 participates from 2035, it can even out its reduction schedule across its
mid-term and long-term consumptions.
B. The effects of Country 1’s near-term (2015) consumption on the future
consumptions of all countries
In the previous section, I investigated how Country 1 would determine its
near-term (2015) consumption level while perceiving other countries’ likelihoods of
participation. Now, I will examine how Country 1’s choice concerning its near-term
consumption will, in turn, affect the future consumptions of Country 1 as well as
those of the other countries. The optimal level of near-term consumptions is
determined by the participation likelihoods and other parameters values (as I
demonstrated in the previous section). Theoretically, Country 1 should choose this
optimal level, but in practice the country might consume more or less than the
optimal level. Therefore, I examine how Country 1’s actual choice of consumption—
or the deviation from the optimal level of consumption—affects the future
consumptions of all countries.
33
(a) Comparative static analysis
I first examine the comparative statics of the mid-term (2035) consumptions
to Country 1’s near-term consumption (App.1: Table 3-2). The participating
countries in 2035 (Country 1 and/or Country 2) would reduce their mid-term
consumptions as Country 1 consumes more in 2015 (App.2: 3B-(a1)-Note 1). Such a
response is anticipated, because the three countries are sharing a finite amount of
exhaustible resource in this simple iterative decision model; one-unit more
consumption by one country should result in one-unit less consumption by the other
countries. However, in the real-world context of climate change, this might not
reflect the relative value of global participation. While the signs of the comparative
statics can be unambiguously determined, their magnitudes depend on the
participation likelihoods of the countries that do not participate in 2035. As the nonparticipating countries in 2035 become less likely to participate in the next period,
the participating countries would show greater response in their mid-term
consumptions to Country 1’s past consumption in 2015 (App.2: 3B-(a1)-Note 2).
Next, I analyze the comparative statics of the countries’ long-term (2050)
consumptions (App.1: Table 3-3). Again, the participating countries should reduce
their long-term consumptions if Country 1 were to consume more than its optimal
level in 2015 (App.2: 3B-(a2)-Note 1). The magnitude of their adjustments depends
on whether they made past adjustments in their mid-term consumptions (App.2:
3B-(a2)-Note 2); if some appropriate adjustments were made in their mid-term
consumptions in response to Country 1’s overconsumption in 2015, then the
34
participating countries in 2050 would not need to make severe reductions in their
long-term consumptions. Nonetheless, the expressions of these comparative statics
(App.1: Table 3-3) suggest that Country 1’s consumption choice in 2015 would have
a heavy influence on long-term consumptions of Countries 2 and 3 if these two latter
countries were participating in the climate policy (App.2: 3B-(a2)-Note 3). A set of
simulation results also demonstrate that Country 1’s economizing on its near-term
consumption would greatly improve potential long-term consumptions of Countries
2 and 3 (App.1: Figure 3-2; Table 3-4). For example, if Country 1 consumes only half
of its optimal level in 2015, then all countries (even including Country 1) would be
able to enjoy a near-maximum level of consumption in 2035 and 2050, whether they
participate in the climate policy or not (App.2: 3B-(a2)-Note 4). This observation
confirms that Country 1’s consumption choice in 2015 exerts a significant influence
on its own future consumptions, as well as on those of the other countries. Thus,
Country 1 should economize on its near-term consumption to seek other countries’
participation; the less Country 1 consumes in 2015, the less reduction the
participating countries have to make in their future consumptions.
(b) Hypothesis test
I test my three initial hypotheses with a scenario in which Country 1 may
choose its near-term (2015) consumption level higher or lower than the optimal
level (App.1: Figure 3-2, Table 3-4). Although Country 1’s choice concerning its nearterm consumption has a significant influence on the consumption trajectories of
each country, all of my initial hypotheses hold at different levels of near-term
35
consumption of Country 1. First, whether Country 1 consumes more or less than its
optimal level in 2015, Country 1 can achieve the highest long-term consumption only
if all the other countries participate in the global climate policy by 2050 (App.2: 3B(b)-Note 1). Thus, Country 1 would still wish for unanimous participation, and my
first hypothesis holds valid.
Second, regardless of its consumption level during the first period, Country 1
would prefer Country 2’s early participation to its late participation. Between the
two outcomes in which all three countries participate, Country 1 can enjoy higher
long-term consumption if Country 2 participates in 2035 rather than in 2050 (App.2:
3B-(b)-Note 1). Moreover, for each country, variance in its potential future
consumption is always smaller if Country 2 participates in 2035 than if it did not
(App.2: 3B-(b)-Note 2). Thus, whether Country 1 consumes too little or too much in
2015, it becomes difficult for Country 1 to encourage all countries to participate if
Country 2 decides not to participate in 2035. Hence, the validity of my second
hypothesis holds.
Lastly, I show that my third hypothesis is robust to Country 1’s near-term
consumption choice: if Country 2 were to eventually participate in the climate policy,
Country 2 would be able to avoid its worst-possible outcome by participating early.
In fact, for Country 2, the advantage of its early participation to its late participation
becomes less significant as Country 1 consumes less in 2015 (App.2: 3B-(b)-Note 3).
This suggests that Country 1’s economizing on its consumption in the near term
36
leaves more resources for other countries to consume in the future; in this scenario,
Country 2’s early participation (i.e., spreading out the required adjustment) is less
necessary. Therefore, I can conclude that the third hypothesis remains valid, but the
validity is rather weak for the cases in which Country 1 consumes significantly less
than its optimal level.
C. Uncertainty in the knowledge of resource capacity level
In the last section of Chapter 3, I investigate how countries would adjust their
future consumptions upon gaining new information about the resource capacity
level in the middle of the decision making process. Although the countries start their
decision-making process with some estimate of the resource capacity, the estimate
might change over time with new information. In this experiment, it is assumed that
all countries are equally exposed to new information and, based on the information,
make a joint estimate of an “accurate” level of resource capacity. The following
analysis discusses the countries’ hypothetical responses in their mid-term and longterm consumptions to the updated resource capacity level, which reflects how the
countries should theoretically respond to new information about resource capacity
level. In a real climate context, however, the countries may or may not react in the
same way to new information.
(a) Comparative static analysis
I first examine the comparative statics of mid-term (2035) consumptions to a
newly updated resource capacity level (App.1: Table 3-5). The non-negative
37
comparative statics suggest that the participating countries would increase their
mid-term consumptions in 2035 if they realize that there are more available
resources than they thought (App.2: 3C-(a1)-Note 1). While the signs of these
comparative statics are unambiguously non-negative, their magnitudes depend on
the participation likelihoods of the countries that do not participate in 2035. The
mid-term consumptions of the participating countries would become less sensitive
to an updated capacity level if the other countries become more likely to participate
in the next period (App.2: 3C-(a1)-Note 2). As the non-participating countries show
more inclination to participate and share the burden of reducing consumptions in
the next period, the currently participating countries would feel less compelled to
adjust their immediate consumption level with new information. After all, there
should be more resources available to consume in the next period.
Next, I study how the countries should adjust their long-term (2050)
consumptions in response to a new capacity level (App.1: Table 3-6). On the one
hand, the comparative statics of long-term consumptions are unambiguously nonnegative (App.2: 3C-(a2)-Note 1); the participating countries in 2050 would increase
their consumptions if they realize that there are more resources available than they
expected. Relatively speaking, long-term consumptions of Country 2 and especially
those of Country 3 would be more sensitive to a new resource capacity level than
those of Country 1 are (App.2: 3C-(a2)-Note 2). On the other hand, the magnitude of
adjustment that the participating countries need to undergo in 2050 would depend
on the prior adjustments made in the mid-term (2035) consumptions with respect to
38
the new capacity level (App.2: 3C-(a2)-Note 3). If the countries are informed of a
new capacity level in 2035 and make a timely adjustment in their mid-term
consumptions, then the countries would not need to make much adjustment in 2050.
In contrast, if the participating countries in 2035 do not update the capacity level, or
if, despite having accurate information, they do not adjust their mid-term
consumptions appropriately, then the countries might need to undergo significant
adjustment in 2050 to make up for their inaction in the previous period. Thus, by
having accurate knowledge on the resource capacity level early on, countries would
have a chance to readily adjust their immediate consumptions and spread out the
required reductions over time. Though there is a value in new information itself,
early response to the new information also matters.
