Rice Model Research Articles

Microscopic and probabilistic approach to thermal steady state based on a dice and coin toy model

In this article we present an educational approach to thermal equilibrium which was tested on a group of 13 undergraduate students at the University of Trento. The approach is based on a stochastic toy model, in which bodies in thermal contact are represented by rows of squares on a cardboard table, which exchange coins placed on the squares based on the roll of two dice. The discussion of several physical principles, such as the exponential approach to equilibrium, the determination of the equilibrium temperature, and the interpretation of the equilibrium state as the most probable macrostate, proceeds through a continual comparison between the outcomes obtained with the toy model and the results of a real experiment on the thermal contact of two masses of water at different temperatures. At the end of the sequence, a re-analysis of the experimental results in view of both the Boltzmann and Clausius definitions of entropy reveals some limits of the toy model, but also allows for a critical discussion of the concepts of temperature and entropy. In order to provide the reader with a feeling of how the sequence was received by students, and how it helped them understand the topics introduced, we discuss some excerpts from their answers to a conceptual item given at the end of the sequence.

EMPIRICALLY CONSTRAINED CLIMATE SENSITIVITY AND THE SOCIAL COST OF CARBON

Integrated Assessment Models (IAMs) require parameterization of both economic and climatic processes. The latter includes Equilibrium Climate Sensitivity (ECS), or the temperature response to doubling CO2 levels, and Ocean Heat Uptake (OHU) efficiency. ECS distributions in IAMs have been drawn from climate model runs that lack an empirical basis, and in Monte Carlo experiments may not be constrained to consistent OHU values. Empirical ECS estimates are now available, but have not yet been applied in IAMs. We incorporate a new estimate of the ECS distribution conditioned on observed OHU efficiency into two widely used IAMs. The resulting Social Cost of Carbon (SCC) estimates are much lower than those from models based on simulated ECS parameters. In the DICE model, the average SCC falls by approximately 40–50% depending on the discount rate, while in the FUND model the average SCC falls by over 80%. The span of estimates across discount rates also shrinks substantially.

Evolution of Modeling of the Economics of Global Warming: Changes in the Dice Model, 1992-2017

Many areas of the natural and social sciences involve complex systems that link together multiple sectors. Integrated assessment models (IAMs) are approaches that integrate knowledge from two or more domains into a single framework, and these are particularly important for climate change. One of the earliest IAMs for climate change was the DICE/RICE family of models, first published in Nordhaus (1992), with the latest version in Nordhaus (2017, 2017a). A difficulty in assessing IAMs is the inability to use standard statistical tests because of the lack of a probabilistic structure. In the absence of statistical tests, the present study examines the extent of revisions of the DICE model over its quarter-century history. The study finds that the major revisions have come primarily from the economic aspects of the model, whereas the environmental changes have been much smaller. Particularly sharp revisions have occurred for global output, damages, and the social cost of carbon. These results indicate that the economic projections are the least precise parts of IAMs and deserve much greater study than has been the case up to now, especially careful studies of long-run economic growth (to 2100 and beyond).

Revisiting the social cost of carbon

The social cost of carbon (SCC) is a central concept for understanding and implementing climate change policies. This term represents the economic cost caused by an additional ton of carbon dioxide emissions or its equivalent. The present study presents updated estimates based on a revised DICE model (Dynamic Integrated model of Climate and the Economy). The study estimates that the SCC is $31 per ton of CO2 in 2010 US$ for the current period (2015). For the central case, the real SCC grows at 3% per year over the period to 2050. The paper also compares the estimates with those from other sources.

Green Bonds, Transition to a Low-Carbon Economy, and Intergenerational Fairness: Evidence from an Extended DICE Model

Perceived intergenerational unfairness is one of the obstacles for a rapid transition to a low carbon economy whereby current generations have to carry the burden of paying for mitigation, while the next generations will enjoy the benefits for free. Green bonds are believed to be able to distribute the burdens over generations more evenly. In this paper, we examine whether green bonds can indeed resolve the intergenerational inequity challenge. To do so, we employ the DICE model and supplement it with bonds and green tax through which future generations repay the debt. We show that bonds can reduce but cannot completely eliminate the intergenerational inequities. Lower interest rates shorten the initial time period when the society is worse off if a mitigation policy is implemented. Additional compensation mechanisms ensuring that the current generation retains the consumption level equal to the one without mitigation are needed to achieve a Pareto improvement of the mitigation scenario for all generations.

