Rice Model Research Articles

AD-DICE: An Implementation of Adaptation in the DICE Mode

Integrated Assessment Models (IAMS) have helped us over the past decade to understand the interactions between the environment and the economy in the context of climate change. Although it has also long been recognized that adaptation is a powerful and necessary tool to combat the adverse effects of climate change, most IAMs have not explicitly included the option of adaptation in combating climate change. This paper adds to the IAM and climate change literature by explicitly including adaptation in an IAM, thereby making the trade-offs between adaptation and mitigation visible. Specifically, a theoretical framework is created and used to implement adaptation as a decision variable into the DICE model. We use our new AD-DICE model to derive the adaptation cost functions implicit in the DICE model. In our set-up, adaptation and mitigation decisions are separable and AD-DICE can mimic DICE when adaptation is optimal. We find that our specification of the adaptation costs is robust with respect to the mitigation policy scenarios. Our numerical results show that adaptation is a powerful option to combat climate change, as it reduces most of the potential costs of climate change in earlier periods, while mitigation does so in later periods.

Optimal Technology R&D in the Face of Climate Uncertainty

This paper explores optimal near-term technology R&D in the face of uncertain damages caused by the buildup of greenhouse gases. The paper puts particular emphasis on understanding how optimal near-term R&D expenditures might vary based on the technologies pursued in the R&D program. The exploration is conducted in the context of varying impacts from R&D on the global abatement cost function. The R&D planning problem is considered first within a theoretical framework and is then pursued in a stylized application using the DICE model. The paper provides intuition into the circumstances under which near-term technology R&D might increase or decrease under uncertainty, thereby serving as a hedge against climate uncertainty.

Multiple equilibria in a stochastic implementation of DICE with abrupt climate change

Integrated assessment modeling of global climate change has focused primarily on gradually occurring changes in the climate system. However, atmospheric and earth scientists have become increasingly concerned that the climate system may be subject to abrupt, discontinuous changes on short time scales, and that anthropogenic greenhouse-gas emissions could trigger such shifts. Incorporating this type of climate dynamics into economic or integrated assessment models can result in model non-convexity and multiple equilibria, and thus complicate policy analysis relative to models with unique, globally optimal policies. Using a version of the Nordhaus DICE model amended in previous research by Keller et al. (2004) [Keller, Klaus, Benjamin M. Bolker, David F. Bradford, 2004. Uncertain climate thresholds and optimal economic growth. Journal of environmental economics and management 48 (1), 723–741], in conjunction with a stochastic global optimization algorithm, we generate “level sets” of solutions, which helps identify multiple equilibria resulting from the potential abrupt cessation of the North Atlantic Thermohaline Circulation. We discuss the implications of this model geometry for formulating greenhouse-gas abatement policy under uncertainty and suggest that this general approach may be useful for addressing a wide range of model non-convexities including those related to endogenous technological change.

The economics of inaction on climate change: a sensitivity analysis

Economic models of climate change often take the problem seriously, but paradoxically conclude that the optimal policy is to do almost nothing about it. We explore this paradox as seen in the widely used DICE model. Three aspects of that model, involving the discount rate, the assumed benefits of moderate warming, and the treatment of the latest climate science, are sufficient to explain the timidity of the model's optimal policy recommendation. With modifications to those three points, DICE shows that the optimal policy is a much higher and rapidly rising marginal carbon price; and that higher carbon price has a greater effect on physical measures of climate impacts. Our modifications exhibit nonlinear interactions; at least at low discount rates, there is synergy between individual changes to the model. At low discount rates, the inherent uncertainty about future damages looms larger in the analysis, rendering long-run economic modelling less useful. Our analysis highlights the sensitivity of the model to three debatable assumptions; it does not, and could not, lead to a more reliably ‘optimal’ cost of carbon. Cost-effectiveness analysis, focusing on the generally shorter-term cost side of the problem, reduces the economic paradoxes of the long run, and may make a greater contribution than economic optimization modelling.

The economics of inaction on climate change: a sensitivity analysis

Abstract Economic models of climate change often take the problem seriously, but paradoxically conclude that the optimal policy is to do almost nothing about it. We explore this paradox as seen in the widely used DICE model. Three aspects of that model, involving the discount rate, the assumed benefits of moderate warming, and the treatment of the latest climate science, are sufficient to explain the timidity of the model's optimal policy recommendation. With modifications to those three points, DICE shows that the optimal policy is a much higher and rapidly rising marginal carbon price; and that higher carbon price has a greater effect on physical measures of climate impacts. Our modifications exhibit nonlinear interactions; at least at low discount rates, there is synergy between individual changes to the model. At low discount rates, the inherent uncertainty about future damages looms larger in the analysis, rendering long-run economic modelling less useful. Our analysis highlights the sensitivity of the model to three debatable assumptions; it does not, and could not, lead to a more reliably ‘optimal’ cost of carbon. Cost-effectiveness analysis, focusing on the generally shorter-term cost side of the problem, reduces the economic paradoxes of the long run, and may make a greater contribution than economic optimization modelling.