(b) Hypothesis test
I will now confirm the validity of my initial hypotheses (App.1: Table 2-5) for
the scenario that allows countries to correct their understanding of resource
capacity level in 2035 and 2050 (App.1: Figure 3-3; Table 3-7). We take three
different cases: for reference, the baseline case in which countries have perfect
knowledge of resource capacity so there is no adjustment; the early adjustment case,
in which countries realize they overestimated the capacity level and update their
knowledge in 2035; and the late adjustment case, in which countries update their
capacity level only in 2050. I show that my initial hypotheses (App.1: Table 2-5) hold
valid in all of these tested cases. First of all, in all tested cases, Country 1 enjoys the
highest long-term (2050) consumption if all other countries join the global climate
39
policy by 2050 (App.2: 3C-(b)-Note 1). Therefore, Country 1 would prefer unanimous
participation, and my first hypothesis holds.
Next, I show that my second hypothesis holds in general, but its validity is
relatively weak in the late adjustment case (App.2: 3C-(b)-Note 2). In the early
adjustment case, given that both Countries 2 and 3 were to participate by 2050,
Country 1 can enjoy higher long-term consumption if Country 2 participates by 2035
instead of by 2050. Thus, Country 1 would wish for Country 2’s early participation in
the early adjustment case. However, in the late adjustment case, Country 1 finds
little advantage in securing early participation of Country 2 over its late participation.
Still, in both cases, all countries would face quite large variance in their potential
long-term consumptions if Country 2 decides not to participate in 2035, so it would
be less difficult for Country 1 to persuade Country 3 to participate after securing
Country 2’s participation in 2035. Based on all of these observations, I conclude that
Country 1 would prefer Country 2’s early participation to its late one for all cases. At
the same time, I admit that such preference of Country 1 might be weakened in the
absence of timely adjustment. This implies that Country 2’s early participation
alone—without accurate information of the resource capacity or timely
adjustment—would not significantly improve Country 1’s long-term consumption.
Finally, I demonstrate that it would be advantageous for Country 2 to
participate early if plans to eventually participate in the climate policy (App.2: 3C(b)-Note 3). In both early- and late adjustment cases, Country 2 would incur its two
40
worst outcomes if it participates by 2050 but Country 3 does not. Between those
two worst outcomes, the outcome in which Country 2 participates in 2035 entails
higher long-term consumption by Country 2 than the other outcome, in which
Country 2 does not participates in 2050. However, the difference is much smaller in
the late adjustment case than in the early adjustment case. Thus, I conclude that my
third hypothesis holds, but weakly in the case of late adjustment. This reiterates the
greater importance of timely adjustment and accurate information over early
participation.
41
Conclusion
In this study, I modeled an iterative process in which three different types of
countries (the developed, the BRIC, and the developing countries) made climate
decisions over three periods. More specifically, I modeled their exhaustible resource
consumption, which is analogous to greenhouse gas emission under an appropriate
climate policy. 2 With this model, I wished to answer my core research question: how
should a country adjust its climate policy with respect to changing information while
simultaneously considering other countries’ decisions? When a country makes
climate decisions, it should consider key information such as historical emissions, an
effective goal of limiting total emissions, and room for future emissions under a
current climate goal. However, drafting an effective climate policy is a problem
characterized with deep uncertainty; available information is often imperfect, and
therefore has to be updated consistently over time (Chapter 1C).
Without recognizing this evolving nature of information, I first gathered
some basic ideas about achieving a consensus on a global climate policy. I started
with rather a naïve scenario, in which all countries had perfect climate knowledge
and did not make subsequent adjustments over time (Chapter 2B). In such a
scenario, I observed that the developed countries—the leading group of a global
climate policy in our model—would want all other countries to participate in the
climate policy, and especially wish for the early participation of the BRIC countries.
2
This analogy was explained at the beginning of Introduction (p.4).
42
As for the BRIC countries, the earlier they participate and limit their emissions (or
consumption), the less adjustment they need to make in their decisions for future
emission down the line (if they were to eventually participate at some point)
(Chapter 2C).
Then, I re-examined these observations in a more realistic context, in which
what countries perceived to be “accurate” information was in fact subject to
uncertainty and had to be consistently updated over time. Having an effective limit
on total emissions (or binding resource capacity) in mind, countries would take an
estimate of future permissible emissions (consumption) into account for their nearterm policy decision (Chapter 3A). A couple of decades later, however, what they
thought to be just the right emission (consumption) level might turn out to be too
high or too low compared to the optimal degree derived with updated information.
Such deviation in past policy decision would induce all countries to re-adjust their
future emissions (consumption) for subsequent periods (Chapter 3B). Or, countries
could plan their future emission (consumption) schedule ahead of time with an
ineffective limit on total emissions (or inaccurate estimate of resource capacity), and
realize their error only after the near-term decision has been made; then, the
countries would adjust their future policy to reflect the updated (and supposedly
more accurate) limit on emissions (Chapter 3C). While I confirmed the robustness of
my initial hypotheses in these dynamic settings, I also collected additional
observations on countries’ response as follows.
43
Obviously, less room for future emissions should require stronger climate
policy in the short and long term. Such downward pressure on future emissions
might come from a variety of factors: some countries’ low inclination to participate
(App.2: 3A-(a)-Note 1), climate policy made in an early period that was too lenient
(App.2: 3B-(a1)-Note 1, 3B-(a2)-Note 1), or correction of a generous total emission
limit to a more stringent one (App.2: 3C-(a1)-Note 1, 3C-(a2)-Note 1). All of these
factors should be considered for a country’s climate decision. For example, if a
country perceives that other countries are very likely to participate in the future and
share the burden of limiting emissions, then the current participants would not need
to concern themselves too much about deviations in past climate policy (App.2: 3B(a1)-Note 2) or a new stringent emission limit (App.2: 3C-(a1)-Note 2). Moreover,
the severity of adjustment in future climate policy would readily depend on past
adjustment. Even if past climate policy were so lenient that too much emission has
been produced already, timely adjustment in immediate climate policy will lessen
the severity of adjustment that the participants in the far future would need to
undertake (App.2: 3B-(a2)-Note 2). Equivalently, if countries find a need to adopt a
more stringent emission limit than the one previously agreed upon, then they can
start adjusting their climate policy immediately to spread out required adjustments
evenly across time, which would greatly alleviate the burden of future participants
(App.2: 3C-(a2)-Note 3). These observations demonstrate the value of a timely
response to new information.
44
Through all of these experiments, I have demonstrated that an iterative
framework is quite useful for understanding the climate decision-making process.
Even though I could have made some observations without modeling climate
decision-making as an iterative process (Chapter 2), I was able to collect richer
insights from those simulations within which countries perceived another’s action
and incessantly adjusted their decisions to changing information under uncertainty
(Chapter 3). It is meaningful that I directly demonstrated a number of intuitive ideas
regarding iterative climate policy by generating concrete simulation results with a
simple iterative decision model. However, it is worth noting that my model is
“simple” in the sense that it incorporates uncertainty in a few dimensions only. Also,
the model spans a finite number of periods, while climate decision-making in reality
is an infinitely ongoing process. Despite these simplifications, my study contributes
to the literature of iterative climate decision-making by using a three-country, threeperiod framework; so far, the majority of relevant studies employ a two-country,
two-period framework (Parson and Karwat, 2011). By considering more than two
actors within an extended time horizon, I successfully elaborated on the implications
of evolving information and interactions within an iterative climate decision process.
For future research, I plan to engage several modeling teams in an
application for imposing a three-country, three-period framework on one or more
integrated assessment (IA) models. I will again investigate how three groups of
countries would choose their permissible emissions through 2050 while they
simultaneously recognize uncertainty in their climate knowledge. Also, I will explore
45
the feasibility of using side-payments to influence the likelihoods of participation
and facilitate global participation. All of this analysis will be conducted in an iterative
decision-making framework that involves sophisticated climate and socioeconomic
interrelationships provided by the IA model. Since an IA model can be regarded as a
theoretical black box (in the sense that we cannot easily expect its output), the
observations made in this study will serve as a foundation for understanding the
complex results from these experiments.
46
Postscript
As discussed earlier (App.2: 2B-(a), 2C-(b)), I based the design of my model
off of an assumption: the resource capacity level had to be high enough to
guarantee unconstrained consumption of countries during the first two periods, and
at the same time, low enough to constrain countries’ consumptions in the third (final)
period. The “high enough” condition allows countries to sustain their economy until
2050, whether the BRICs and other developing countries participate by then or not;
this simplifies the resulting analysis of my three-period framework. The “low enough”
condition is imposed to make the resource capacity a binding constraint, and
therefore relevant to the countries’ decision-making process. While these two
conditions are imposed primarily for convenience, they do not seem to render too
hypothetical a picture. To begin with, the major sources of energy are finite and
non-renewable, so countries are bound to exhaust them at certain point. More
importantly for the motivation of this work, though, any climate target imposes a
limit on the total permissible emissions, and we are destined to reach this limit in
the very far future.