Projections and Uncertainties About Climate Change in an Era of Minimal Climate Policies

Climate change remains one of the major international environmental challenges facing nations. Yet nations have to date taken minimal policies to slow climate change. Moreover, there has been no major improvement in emissions trends as of the latest data. The current study uses the updated DICE model to present new projections and the impacts of alternative climate policies. It also presents a new set of estimates of the uncertainties about future climate change and compares the results will those of other integrated assessment models. The study confirms past estimates of likely rapid climate change over the next century if there are not major climate-change policies. It suggests that it will be extremely difficult to achieve the 2°C target of international agreements even if ambitious policies are introduced in the near term. The required carbon price needed to achieve current targets has risen over time as policies have been delayed.

Global warming projections using the human–earth system model BNU-HESM1.0

Future climate change is usually projected by coupled earth system models under specific emission scenarios designed by integrated assessment models (IAMs), and this offline approach means there is no interaction between the coupled earth system models and the IAMs. This paper introduces a new method to design possible future emission scenarios and corresponding climate change, in which a simple economic and climate damage component is added to the coupled earth system model of Beijing Normal University (BNU-ESM). With the growth of population and technological expertise and the declining emission-to-output ratio described in the Dynamic Integrated Climate-Economy model, the projected carbon emission is 13.7Gt C, resulting in a 2.4 °C warming by the end of the twenty-first century (2080–2099) compared with 1980–1999. This paper also suggests the importance of the land and ocean carbon cycle in determining the CO2 concentration in the atmosphere. It is hoped that in the near future the next generation of coupled earth system models that include both the natural system and the social dimension will be developed.

Projections and Uncertainties about Climate Change in an Era of Minimal Climate Policies

Climate change remains one of the major international environmental challenges facing nations. Up to now, nations have adopted minimal policies to slow climate change. Moreover, there has been no major improvement in emissions trends as of the latest data. The current study uses the updated DICE model to develop new projections of trends and impacts of alternative climate policies. It also presents a new set of estimates of the uncertainties about future climate change and compares the results with those of other integrated assessment models. The study confirms past estimates of likely rapid climate change over the next century if major climate-change policies are not taken. It suggests that it is unlikely that nations can achieve the 2°C target of international agreements, even if ambitious policies are introduced in the near term. The required carbon price needed to achieve current targets has risen over time as policies have been delayed. (JEL Q54, Q58)

A Recursive Method for Solving a Climate–Economy Model: Value Function Iterations with Logarithmic Approximations

A recursive method for solving an integrated assessment model of climate and the economy is developed in this paper. The method approximates a value function with a logarithmic basis function and searches for solutions on a set satisfying optimality conditions. These features make the method suitable for a nonlinear model with many state variables and various constraints. The method produces exact solutions to a simple economic growth model and is useful for solving more demanding models such as the well-known DICE model (dynamic integrated model of climate and the economy).

Detection of Allelic Frequency Differences between the Sexes in Humans: A Signature of Sexually Antagonistic Selection.

Sexually antagonistic (SA) selection, a form of selection that can occur when both sexes have different fitness optima for a trait, is a major force shaping the evolution of organisms. A seminal model developed by Rice (Rice WR. 1984. Sex chromosomes and the evolution of sexual dimorphism. Evolution 38:735–742.) predicts that the X chromosome should be a hotspot for the accumulation of loci under SA selection as compared with the autosomes. Here, we propose a methodological framework designed to detect a specific signature of SA selection on viability, differences in allelic frequencies between the sexes. Applying this method on genome-wide single nucleotide polymorphism (SNP) data in human populations where no sex-specific population stratification could be detected, we show that there are overall significantly more SNPs exhibiting differences in allelic frequencies between the sexes on the X chromosome as compared with autosomes, supporting the predictions of Rice’s model. This pattern is consistent across populations and is robust to correction for potential biases such as differences in linkage disequilibrium, sample size, and genotyping errors between chromosomes. Although SA selection is not the only factor resulting in allelic frequency differences between the sexes, we further show that at least part of the identified X-linked loci is caused by such a sex-specific processes.

Empirically-Constrained Climate Sensitivity and the Social Cost of Carbon

Integrated Assessment Models (IAMs) require parameterization of both economic and climatic processes. The latter include Ocean Heat Uptake (OHU) efficiency, which represents the rate of heat exchange between the atmosphere and the deep ocean, and Equilibrium Climate Sensitivity (ECS), or the surface temperature response to doubling of CO2 levels after adjustment of the deep ocean. Due to a lack of adequate data, OHU and ECS parameter distributions in IAMs have been based on simulations from climate models. In recent years, new and sufficiently long observational data sets have emerged to support a growing body of empirical ECS estimates, but the results have not been applied in IAMs. We incorporate a recent observational estimate of the ECS distribution conditioned on observed OHU efficiency into two widely-used IAMs. The resulting Social Cost of Carbon (SCC) estimates are much smaller than those from models based on simulated parameters. In the DICE model the average SCC falls by 30-50% depending on the discount rate, while in the FUND model the average SCC falls by over 80%. The span of estimates across discount rates also shrinks considerably, implying less sensitivity to this parameter choice.