A generalized framework for solving dynamic optimization problems using the artificial chemical process paradigm: Applications to particulate processes and discrete dynamic systems

The solution of optimal control problems (OCPs) becomes a challenging task when the analyzed system includes non-convex, non-differentiable, or equation-free models in the set of constraints. To solve OCPs under such conditions, a new procedure, LARES-PR, is proposed. The procedure is based on integrating the LARES algorithm with a generalized representation of the control function. LARES is a global stochastic optimization algorithm based on the artificial chemical process paradigm. The generalized representation of the control function consists of variable-length segments, which permits the use of a combination of different types of finite elements (linear, quadratic, etc.) and/or specialized functions. The functional form and corresponding parameters are determined element-wise by solving a combinatorial optimization problem. The element size is also determined as part of the solution of the optimization problem, using a novel two-step encoding strategy. These building blocks result in an algorithm that is flexible and robust in solving optimal control problems. Furthermore, implementation is very simple. The algorithm's performance is studied with a challenging set of benchmark problems. Then LARES-PR is utilized to solve optimal control problems of systems described by population balance equations, including crystallization, nano-particle formation by nucleation/coalescence mechanism, and competitive reactions in a disperse system modeled by the Monte Carlo method. The algorithm is also applied to solving the DICE model of global warming, a complex discrete-time model.

Cycle-transitive comparison of independent random variables

The discrete dice model, previously introduced by the present authors, essentially amounts to the pairwise comparison of a collection of independent discrete random variables that are uniformly distributed on finite integer multisets. This pairwise comparison results in a probabilistic relation that exhibits a particular type of transitivity, called dice-transitivity. In this paper, the discrete dice model is generalized with the purpose of pairwisely comparing independent discrete or continuous random variables with arbitrary probability distributions. It is shown that the probabilistic relation generated by a collection of arbitrary independent random variables is still dice-transitive. Interestingly, this probabilistic relation can be seen as a graded alternative to the concept of stochastic dominance. Furthermore, when the marginal distributions of the random variables belong to the same parametric family of distributions, the probabilistic relation exhibits interesting types of isostochastic transitivity, such as multiplicative transitivity. Finally, the probabilistic relation generated by a collection of independent normal random variables is proven to be moderately stochastic transitive.

EPR imaging to estimate the in vivo intracerebral reducing ability of mature rats after neonatal hypoxic–ischemic brain injury

A rat model of neonatal hypoxic-ischemic encephalopathy (Rice's model) was obtained by unilateral ligation of the common carotid artery of 7-day-old rats with hypoxia (exposure to 8% oxygen). To estimate the in vivo intracerebral reducing ability of the mature rats (8 weeks old) of Rice's model, temporal electron paramagnetic resonance (EPR) imaging of the brain of a rat receiving a blood-brain barrier-permeable nitroxide radical, 3-hydroxymethyl-2,2,5,5-tetramethylpyrrolidine-1-oxyl, was performed. In this imaging technique, the decay rate of the EPR signal intensity in a selected region of the brain is indicative of region-specific reducing ability. The effect of neonatal treatment of an antioxidant agent, 3-methyl-1-phenyl-2-pyrazolin-5-one (MCI-186), after a hypoxic-ischemic insult was also tested. It was found that the reducing ability had been depleted in the contralateral hemisphere of Rice's model rats; this depletion was suppressed by administering MCI-186.

ENTICE: endogenous technological change in the DICE model of global warming

Despite growing empirical evidence of the link between environmental policy and innovation, most economic models of environmental policy treat technology as exogenous. For long-term problems such as climate change, this omission may be significant. In this paper, I modify the DICE model of climate change (Managing the Global Commons: the Economics of the Greenhouse Effect, MIT press, Cambridge, MA, 1994; Warming the World: Economic Models of Global Warming, MIT press, Cambridge, MA, 2000) to allow for induced innovation in the energy sector. Ignoring induced technological change overstates the welfare costs of an optimal carbon tax policy by 9.4%. However, cost savings, rather than increased environmental benefits, appear to drive the welfare gains, as the effect of induced innovation on emissions and mean global temperature is small. Sensitivity analysis shows that potential crowding out of other R&D and market failures in the R&D sector are the most important limiting factors to the potential of induced innovation. Differences in these key assumptions explain much of the variation in the findings of other similar models.

On the cycle-transitivity of the dice model

We introduce the notion of a dice model as a framework for describing a class of probabilistic relations. We investigate the transitivity of the probabilistic relation generated by a dice model and prove that it is a special type of cycle-transitivity that is situated between moderate stochastic transitivity or product-transitivity on the one side, and Łukasiewicz-transitivity on the other side. Finally, it is shown that any probabilistic relation with rational elements on a three-dimensional space of alternatives which possesses this particular type of cycle-transitivity, can be represented by a dice model. The same does not hold in higher dimensions.