Since their knowledge of climate science is subject to uncertainty, countries
might find out that the true level of resource capacity is “too high” or “too low”;
equivalently, countries might find that the true permissible emissions budget is “too
large” or “too small.” The reasons for this could be that the science has changed, or
that they may discover that some countries are not participating fully in any
47
international agreement. In any of these cases, the question is how countries would
plan their future emissions and undertake the appropriate preliminary investments,
and how they would make “mid-course corrections” as the future unfolds.
My simulation results demonstrated that countries’ participation enabled
them to spread out their permissible consumption (and by analogy, emissions)
across periods, but that was when countries had a large enough emissions budget.
What if the amount of total permissible emissions were too small to spread out? Or,
what if they found out that “downstream” limitations were more severe than
anticipated? Countries might emit the entire permissible amount within a short
period, and thereby put an end to the world. Or, they might spread out as much as
they can, while searching for other ways to sustain their economy (e.g. slowing
down the rate of emissions or discovering alternative clean energy resources) while
hedging against future uncertainty. I believe that countries would choose the second
option over the first option, because spreading their emissions would buy additional
time, allowing for further possibilities; additionally, it might be possible that sidepayments could increase the likelihood of this more preferable outcome.
48
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National Academies Press
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51
Appendix 1: Figures and Tables
I. Figures
[Figure 1-1] Relationship between cumulative emissions and global mean
temperature change
Cumulative carbon emissions have a consistent relationship with global mean
temperature changes of 1 to 5⁰C. Best estimates are based on 1.75⁰C per 1,000 gigatonne of carbon (GtC) emitted, and the uncertainty ranges from 70 to 140% of the
best estimate. The dashed line is the level of cumulative emission to the year 2009,
which is 530 GtC.
Source: National Research Council (2011) Climate Stabilization Targets: Emissions,
Concentrations, and Impacts over Decades to Millennia. Washington, DC: National
Academies Press. (FIGURE 3.6 in p.101)
52
[Figure 1-2] The iterative nature of the climate policy process
The above diagram describes a simple iterative decision-making process:
throughout the process, decision-makers make decisions (at the square
nodes), evaluate their previous action, and reduce uncertainty by learning (at
the circles). The diagram suggests that decision processes in real world are
“continuous, overlapping, and iterative.”
Source: IPCC (2007) Climate Change 2007: Mitigation. Contribution of Working
Group III to the Fourth Assessment Report of the Intergovernmental Panel on Climate
Change. B Metz, OR Davidson, PR Bosch, R Dave, LA Meyer, eds. Cambridge, U.K.
and New York, U.S.A.: Cambridge University Press, FIGURE 3.37 in p.225
53
[Figure 2-1] Net benefit as a function of exhaustible resource
consumption
Benefit
Consumption
Exhaustible Resource Consumption is on the X-axis, and Net Benefits on the Yaxis. Note that the order of optimal level of consumption is the same as the order
of maximized net benefits across three countries. In other words, ̂
̂
̂
̂
̂
̂
and
for .
54
[Figure 2-2] Overall structure of the model
2015
2035
2050
55
[Figure 2-3] Baseline simulation results
[Figure 2-3A] Country 1
Consumption Trajectories
Benefits Trajectories
[Figure 2-3B] Country 2
Consumption Trajectories
Benefits Trajectories
[Figure 2-3C] Country 3
Consumption Trajectories
Benefits Trajectories
56
[Figure 2-4A] Results of the robustness test with respect to the
participation likelihoods (p and q): Consumption trajectories of Country 1
Case 1 “Baseline Scenario”
:
Case 2:
Case 3:
Case 4:
Case 5:
57
[Figure 2-4B] Results of the robustness test with respect to the
participation likelihoods (p and q): Consumption trajectories of Country 2
Case 1 “Baseline Scenario”
:
Case 2:
Case 3:
Case 4:
Case 5:
58
[Figure 2-4C] Results of the robustness test with respect to the
participation likelihoods (p and q): Consumption trajectories of Country 3
Case 1 “Baseline Scenario”
:
Case 2:
Case 3:
Case 4:
Case 5:
59
60
Country 3
Country 2
Country 1
Case 1: 𝐗
𝟏𝟗𝟎
Case 2: 𝐗
𝟐𝟎𝟎
Case 3: 𝐗
𝟐𝟏𝟎
[Figure 2-5] Results of the robustness test with respect to the resource capacity (X): Consumption trajectories
61
Country 3
Country 2
Country 1
Case 1
𝒓 𝟎
Case 2
𝒓 𝟎 𝟎𝟐𝟓
Case 3
𝒓 𝟎 𝟎𝟓𝟎
Case 4
𝒓 𝟎 𝟎𝟕𝟓
Case 5
𝒓 𝟎 𝟏𝟎𝟎
[Figure 2-6] Results of the robustness test with respect to the discount rate (𝑟): Consumption trajectories
62
p=1
p=0.75
p=0.50
p=0.25
p=0
q=0.25
*In each simulation, X
q=0
19 𝑟
4
q=0.50
q=0.75
q=1
[Figure 3-1A] Consumption trajectories of Country 1 at different levels of the participation
likelihoods (p and q)
63
p=1
p=0.75
p=0.50
p=0.25
p=0
q=0.25
*In each simulation, X
q=0
19 𝑟
4
q=0.50
q=0.75
q=1
[Figure 3-1B] Consumption trajectories of Country 2 at different levels of the participation
likelihoods (p and q)
64
p=1
p=0.75
p=0.50
p=0.25
p=0
19 𝑟
q=0.25
*In each simulation, X
q=0
4
q=0.50
q=0.75
q=1
[Figure 3-1C] Consumption trajectories of Country 3 at different levels of the participation
likelihoods (p and q)
65
Country 3
Country 2
Country 1
𝟎 𝟓 ⋅ 𝐱̂ 𝟏𝟏
*In each case, 𝑝
Case 1: 𝐱 𝟏𝟏
𝑞
X
𝟎 𝟖 ⋅ 𝐱̂ 𝟏𝟏
19 𝑟
Case 2: 𝐱 𝟏𝟏
4
Case 3: 𝐱 𝟏𝟏
𝟏 ⋅ 𝐱̂ 𝟏𝟏
Case 4: 𝐱 𝟏𝟏
𝟏 𝟐 ⋅ 𝐱̂ 𝟏𝟏
[Figure 3-2] Consumption trajectories in different cases of Country 1’s near-term (2015) consumption (x )
66
X
X
X
X
X
2
;
19
X
X
2
19
Case 3:
X
Case 2:
X
Case 1:
;
19
*In each case, 𝑝
Country 1
𝑞
𝑟
4
Country 2
Country 3
[Figure 3-3] Consumption trajectories in different cases of resource capacity adjustments
II. Tables
[Table 2-1] Key variables and functional forms
For all Period 𝑡 ∈ { , 2, 3} and Country 𝑖 ∈ { , 2, 3},
𝑥𝑡𝑖 : Exhaustible resource consumption by Country 𝑖 in Period 𝑡
𝑋 : Total resource capacity such that 𝑋 ≥ 3𝑡=1 3𝑖=1 𝑥𝑡𝑖
𝑋𝑡 : The resource capacity level known in Period 𝑡
𝐵𝑡𝑖 : Net benefits earned by Country 𝑖 in Period 𝑡
For ∀𝑡 ∈ { ,2,3},
Net Benefits earned by Country 1 in Period 𝑡: 𝐵𝑡1 = 8𝑥𝑡1 0.3 𝑥𝑡1
Net Benefits earned by Country 2 in Period 𝑡: 𝐵𝑡 = 0𝑥𝑡 0.2 𝑥𝑡
Net Benefits earned by Country 3 in Period 𝑡: 𝐵𝑡3 = 3𝑥𝑡3 0. 𝑥𝑡3
*These benefit functions are graphed in Figure 2-1.
𝑟 : Discount rate
𝑝 : The likelihood of Country 2’s participating in the climate policy
𝑞 : The likelihood of Country 3’s participating in the climate policy
[Table 2-2] Probability of resulting in each outcome
Outcome 1
Outcome 2
Outcome 3
Outcome 4
Outcome 5
Outcome 6
67
[Table 2-3] Baseline scenario
p
q
𝑋
r
0.7
0.3
190
0.04
* In the baseline scenario, countries have perfect information on the resource
capacity level, and thus: 𝑋1 = 𝑋 = 𝑋3 = 0
[Table 2-4] Probability of resulting in each outcome in the baseline
scenario
Outcome 1
Outcome 2
Outcome 3
0.210
0.490
0.063
Outcome 4
Outcome 5
Outcome 6
0.147
0.027
0.063
[Table 2-5] Hypotheses based on the baseline simulation results
1. Country 1 wants all countries to participate in the global climate policy,
and is willing to provide them with encouragement.