Global Warming and a Potential Tipping Point in the Atlantic Thermohaline Circulation: The Role of Risk Aversion

The risk of catastrophes is one of the greatest threats of climate change. Yet, conventional assumptions shared by many integrated assessment models such as DICE lead to the counterintuitive result that higher concern about climate change risks does not lead to stronger near-term abatement efforts. This paper examines whether this result still holds in a refined DICE model that employs the Epstein–Zin utility specification and that is fully coupled with a dynamic tipping point model describing the evolution of the Atlantic thermohaline circulation (THC). Risk is captured by the possibility of a future collapse of the circulation and it is nourished by fat-tailed uncertainty about climate sensitivity. This uncertainty is assumed to resolve in the middle of the second half of this century and the near-term abatement efforts, which are undertaken before that point of time, can be adjusted afterwards. These modelling choices allow posing the question of whether aversion to this specific tipping point risk has a significant effect on near-term policy efforts. The simulations, however, provide evidence that it has little effect. For the more likely climate sensitivity values, a collapse of the circulation would occur in the more distant future. In this case, acting after learning can prevent the catastrophe, implying the remarkable insensitivity of the near-term policy to risk aversion. For the rather unlikely and high climate sensitivity values, the expected damage costs are not great enough to justify taking very costly measures to safeguard the THC. Our simulations also provide some indication that risk aversion might have some effect on near-term policy, if inertia limiting the speed of decarbonisation is accounted for. As it is highly uncertain how restrictive this kind of inertia will be, future research might investigate the effects of risk aversion if additional uncertainty about inertia is considered.

Engaging Students with the DICE Model: Design Thinking, Innovation, Creativity, and Entrepreneurship

DICE: Design, Innovation, Creativity, and Entrepreneurship is a new interdisciplinary Provost-level university course that is collaboratively developed by faculty from three colleges (COS, VSE, and CEHD) with a goal to engage students at Mason. Creativity and innovation require free thinking and a combination of top-down support and grass-roots innovation propelled by passion to make a deep impact. The focus of this course is on creating the next generation STEAM (Science, Technology, Engineering, Arts, and Mathematics) scholars with (1) social/human focus, (2) interdisciplinary interest, and (3) entrepreneurial streak, who are empowered to break down disciplinary boundaries for solutions of deep impact on pressing human needs. Furthermore, the next generation STEAM students need to use "design thinking" to harness the state-of-the-art capabilities to innovate and multidisciplinary STEAM or similar approaches to solve real-world challenges which is a focus of this course. Student engagement in 21st century skills including communication, collaboration, creativity, and critical thinking is an integral part of the course. In this session, we will share the implementation of this course that helped engage a group of students from Mason working with students from POSTECH University in South Korea to collaboratively work on global problem solving using DICE. We will explain how the DICE model can be modified and used in other settings/courses.

Natural capital in integrated assessment models of climate change

In integrated assessment models (IAMs) economic activity leads to global warming, which causes future economic costs. However, typical IAMs do not explicitly represent the role of natural capital. In this paper, the DICE model by Nordhaus (2008) is expanded with a natural capital variable that is affected both by climate change and by depletive effects of economic activity. Due to a synergy between the two effects, the optimal policy of the expanded model features more and earlier abatement of CO2 emissions than DICE. Interestingly, the policy implications are different from what follows if one tries to capture the depletive effects on natural capital by simply reducing factor productivity growth in DICE. Acknowledging considerable uncertainty, simulations show that climate- and savings rate policies from the expanded model are more robust in the long term than policies that do not consider non-climatic depletion effects on natural capital.

Convexity Analysis of the Dynamic Integrated Model of Climate and the Economy (DICE)

We study the convexity properties of Dynamic Integrated Model of Climate and the Economy (DICE), which is a nonlinear optimization problem. Through some optima-preserving transformations and convex function analysis, we conclude that the DICE model is a hidden convex optimization problem when using the standard parameter values. This result implies that the solutions obtained from the model under these settings are globally optimal and are accurately reflective of the complex economic relationships modeled. We also provide sufficient conditions on the parameter space that assure this property.

