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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 2 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. 3 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 5 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. 6 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). 7 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 8 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. 9 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. 10 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 11 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). 12 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 13 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). 14 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. 19 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, 20 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. 21 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. 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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 94 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