2. Country 1 prefers early participation of Country 2 (in 2035) to its late
participation (in 2050). Countries would become more hesitant to
participate if Country 2 were not to participate early; in this case, it would
be more difficult for Country 1 to encourage all participation.
3. If Country 2 were to participate at some point in the future, Country 2
would be able to prevent its worst-possible outcome by participating early
in 2035.
68
[Table 2-6] Robustness test with respect to the participation likelihoods (p and q)
Cases
,
Case 1 (Baseline)
(0.7,0.3)
Case 2
(0.3,0.3)
Case 3
(0.5,0.5)
Case 4
(0.7,0.7)
Case 5
(0.3,0.7)
*In all of the five cases: 𝑋 =
0,
= 0.0
[Table 2-7] Robustness test with respect to the total resource capacity (𝑋 )
Cases
̅
Case 1 (constrained)
190
Case 2 (constrained)
200
Case 3 (unconstrained)
210
*In all of the three cases:
= 0. ,
= 0.3,
= 0.0
[Table 2-8] Robustness test with respect to the discount rate ( )
Cases
Case 1
0
Case 2
0.025
Case 3
0.050
Case 4
0.075
Case 5
0.10
*In all of the five cases:
= 0. ,
= 0.3, 𝑋 =
0
69
[Table 3-1] Near-term (2015) consumption of Country 1 (̂ ) at different
levels of the participation likelihoods (p and q)
̂
q=0
q=0.25
q=0.50
q=0.75
q=1
p=0
23.593
24.207
25.093
26.481
28.966
p=0.25
25.036
25.597
26.360
27.460
29.181
p=0.50
26.531
26.978
27.548
28.302
29.345
p=0.75
27.863
28.144
28.485
28.908
29.453
p=1
28.597
28.745
28.931
29.173
29.503
*Other parameter values are held constant: ̅ =
0, = 0.0
70
[Table 3-2] Comparative statics of mid-term (2035) consumptions to
Country 1’s near-term (2015) consumption
State 1: Country 2 decides to participate in 2035
- The comparative static of the mid-term consumption of Country 1:
̂1
1
1
2.
( )
.
=( )
2.
=
2.
( )
.
{
{
}
}
0
- The comparative static of the mid-term consumption of Country 2:
̂
1
1
=
̂1
̂
̂1
1
1
=
.
0
- The comparative static of the mid-term consumption of Country 3:
̂3
1
1
=0
State 2: Country 2 decides not to participate in 2035
- The comparative static of the mid-term consumption of Country 1:
̂1
1
1
=
.
2.
{
.
=
}
2.
{
}
0
- The comparative statics of the mid-term consumptions of Country 2 and Country 3:
̂
1
1
=
̂3
1
1
=0
71
[Table 3-3] Comparative statics of long-term (2050) consumptions to
Country 1’s near-term (2015) consumption
̂
Country 1:
Outcome 1
Outcome 2
Outcome 3
Outcome 4
[
.
[
2.
̂22
̂2
̂22
̂2
̂2
[
2.
[
Outcome 5
Outcome 6
̂2
[
.
[
Country 2:
̂2
̂2
]
]
.
.
[
]
.
2.
[
]
.
.
[
]
.
2.
[
]
0
0
̂
Country 3:
̂2
̂22
̂2
̂22
̂2
̂2
]
]
3
.
̂
̂22
̂2
[
]
0
]
3
.
[
]
̂2
]
0
3
̂2
[
]
0
72
[Table 3-4] Cases investigated in Chapter 3B simulation
Case 1
Case 2
Case 3
Case 4
Country 1 consumes 50% of its optimal level during Period 1
(i.e., 11 = 0. ̂11 )
Country 1 consumes 80% of its optimal level during Period 1
(i.e., 11 = 0.8 ̂11 )
Country 1 consumes 100% of its optimal level during Period 1
(i.e., 11 =
̂11 )
Country 1 consumes 120% of its optimal level during Period 1
(i.e., 11 = .2 ̂11 )
*In all of the four cases:
= 0. ,
= 0.3, ̅ =
0,
= 0.0
73
[Table 3-5] Comparative statics of mid-term (2035) consumptions to a
new capacity level
State 1: Country 2 decides to participate in 2035
- The comparative static of the mid-term consumption of Country 1:
2.
( )
.
̂1
=
̅ 2.
=
2.
( )
.
{
{
}
}
0
- The comparative static of the mid-term consumption of Country 2:
̂
̂
= 1
̅
̂
̂1
= .
̅
0
- The comparative static of the mid-term consumption of Country 3:
̂3
=0
̅
State 2: Country 2 decides not to participate in 2035
- The comparative static of the mid-term consumption of Country 1:
̂1
=
̅
.
2.
{
.
=
}
2.
{
}
0
- The comparative statics of the mid-term consumptions of Country 2 and Country 3:
̂
̂3
=
=0
̅
̅
74
[Table 3-6] Comparative statics of long-term (2050) consumptions to a
new capacity level
̂
̅
Country 1:
Outcome 1
Outcome 2
Outcome 3
Outcome 4
Outcome 5
Outcome 6
.
2.
Country 2:
̂
̅
[
̂1
̅
̂
]
̅
.
.
[
̂1
̅
̂
]
̅
[
̂1
̅
̂
]
̅
.
2.
[
̂1
̅
̂
]
̅
.
2.
[
[
̂1
]
̅
.
.
[
̂1
]
̅
[
̂1
]
̅
.
2.
[
̂1
]
̅
̂1
]
̅
̂1
̅
0
0
Country 3:
3
.
̂
̅
̂1
̅
[
̂
]
̅
0
3
.
̂1
]
̅
[
0
3
̂1
]
̅
[
0
75
[Table 3-7] Cases investigated in Chapter 3C simulation
Case 1
Case 2
Case 3
Countries know the exact level of resource capacity from the beginning
and do not adjust the capacity level over time (the baseline case)
(i.e., ̅1 = ̅ = ̅ 3 = 0)
Countries start with an overestimated resource capacity level and
adjust the capacity level in 2035 (the “early adjustment” case)
(i.e., ̅1 = 200, ̅ = ̅ 3 = 0)
Countries start with an overestimated resource capacity level and
adjust the capacity level in 2050 (the “late adjustment” case)
(i.e., ̅1 = ̅ = 200, ̅ 3 = 0)
*In all of the three cases:
= 0. ,
= 0.3,
= 0.0
76
Appendix 2: Technical Summary
I. Technical Details of Chapter 2
2A. Detailed description on the model
Each of the three groups of countries is represented a single country in my
model: Country 1 represents the group of developed countries, Country 2 the group
of BRIC countries, and Country 3 the group of developing countries.1 The three
countries make two kinds of decisions over three periods. First, each country
chooses its level of exhaustible resource consumption at the beginning of each
period (App.1: Table 2-1). By consuming resources, countries generate economic
benefits according to their net benefit functions (App.1: Figure 2-1). Functions are
designed in a way that the maximum level of net benefits of Country 1 is the highest
and that of Country 3 is the lowest. Also, the optimal resource consumption of
Country 1 is the highest while that of Country 3 is the lowest. Across all three
periods, there is a limit on the total resource capacity, which constrains
consumptions of all three countries.
Second, Country 2 and Country 3 individually decide whether or not to
participate in the global climate policy at the beginning of Period 2 and/or Period 3.
If they participate, then they will solve the benefit maximization problem jointly with
Country 1, considering all discounted benefits in subsequent periods. If they do not
participate, then they will keep their myopic perspective and maximize their own
immediate benefit for that period only. Their choice is associated with a set of fixed
likelihoods—Country 2 would choose to participate by the probability of p, and
Country 3 would do so by q.2 Depending on their decision, countries fall into one of
the two different states in Period 2, ultimately resulting in one of the six distinct
outcomes in Period 3 (App.1: Figure 2-2, Table 2-2).
At the beginning of Period 1, each of Country 2 and Country 3 individually
chooses the level of consumption that maximizes its own immediate benefits.
without any constraint
1
Countries in each group have homogeneous economic characteristics, so they can be grouped
together.
2
In other words, it is assumed that the BRIC and developing countries have some inherent inclination
to participate in the climate policy.
77
Country 1, on the other hand, is aware of resource scarcity and chooses the level of
consumption to maximize the expected value of its discounted benefits across three
periods,
{
(
)
(
)
} subject to (∑
∑
̅
)
where is the discount rate.