Analyzing Climate Uncertainty and Risk with an Integrated Assessment Model

Uncertainty over the consequences of unprecedented global warming is central to environmental insecurity. Global warming threatens to exacerbate all other ecological stresses and menaces human populations and economies. Despite scientific efforts, great uncertainties still pervade crucial aspects of the climate change process and its consequences. Yet integrated assessment models widely used to analyze climate policy options, such as the Nordhaus DICE model, establish that model outputs are highly sensitive to plausible alternative parameter values. This paper further explores uncertainties by substituting probability distributions for pre-determined values of key parameters in the DICE model. It then draws randomly from these probability distributions to implement a Monte Carlo analysis of policy outcomes, generating hundreds of policy simulations. An important finding is that the sacrifice in world consumption entailed in keeping the rise in global temperatures below two degrees centigrade would likely be negligible if emitting countries cooperate in adopting efficient mitigation policies. In other words, the cost of insurance against dangerous climate change is close to zero. Thus, the result of this analysis suggests that science and economics agree on keeping climate change below a level threatening serious damage.

Impact of Nonlinearity of Climate Damage Functions on Long-term Macroeconomic Projections under Conditions of Global Warming

A weakly nonlinear climate damage function used by Nordhaus in his DICE model and a strongly nonlinear climate damage function recently proposed by Weitzman are incorporated in the Kellie-Smith—Cox Integrated Assessment model of coupled climate—conomic dynamics, the initial version of which contained only linear climate damages. Long-term projections of the dynamics of coupled climate—economic system are computed with the modified versions of the model. Simulation results for Weitzman function demonstrate pronounced nonlinear emergent dynamics and suggest extremely dramatic long-term economic scenarios for high values of background economic growth rates.

Increase in carbon prices: analysis of energy-economy modeling

This study examines the mechanisms of social cost of carbon (SCC) and marginal abatement cost (MAC) in climate change modeling. To examine these mechanisms, we observed the shifts in the marginal benefit (MB) and marginal cost (MC) curves of carbon dioxide (CO2) abatement when parameter values are changed. In the observation, we used the DICE model proposed by Nordhaus (A question of balance: weighing the options on global warming policies. Yale University Press, New Haven, 2008) changing 24 parameters for the observation. In consequent, firstly, we have found that discount rate is not only one of the parameters which significantly raise the carbon price, that is, other parameters may have significant impact too. Secondly, we have found that there are two patterns in the rise of the SCC, and three patterns in the rise of the MAC. Thirdly, we have found that the difference between the rise of the SCC and MAC is primarily caused by the horizontal MB curve in CO2 emissions reduction; an upward shift of MC curve raises MAC but never raises the SCC. Thus, the choice of the SCC or MAC may make the change of carbon price different, affecting global warming policy.

Towards a more inclusive and precautionary indicator of global sustainability

We construct a hybrid, economic indicator of the sustainability of global well-being, which is more inclusive than existing indicators and incorporates an environmentally pessimistic, physical constraint on global warming. Our methodology extends the World Bank's Adjusted Net Saving (ANS) indicator to include the cost of population growth, the benefit of technical progress, and a much higher, precautionary cost of current CO2 emissions. Future warming damage is so highly unknowable that valuing emissions directly is rather arbitrary, so we use a novel, inductive approach: we modify damage and climate parameters in the deterministic DICE climate-economy model so it becomes economically optimal to control emissions in a way likely to limit warming to an agreed target, here 2°C. If future emissions are optimally controlled, our ANS then suggests that current global well-being is sustainable. But if emissions remain uncontrolled, our base-case ANS is negative now and our corresponding, modified DICE model has an unsustained development path, with well-being peaking in 2065. Current ANS on an uncontrolled path may thus be a useful heuristic indicator of future unsustainability. Our inductive method might allow ANS to include other very hard-to-value, environmental threats to global sustainability, like biodiversity loss and nitrogen pollution.

A 4-Stated DICE: Quantitatively Addressing Uncertainty Effects in Climate Change

We introduce a version of the DICE-2007 model designed for uncertainty analysis. DICE is a wide-spread deterministic integrated assessment model of climate change. Climate change, long-term economic development, and their interactions are highly uncertain. The quantitative analysis of optimal mitigation policy under uncertainty requires a recursive dynamic programming implementation of integrated assessment models. Such implementations are subject to the curse of dimensionality. Every increase in the dimension of the state space is paid for by a combination of (exponentially) increasing processor time, lower quality of the value or policy function approximations, and reductions of the uncertainty domain. The paper promotes a state-reduced, recursive dynamic programming implementation of the DICE-2007 model. We achieve the reduction by simplifying the carbon cycle and the temperature delay equations. We compare our model’s performance and that of the DICE model to the scientific AOGCM models emulated by MAGICC 6.0 and find that our simplified model performs equally well as the original DICE model. Our implementation solves the infinite planning horizon problem in an arbitrary time step. The paper is the first to carefully analyze the quality of the value function approximation using two different types of basis functions and systematically varying the dimension of the basis. We present the closed form, continuous time approximation to the exogenous (discretely and inductively defined) processes in DICE, and we present a numerically more efficient re-normalized Bellman equation that, in addition, can disentangle risk attitude from the propensity to smooth consumption over time.