Then, at the beginning of Period 2, Country 2 decides whether or not to
participate in the climate policy. Depending on the decision made by Country 2, the
world falls into one of two different states. If Country 2 decides to participate in the
plan, then the world falls into State 1 and Country 2 is bound to its decision in both
Period 2 and Period 3; if it doesn’t, then the world falls into State 2, and Country 2
and Country 3 would individually consider their participation at the beginning of
Period 3.
In State 1, on the one hand, Country 2 decides to participate in the plan at
the beginning of Period 2. With Country 1, Country 2 jointly maximizes the expected
sum of their discounted benefits in subsequent periods:
(
)
subject to (∑
∑
̅
)
Despite Country 2’s decision, Country 3 still acts myopically and maximizes its own
immediate benefit in Period 2:
without any constraint
Country 3 does not choose whether or not to participate until Period 3. If it
participates (resulting in Outcome 1), then all three countries jointly maximize the
sum of their benefits in Period 3:
(
) subject to (∑
∑
)
̅
If Country 3 does not participate (Outcome 2), then it maximizes its own immediate
benefit in period 3,
without any constraint
while other countries jointly maximize:
(
) subject to (∑
∑
)
̅
78
On the other hand, in State 2, Country 2 decides not to participate in Period
2. As a result, Country 2 and Country 3 myopically maximize their own immediate
benefits in Period 2,
without any constraints
while Country 1 maximizes the expected value of its discounted benefits across
Period 2 and Period 3:
(
)
subject to (∑
∑
̅
)
Then, Country 2 and Country 3 reconsider their participation at the beginning of
Period 3. The world falls into one of the four different outcomes (Outcome 3 through
Outcome 6) depending on the decisions made by these two countries. In Outcome 3,
both Country 2 and Country 3 participate in the plan so that all three countries
jointly maximize their sum of benefits in Period 3.
) subject to (∑
(
∑
)
̅
In Outcome 4, Country 2 participates but Country 3 doesn’t—Countries 1 and 2
would jointly maximize their sum of benefits while Country 3 maximizes its own
benefits.
(
) subject to (∑
∑
)
̅
without any constraint
Outcome 5 is equivalent to Outcome 4, except that Country 3 participates while
Country 2 does not.
(
) subject to(∑
∑
)
̅
without any constraint
In Outcome 6, neither Country 2 nor Country 3 decides to participate. Each of the
three countries maximizes its own benefits in Period 3, but only Country 1 takes the
resource constraint into account:
subject to(∑
∑
)
̅
without any constraints
79
2B. Baseline scenario and the simulation results
(a) Details of the baseline scenario
In the baseline scenario, the likelihood of Country 2’s participating in the plan
(or p) is set at 0.7, while that of Country 3 (or q) is set at 0.3 (App.1: Table 2-3). In
other words, this is the case in which the BRIC country group is more likely to
participate in the global climate policy than the developing country group is. In this
scenario, the most likely result is Outcome 2, in which Country 2 decides to
participate in 2035 but Country 3 doesn’t in 2050. The least likely outcome is
Outcome 5, in which Country 2 chooses not to participate in both 2035 and 2050
while Country 3 chooses to participate in 2050 (App.1: Table 2-4). Discount rate is
set at 0.04, and the total resource capacity is set at 190. This level of total resource
capacity allows countries to consume as much as they want until the end of Period 2.
(b) Simulation results
In this section, I provide details of the baseline simulation results. For
convenience, I define one outcome is “better” for a country than another outcome if
the country can enjoy larger long-term (2050) consumption in the former outcome
than in the latter outcome.
[Note 1] First of all, the best outcome for Country 1 is Outcome 1 (App.1: Figure 23A), in which Country 1 enjoys its highest-possible long-term consumption level at
28.1. The second-best outcome of Country 1 is Outcome 3, in which the country
enjoys its second-highest long-term consumption level at 27.5. In other words,
Country 1 should wish for all countries to participate, and prefer the early
participation of Country 2 in 2035 to its late participation in 2050. However, neither
Outcome 1 nor Outcome 3 is the best outcome of Country 2 or Country 3.
[Note 2] There are two more reasons why Country 1 would prefer Country 2’s early
participation in 2035. First, variance in Country 1’s potential long-term (2050)
consumptions is greater under State 2 than under State 1. In Figure 2-3A (App.1),
the consumption trajectories of Outcomes 1 and 2 are less spread out compared to
the trajectories of Outcomes 3 through 6. Greater variance means greater risks, and
a risk-aversive country would prefer the state with smaller variance. Second, the
probability of reaching Outcome 6, the worst outcome for Country 1, increases from
6.3% to 21% if Country 2 decides not to participate in Period 2. Before Country 2
)
makes decision in 2035, the probability of resulting in Outcome 6 is: (
(
) (
) (
)
(App.1: Table 2-4). After Country 2 makes such
) (
)
decision (State 2), the probability of having Outcome 6 becomes: (
80
(
) (
)
. Because of these two reasons, Country 1 would prefer
State 1 to State 2 and persuade Country 2 to participate in 2035.
[Note 3] While Country 1 should wish for Country 2 to participate early, the best
strategy for Country 2 is not participating at all and resulting in either Outcome 5 or
Outcome 6, which guarantees Country 2 with the highest-possible long-term
consumption level at 25 (App.1: Figure 2-3B). However, the chance of resulting in
(
)
(
)
either outcome is only 9% (
; App.1: Table 2-4), because the baseline scenario assumes that Country 2 is
much inclined to participate (p=0.7). In other words, it is more likely than not that
Country 2 would participate in either 2035 or 2050. In contrast, the baseline
scenario assumes that Country 3 is not likely to participate in 2050 (q=0.3). There is a
63.7% chance of resulting in either Outcome 2 or Outcome 4—within which Country
2 participates at some point while Country 3 does not participate at all
(
)
(
)
(
App.1: Table 2-4). Note
that these outcomes are two worst outcomes for Country 2; between those two
outcomes, Outcome 4 is even worse than Outcome 2, since the former outcome
entails smaller long-term consumption than the latter outcome does (App.1: Figure
2-3B). Based on these observations, I may draw two conclusions: First, the two worst
outcomes for Country 2 are the outcomes in which Country 2 participates but
Country 3 does not. Second, if Country 2 will eventually participate in the climate
policy at some point, and if the country knows that Country 3 is not likely to
participate in 2050, then Country 2 would find it more advantageous to participate
in 2035 than in 2050.
[Note 4] Similar to the case of Country 2, the best strategy of Country 3 is not
participating in all three periods. Country 3 can enjoy the highest level of long-term
(2050) consumption in Outcomes 2, 4, and 6 within which Country 3 does not
participate at all periods (App.1: Figure 2-3C). Although Country 1 understands that
Country 3 is not much likely to participate in 2050 (q=0.3), it might be even more
difficult for Country 1 to encourage Country 3’s participation in State 2 than in State
1 for the following reason: Country 3 would have higher variance in its potential
long-term consumptions in State 2 than in State 1. This is demonstrated in Figure 23C (App.1), in which consumption trajectories of Country 3 is more spread out
among Outcomes 3 through 6 (State 2) than between Outcomes 1 and 2 (State 1).
This means that Country 3 would face more risk in State 2 than in State 1 if it were to
consider its participation. In fact, this makes an intuitive sense: in State 1, when
Country 3 makes a decision in 2050, Country 3 already knows that Country 2 is
participating in the climate policy. However, in State 2, Country 3 is still uncertain
81
whether Country 2 would participate or not. If it were to participate in 2050,
Country 3 would expose itself to the risk that Country 2 might not participate; in this
case, Country 3 would result in its worst-possible outcome, Outcome 5, in which the
country gets lowest-possible long-term consumption level at 4.5 (App.1: Figure 23C). Because of this risk, Country 3 would be more hesitant to participate in State 2
than in State 1, and hence Country 1 would have to alleviate Country 3’s concerns
with greater encouragement in State 1.
2C. Robustness test
To demonstrate the robustness of my model, I will check whether the model
generates a reliable output at a wide range of parameter values. Just as in the
baseline simulation, the following discussion is exclusively based on consumption
trajectories for convenience.
(a) Likelihoods of participation
As for the first round of robustness test, I simulate the model with different
values of participation likelihoods (p and q). The five different cases investigated in
this simulation are presented in Table 2-6 (App.1). Case 1 is the baseline case
(
) simulated again for comparison. Case 2 is the scenario in which
both Country 2 and Country 3 are not likely to participate in the global climate policy
(
). In Case 3 both countries are indifferent to participate (
),
and in Case 4 both are quite much inclined to participate (
). Case 5 is the
opposite case of Case 1; in Case 5, Country 3 is more likely to participate than
Country 2 is (
). All other parameters are held constant at the values
used in the baseline simulation ( ̅
,
).
The resulting consumption trajectories for each country are presented in
Figures 2-4A, B, and C (App.1). In all five cases, I could make similar observations as
in the baseline simulation results: (1) for Country 1, Outcomes 1 and 3 respectively
entail first- and second-highest possible long-term (2050) consumption levels in all
of the five cases (App.2: Figure 2-4A); (2) for every country, Consumption
trajectories of Outcomes 1 and 2 (which belong to State 1) are less spread out than
those of Outcomes 3 through 6 (State 2) (App.2: Figure 2-4A,B,C); (3) for Country 2,
Outcomes 2 and 4 entail the two lowest possible long-term consumption, but the
former outcome guarantees higher consumption level than the latter one does
(App.2: Figure 2-4B). From these observations, I conclude that the model can work
with a reasonably wide range of the participation likelihoods.
82
(b) Resource capacity level
In the design of my theoretical model, I imposed a condition that the
resource capacity (̅) should be at the level that allows countries to consume
without any constraint during the first two periods; in 2050, they would find
themselves constrained by the scarcity constraint. Then, my model should
theoretically work with any capacity level between 140 and 210. However, the
model generates reasonable results at a capacity level above 180 only; with the
capacity level at 180 or lower, the model predicts that some countries would choose
negative consumption level for particular periods.
Thus, I show instead that the model works well with a capacity level between
190 and 210. I test with the three different capacity levels at 190, 200, and 210
(App.1: Table 2-7). In the resulting consumption trajectories (App.1: Figure 2-5), I
observe that the countries tend to consume more with a higher level of resource
capacity: as the capacity level increases from 190 (Case 1: constrained level) to 210
(Case 3: unconstrained level), the consumption trajectories of each country
converge to the unconstrained optimal level. This observation makes an intuitive
sense, because countries would consume more to maximize their benefits given
with more resources. Therefore, I conclude that the model generates reasonable
results with the capacity level between 190 and 210, inclusive.
(c) Discount rate
Lastly, I conduct robustness test with respect to the discount rate by varying
the rate from 0 to 0.10. (App.1: Table 2-8). In fact, varying discount rate doesn’t
seem to change the consumption trajectories that much (App.1: Figure 2-6).
Nonetheless, if discount rate were to increase from 0% (Case 1) to 10% (Case 5),
potential long-term (Period 3) consumptions of each country would slightly decrease,
while potential near-term (Period 1) consumptions of the country would slightly
increase. In other words, with a higher discount rate, countries tend to plan smaller
consumption in the long term and larger consumption in the short term. This is not
surprising because an increase in discount rate means that countries value less of
their future consumption than their current consumption. Thus, I conclude that the
model works well with a reasonably wide range of discount rates.
83
II. Technical Details of Chapter 3
I will interpret the results of my simulations in Chapter 3 and provide the technical
details behind the intuitive ideas discussed in the main text. Major component of my
analysis is based on comparative statics, but I also report some simulation results to
test my initial hypotheses (App.1: Table 2-5).
3A. Sensitivity of Country 1’s near-term (2015) resource
consumption to other countries’ likelihoods of participation
In the first section, I will examine how much Country 1 would hypothetically
consume in 2015 while simultaneously considering the likelihoods of other countries’
future participation.
(a) Comparative static analysis
I first investigate comparative statics of Country 1’s near-term consumption ( ̂ ) to
the likelihoods of participation by other countries (p and q). Other parameter values
are held the same as in the baseline simulation (̅
). The near-term
consumption level that I examine in this experiment is the hypothetical level
determined by the benefit optimization. Theoretically, Country 1 should choose the
optimal level of consumption to maximize the discounted net benefit of all
participating countries.
[Note 1] From Table 3-1 (App.1), I infer that the comparative statics,
̂
and
̂
,
have a strictly positive sign. For example, at q=0.25, the near-term consumption of
Country 1 would increase if the likelihood of participation by Country 2 (p) were to
increase from 0 to 1. This holds true at each level of Country 3’s participation
likelihood (q), and hence
̂
. Likewise, the near-term consumption of Country 1
would increase in q at each level of p, so
̂
. Therefore, the comparative statics
of Country 1’s near-term consumption to p and q are strictly positive.
[Note 2] Also, I find in Table 3-1 (App.1) that an increase in Country 1’s near-term
consumption associated with an increase in p is smaller at a higher value of q. For
example, at q=0.25, an increase in p from 0.5 to 1 is associated with an increase in
consumption from 27 to 28.7. At q=0.75, the equivalent change in p is associated
with an increase in consumption from 28.3 to 29.2. Therefore, I conclude that p and
q have negative cross-partial effect on Country 1’s near-term consumption.
84
(b) Hypothesis test
To test the validity of my initial hypotheses (App.1: Table 2-5), I run simulations with
different values of participation likelihoods (0, 0.25, 0.50, 0.75, and 1), while holding
other parameter values constant as in the baseline simulation (̅
).
Figures 3-1A, B, and C (App.1) are the resulting consumption trajectories of three
countries.
[Note 1] Figure 3-1A (App.1) shows that, at every level of participation likelihoods,
Country 1 achieves its highest and second-highest long-term (2050) consumption
levels in Outcomes 1 and 3, respectively. Therefore, regardless of the participation
likelihoods, Country 1 would want all countries to participate, and particularly want
Country 2 to participate in 2035 (Outcome 1) than in 2050 (Outcome 3). This
supports the validity of my first hypothesis at different levels of participation
likelihoods.
[Note 2] I also confirm that, at all levels of participation likelihoods, Country 2’s
decision not to participate in 2035 would entail a high risk in long-term consumption
of all countries. In each of Figures 3-1A, B, and C (App.1), variance in potential longterm consumptions (of each country) is always smaller between Outcomes 1 and 2
(under State 1) than across Outcomes 3 through 6 (under State 2), at all values of
participation likelihoods. The larger the variance in potential consumption, the
higher risk the associated country would face in its future consumption. Therefore,
countries would hesitate to participate more in State 2 than in State 1. Perceiving
this, Country 1 would prefer Country 2’s participation in 2035 to its participation in
2050, and thus I conclude that my second hypothesis holds.
[Note 3] Third, I test whether, at all values of participation likelihoods, Country 2 can
avoid its worst possible outcome by participating early in 2035. In Country 2’s point
of view (App.1: Figure 3-1B), Outcomes 2 and 4 entail the two lowest possible
consumption levels in the long term (2050), and therefore they are the two worst
outcomes for Country 2. In particular, the long-term consumption level of Country 2
is always lower in Outcome 4 than in Outcome 2, regardless of the levels of
participation likelihoods. Thus, my third hypothesis holds at different values of
participation likelihoods: it would be better for Country 2 to participate early than
late, given that Country 2 were to eventually participate in the climate policy.
85
3B. The effects of Country 1’s near-term (2015) consumption on the
future consumptions of all countries
Next, I will investigate how Country 1’s decision on its near-term (2015)
consumption would affect the future consumption choices of all three countries.
There are two decision-points following Country 1’s decision in 2015: countries will
choose their mid-term consumption levels in 2035 and then choose their long-term
consumption levels in 2050. I will analyze comparative statics of these mid-term
(2035) and long-term (2050) consumption choices with respect to Country 1’s actual
consumption choice in 2015 (i.e.,
̂
where
and
). Recall that,
though the optimal level of Country 1’s near-term consumption choice ( ̂ ) can be
determined with some parameters, Country 1 in practice might consume higher or
lower than the optimal level (i.e.,
̂ ).
(a1) Comparative statics of mid-term (2035) consumptions to
Country 1’s near-term (2015) consumption
[Note 1] Table 3-2 (App.1) shows that each comparative static of mid-term (2035)
consumption to Country 1’s near-term (2015) consumption cannot be positive. Since
the likelihood parameters (p and q) are greater than zero and less than one,
̂
a strictly negative sign in either state. In State 1,
is a multiple of
has a strictly negative sign as well. In State 2, we see that
̂
̂
̂
has
by 1.5, so it
since Country 2
does not participate in 2035; Country 2 would not consider Country 1’s past
consumption level in 2015 and make appropriate adjustment in its mid-term
consumption. Note that
̂
in either state, because Country 3 does not
participate in 2035. Thus, the countries participating in 2035 have strictly negative
comparative statics, while non-participating countries have zero comparative statics.
[Note 2] I also examine how the magnitudes of
̂
(App.1: Table 3-2) change with
respect to the likelihoods of participation. A simple numerical exercise on the
comparative statics (in the following page) suggests that the participating countries
in 2035 would show greater response in their mid-term consumption if the nonparticipating countries were to become less likely to participate in 2050.
86
- State 1: The value of
q
̂
̂
at each level of q
0
0.25
0.5
0.75
1
-0.490
-0.435
-0.367
-0.280
-0.166
̂
In State 1, the magnitudes of both
and
above table, we see that the magnitude of
Since
̂
is a constant multiple of
̂
̂
̂
are determined by q. From the
is smaller at a higher level of q.
, the magnitude of
̂
is also smaller at
a higher level of q. Given that Country 1 consumed more than optimal
amount in 2015, Countries 1 and 2 would expect that they need to reduce
their mid-term consumptions. At the same time, if they find out that Country
3 is quite much likely to participate in 2050, then Countries 1 and 2 would
not take too strong reduction in their mid-term consumption, since Country 3
would participate in 2050 and reduce its long-term consumption.
- State 2: The value of
̂
at given levels of p and q
̂
p=0
p=0.25
p=0.50
p=0.75
p=1
q=0
-0.490
-0.432
-0.358
-0.262
-0.133
q=0.25
-0.424
-0.368
-0.301
-0.217
-0.110
q=0.50
-0.338
-0.289
-0.232
-0.165
-0.085
In State 2, only the magnitude of
the magnitudes of
̂
that the magnitude of
and
̂
̂
̂
q=0.75
-0.222
-0.187
-0.148
-0.106
-0.059
q=1
-0.057
-0.050
-0.044
-0.037
-0.031
changes with respect to p and q, while
is fixed at zero. From the above table, we see
decreases with increasing p or q. In other words,
Country 1’s adjustment in its mid-term consumption in response to another
country’s participation likelihood would become smaller if the other country
were to show more inclination to participate in 2050.
87
(a2) Comparative statics of long-term (2050) consumptions to
Country 1’s near-term (2015) consumption
[Note 1] I also investigate the comparative statics of long-term (2050) consumptions
to Country 1’s near-term (2015) consumption (i.e.
̂
for
) (App.1: Table 3-
3). In the following numerical exercise, I prove that the participating countries in
2050 have strictly negative comparative statics. The countries that do not participate
in 2050 have zero comparative statics, because they would not consider Country 1’s
past consumption and adjust their consumptions accordingly.
- State 1: If Country 2 participates in 2035 (Outcome 1 and Outcome 2):
̂
(
(
)
(
)
̂
)
(
(
)
{
̂
)
(
(
̂
)
̂
̂
(
)}
)
̂
̂
[
̂
(
)
]
- State 2: If Country 2 does not participate in 2035 (Outcomes 3 through 6):
̂
(
(
)
(
)
)
{
(
(
) (
)
(
( )
( )
(
) (
)
)
( )
( )
) (
(
) (
̂
(
(
)
̂
Therefore, in either state,
̂
[
̂
)
)}
)
]
for
(
̂
only if Country i
does not participate in 2050).
[Note 2] The comparative static expressions of long-term consumptions (App.1:
Table 3-3) also indicate that countries can spread out the required amount of
reduction in future consumptions across Period 2 and Period 3. The participating
countries in 2050 have comparative statics that have
̂
or
̂
in their expressions.
Because these two latter comparative statics are non-positive (App.2: 3B-(a1)88
Note1), the magnitudes of
̂
̂
can get smaller if we have
̂
or
. Thus,
the participating countries in 2050 would undergo less severe adjustment, if Country
1 or Country 2 were to make appropriate adjustments in their mid-term (2035)
consumptions.
[Note 3] Another point suggested by these comparative static expressions (App.1:
Table 3-3) is that Country 2 and Country 3, if they were to participate in 2050, would
have comparative statics larger than the comparative static of Country 1; especially
in Outcomes 1 and 3 (in which all three countries participate), Country 3 has even
larger comparative static than that of Country 2 (i.e., |
̂
|
|
̂
|
|
̂
|). This
suggests that, if Countries 2 and 3 were to participate in 2050, then their potential
long-term consumptions would become quite vulnerable to Country 1’s
consumption choice made in 2015.
[Note 4] The simulation results (App.1: Figure 3-2; Table 3-4) also support my
inference that all countries would enjoy larger future consumptions if Country 1
were to consume less during Period 1. I simulate four different cases, in which
Country 1 consumes 50%, 80%, 100%, and 120% of its optimal consumption level in
2015 (i.e.,
̂ , where
in Case 1;
in Case 2;
in Case 3;
in Case 4). Recall that the optimal consumption level ( ̂ ) is the hypothetical
consumption level that the country should follow in order to maximize is discounted
net benefits. Other parameter values are the same as in the baseline simulation
̅
(
).
If the near-term consumption of Country 1 were to decrease from 120% to 50% of
the optimal level (moving from Case 4 to Case 1), the consumption trajectories of
Country 2 and Country 3 would nearly converge to their unconstrained optimal
levels (App.1: Figure 3-2: Countries 2 and 3).3 Based on this observation, I conclude
that Country 1's economizing on its near-term consumption would alleviate other
countries’ hesitation to participate: if Country 1 were to consume less in 2015, then
variance in future consumption of other countries would shrink, which means that
they would face a smaller risk in their future consumption.
To some extent, even Country 1 would benefit from economizing on its own nearterm consumption. Its mid-term (2035) and long-term (2050) potential
3
A country would choose its unconstrained optimal consumption level if it does not participate in the
climate policy (i.e. the country would myopically maximize its own immediate benefit without
considering the resource scarcity); for Country 2, its unconstrained optimal level is 25, and for
Country 3 it is 15.
89
consumptions would increase if Country 1 were to consume less in 2015 (App.1:
Figure 3-2: Country 1). If Country 1 were to take a drastic measure of consuming
only half of its optimal level in 2015 (App.1: Figure 3-2: Country 1: Case 1), its future
consumptions in 2035 and 2050 would nearly reach the unconstrained optimal level
(which is 30). While Country 1 may wish for large future consumption, the country
would also want to even out its consumption across three periods instead of
severely constraining its economy in any particular period. Therefore, the actual
consumption choice of Country 1 in 2015 would depend on Country 1’s two
opposing interests: one is to even out its consumptions across time, and the other is
to secure large future consumption.
(b) Hypothesis test
With these simulation results (App.1: Figure 3-2; Table 3-4), I also test the validity of
my initial hypotheses (App.1: Table 2-5). I show that the hypotheses hold valid in all
of the four cases investigated in the simulation. Note again that all parameter values
̅
are held the same as in the baseline simulation (
).
[Note 1] First, whether it were to consume more or less than its optimal level in
2015, Country 1 would still wish for unanimous participation. In all of the four cases,
Country 1 gets its first- and second-highest long-term (2050) consumptions in
Outcomes 1 and 3, respectively (App.1: Figure 3-2: Country 1). Therefore, Country 1
would prefer those “all participation” outcomes to other outcomes and, in order to
result in Outcome 1 or Outcome 3, would encourage all countries to participate by
2050 at the latest. This supports the validity of our first hypothesis.
[Note 2] Second, I show that my second hypothesis holds in all of the four cases: it
would be less difficult for Country 1 to encourage others’ participation in State 1
than in State 2. In each case, for Country 2 and Country 3, variance in their potential
long-term consumptions is smaller between Outcomes 1 and 2 (State 1) than across
Outcomes 3 through 6 (State 2) (App.1: Figure 3-2: Countries 2 and 3). In other
words, Countries 2 and 3 would face a smaller risk in their long-term consumptions
under State 1 than under State 2. On one hand, if Country 2 decides not to
participate in 2035, then Countries 2 and 3 would find their future consumptions
highly uncertain, so they would become hesitant to participate. On the other hand, if
Country 2 participates in 2035, there would be less uncertainty in future
consumption, since there would be only two possible outcomes in 2050. Then, it
would become more difficult to have unanimous participation in Stat 2 than in State
90
1. Therefore, my second hypothesis holds regardless of Country 1’s consumption
choice in 2015.
[Note 3] Third, in all of the four cases, it is still true that Country 2 can avoid its
worst possible outcome by participating in 2035 rather than in 2050. The two worst
outcomes for Country 2 are Outcomes 2 and 4, and long-term consumption of
Country 2 is strictly higher in Outcome 2 than in Outcome 4 in all of the four cases
(App.1: Figure 3-2: Country 2). Thus, Outcome 4 is the worse outcome for Country 2,
and Outcome 2 is the second-worst. However, the difference in long-term
consumption levels between the two outcomes is very small in Case 1, in which
Country 1 consumes very little in 2015 (App.1: Figure 3-2: Country 2: Case 1). This
suggests that Country 2’s early participation would become less necessary if Country
1 were to commit extreme economization on its near-term (2015) consumption.
3C. Uncertainty in the knowledge of resource capacity level
In the last section, I will explore the possibility that countries might update their
knowledge of resource capacity level (̅) in the middle of decision-making process. I
will suppose that all countries agree on what should be an “accurate” capacity level
before they jointly update their knowledge. If countries were to adjust their
knowledge to a new capacity level, they would also adjust their previous plan
concerning future consumption. Throughout the following analysis, I will examine
this influence of a new capacity level on future consumption choices of all countries.
First, I will analyze comparative statics of mid-term (2035) and long-term (2050)
consumptions of all countries (App.1: Tables 3-5, 3-6). Then, I will test my initial
hypotheses (App.1: Table 2-5) with by simulating four different cases of capacity
level adjustment (App.1: Figure 3-3; Table 3-7).
(a1) Comparative statics of mid-term (2035) consumptions to a new
capacity level
[Note 1] Table 3-5 (App.1) presents the comparative statics of mid-term
consumptions to a new capacity level. Since the likelihoods of participation (p and q)
are greater than zero and less than one, these comparative statics cannot have a
negative sign. The countries that are not participating in 2035 have zero
comparative statics, while the participating countries have strictly positive
comparative statics. This implies that the countries participating in 2035 would
91
consume less during Period 2 if they were to adopt a new capacity level that is lower
than the previous level.
[Note 2] While the signs those comparative statics (App.1: Table 3-5) can be
determined without ambiguity, their magnitudes depend on the future participation
likelihoods of the countries that do not participate in 2035; the countries
participating in 2035 would consider the possibility of sharing the burden of
adjusting future consumption with those countries that are not participating in 2035
but might participate in 2050. The following numerical exercise demonstrates that
the comparative statics of mid-term (2035) consumptions to a new capacity level
have magnitudes that are non-increasing with higher participation likelihoods.
̂
̅
- State 1:
at each level of q
q
0
0.25
0.50
0.75
1
̂
̅
0.196
0.174
0.147
0.112
0.066
Since
̂
̅
is a multiple of
̂
̅
by 1.5, the magnitudes of these two comparative
statics would change in the same direction if q changes. In the above table,
̂
̅
we see that the magnitude of
̂
).
̅
is smaller at a higher level of q (hence, so is
In other words: if Country 3 were not to participate in 2035 but were
more likely to participate in 2050, then Countries 1 and 2 would less
responsively adjust their mid-term consumptions in response to a new
capacity level.
- State 2:
̂
̅
̂
̅
p=0
p=0.25
p=0.50
p=0.75
p=1
at different levels of p and q
q=0
0.490
0.432
0.358
0.262
0.133
In State 2, the magnitude of
q=0.25
0.424
0.368
0.301
0.217
0.110
̂
̅
q=0.50
0.338
0.289
0.232
0.165
0.085
q=0.75
0.222
0.187
0.148
0.106
0.059
q=1
0.057
0.050
0.044
0.037
0.031
decreases either with increasing p or
increasing q; Country 1 would less readily adjust its mid-term (2035)
consumption as the currently non-participating countries (Countries 2 and 3)
were more likely to participate in 2050. In contrast, comparative statics of
92
̂
̅
Countries 2 and 3 are zero (i.e.,
̂
̅
), because those two non-
participating countries would not adjust their mid-term consumptions in
response to any new information.
(a2) Comparative statics of long-term (2050) consumptions to a new
capacity level
[Note 1] I also analyze comparative statics of long-term (2050) consumptions to a
new capacity level (App.1: Table 3-6). In the following numerical exercise, I prove
that all of these comparative statics have non-negative signs. Recall that the
likelihood parameters (p and q) are always greater than zero and less than one.
- State 1: Country 2 participates in 2035 (Outcome 1 and Outcome 2):
(
̂
̅
(
)
̂
̅
̂
̅
{
̂
̅
(
(
)
̂
̅
̂
̅
[
)
)
(
(
)}
̂
̅
)
̂
̅
̂
]
̅
The countries that are not participating in 2050 would have zero comparative
statics.
- State 2: Country 2 does not participate in 2035 (Outcomes 3 through 6):
̂
̅
(
(
)
)
{
(
(
(
) (
)
(
( )
( )
(
) (
)
)
( )
( )
(
)
) (
)}
̂
̅
)
̂
̅
) (
[
̂
]
̅
Again, the non-participating countries would have zero comparative statics.
[Note 2] In particular, I report that Countries 2 and 3 are potentially more sensitive
to a change in the capacity level than Country 1 is. If either Country 2 or Country 3
were to participate in 2050 (App.1: Table 3-6: Outcomes 1 through 5), then the
participating country would have a comparative static larger than that of Country 1.
Especially, if both Countries 2 and 3 were to participate (App.1: Table 3-6: Outcomes
1 and 3), then comparative static of Country 3 would be the largest and that of
93
Country 1 would be the smallest (i.e., |
̂
|
̅
|
̂
|
̅
|
̂
|).
̅
In other words, long-
term (2050) consumption of Country 3 is potentially most vulnerable to a new
capacity level, while that of Country 1 is the least vulnerable.
[Note 3] These comparative statics of long-term (2050) consumptions have
magnitudes determined by the comparative statics of mid-term (2035)
consumptions (App.1: Table 3-6). Note that the comparative statics of the
participating countries in 2050 (
previously saw that
̂
̅
and
specifically, we showed that
̂
̅
̂
̅
̂
)
̅
include
̂
̅
or
̂
̅
in their expressions. We
are non-negative (App.2: 3C-(a1)-Note1). More
is strictly positive in all outcomes, while
̂
̅
is
positive in Outcomes 1 and 2 (State 1) only. Thus, appropriate adjustments made in
2035 (i.e.,
̂
̅
and/or
̂
̅
) in response to a new capacity level would reduce
the magnitude of adjustment required in long-term consumption; in other words,
timely adjustment of the participating countries in 2035 would lessen the severity of
future adjustment that the participants in 2050 should carry out.
(b) Hypothesis Test
I test my initial hypotheses by simulating three cases in which countries may or may
not update the resource capacity level in 2035 and 2050 (App.1: Figure 3-3; Table 37). In the baseline case, countries have perfect information of the resource capacity
̅
̅
level in all periods (Case 1: ̅
, where ̅ is the agreed level of
resource capacity in Period t). In addition, two more cases are explored: countries
start with a rather optimistic estimation of the capacity level and correct their
̅
overestimation either in 2035 (Case 2: ̅
,̅
) or in 2050 (Case 3:
̅
̅
,̅
). I will refer to the former case as the “early adjustment”
case (Case 2) and the latter case as the “late adjustment” case (Case 3).
[Note 1] First, I confirm that Country 1 would wish for all countries to participate in
the global climate policy, whether the resource capacity level is updated or not. In all
three cases, long-term (2050) consumption of Country 1 is higher in Outcomes 1 and
3 than in other outcomes (App.1: Figure 3-3: Country 1). This supports the validity of
my first hypothesis.
[Note 2] Second, I examine whether Country 1 would prefer State 1 to State 2 in
every case. Although long-term consumption level of Country 1 tends to be higher in
Outcome 1 than in Outcome 3 (App.1: Figure 3-3: Country 1), the difference is very
small in the late adjustment case. In other words, Country 2’s early participation
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would not significantly improve Country 1’s long-term consumption unless the
participating countries in 2035 appropriately adjust their immediate consumptions
with respect to a newly updated capacity level. Nevertheless, in all cases, for each
country, variance in its potential long-term consumptions is larger in State 2 than in
State 1 (App.1: Figure 3-3: Countries 1, 2, 3). Then, Countries 2 and 3 would become
more hesitant to participate in State 2 than in State 1, whether they adjust the
resource capacity level early or late. Thus, I conclude that my second hypothesis
holds in nearly all cases, but weakly in the late adjustment case.
[Note 3] Lastly, I show that the validity of my third hypothesis is robust to a change
in the resource capacity level. In all of the three cases, the long-term consumption of
Country 2 is lowest in Outcome 4 and second-lowest in Outcome 2 (App.1: Figure 33: Country 2); while those two outcomes are the two worst outcomes for Country 2,
we see that Outcome 2 entails higher long-term consumption of Country 2 than
Outcome 4 does. However, this difference between the two outcomes is very small
in the late adjustment case. Therefore, I conclude that the third hypothesis holds
weakly in the late adjustment case. This reiterates the significance of timely
adjustment in response to new information.
95