Integrated Assessment Modeling for Global Climate Change: An Infinite Horizon Optimization Viewpoint

In this paper one uses an infinite time horizon optimal control paradigm to deal with three important issues in global climate change integrated assessment, namely the equitable treatment of all the generations involved, the representation of technical progress, and the uncertainty concerning technological progress and climate change processes. The notion of economic sustainability is associated with the concept of turnpike in infinite horizon optimization models. The issue of deciding on the proper discount rate is addressed in this context and a method is proposed to reconcile long term sustainability and short term time preference for current generations. One also formulates a model where environmental damage and/or technical progress are represented as stochastic jump processes. One calls this random evolution a mode switching process. In this context, sustainability is represented by a family of turnpikes, and the economy will be driven from one steady state to the other as the modes switch. These concepts are illustrated on the DICE model and their possible implementation in other types of integrated assessment models is discussed.

Economic development and climate change in South East Asia: the SEADICE model and its forecasts for growth prospects and policy strategies

Increased environmental problems in the form of global warming have reshaped human thinking about the prospects of human survival on this planet. The 1996 IPCC study has confirmed that increased GHG concentrations in the atmosphere will substantially increase global temperatures. South East Asia's (SEA) particular vulnerabilities to the impacts of climate change need to be explored. The primary production levels, tourism industry, agricultural productivity, energy sector and urban water supply systems are sensitive to potential climate changes. To address these issues and options, the study undertakes an integrated climate change and economic growth modelling study with a comprehensive coverage of the SEA region. The model is based on the work done by Nordhaus (the DICE model) and Islam (the Asia-DICE model), and named the South East Asia Dynamic Integrated Climate and the Economy (SEADICE) model. The results address issues related to global environmental change and sustainable development for SEA. The results suggest the following: 1) GHG abatement costs are justifiable for the region; 2) optimal abatement control rates are significantly higher compared to other models; and 3) this suggests that regional or country specific abatement policies should be implemented in the region.

Bandgap renormalization of ZnO epitaxial thin films

Optical gain spectra in ZnO thin films were observed by pump-probe method. The carrier density in this experiment was estimated to be n=2.7×10 19 cm −3 and bandgap energy shift was estimated to be 350 meV from the optical gain spectra. Renormalized bandgap energy was calculated using two theoretical models and was compared with the experimental results. It was found that Beni and Rice's model explains the experimental data.

BANDGAP RENORMALIZATION DUE TO HIGH-DENSITY CARRIERS IN ZnO EPITAXIAL THIN FILMS

Renormalized bandgap energy due to high-density carriers in ZnO is calculated and compared with our experimental results. Two different reported treatments for the correlation energy are employed for the calculation, and we prove that Beni and Rice's model sufficiently explains the experimental data. Furthermore, we calculate optical gain spectrum, which reproduces well the experimental data.

Analysis of Crack Growth Kinetics and Crack Tip Strain Rates of Sensitized Type 304 Stainless Steel in Simulated Boiling Water Reactor Environment : Experiments and Theory(EAC2)

Three slow strain rate tests (SSRT) on one-inch thick-compact tension (1T-CT) specimens, which were fabricated from sensitized 304L stainless steel, were performed with different extension rates in a simulated boiling water reactor (BWR) environment, to derive the environmentally assisted cracking (EAC) growth kinetics. The crack growth kinetics, depending on the testing conditions, were also described theoretically by Shoji's model. Inverse analysis was performed by fitting the experimental data to the theoretical data, to determine the model parameters r_0, which represents a characteristic distance to define crack tip strain rate (CTSR), and m, which is a slope of the current decay curve and a function of crack tip water chemistry. Both r_0 and m can be determined using experimental crack growth data in the analysis. Theoretical CTSR of sensitized 304 stainless steel during constant load line displacement rate tests was calculated using Shoji's model and experimental data of P. Aaltonen et al. The calculation shows that dependences of experimental crack growth rate (CGR) on theoretical CTSR for tests under different loading conditions are quite consistent. The theoretical CTSR was also compared to that evaluated using Rice's model under the same experimental conditions. Differences between the two theoretical CTSRs were found and the causes are discussed.

Climate change policy: quantifying uncertainties for damages and optimal carbon taxes

Controversy surrounds climate change policy analyses because of uncertainties in climatic effects, impacts, mitigation costs and their distributions. Here we address uncertainties in impacts, and provide a method for quantitative estimation of the policy implications of such uncertainties. To calculate an “optimal” control rate or carbon tax a climate-economy model can be used on estimates of climate damages resulting from warming scenarios and several other key assumptions. The dynamic integrated climate-economy (DICE) model, in its original specification, suggested that an efficient policy for slowing global warming would incorporate only a relatively modest amount of abatement of greenhouse gas emissions, via the mechanism of a small (about $5 per ton initially) carbon tax. Here, the DICE model is reformulated to reflect several alternate published estimates and opinions of the possible damages from climatic change. Our analyses show that incorporating most of these alternate damage estimates into DICE results in a significantly more aggressive optimal policy than that suggested by the original model using a single damage function. In addition, statistical distributions of these damage estimates are constructed and used in a probabilistic analysis of optimal carbon tax rates, resulting in mostly much larger (but occasionally smaller) carbon taxes than those of DICE using point values of damage estimates. In view of the large uncertainties in estimates of climate damages, a probabilistic formulation that links many of the structural and data uncertainties and thus acknowledges the wide range of “optimal” policies is essential to policy analysis, since point values or “best guesses” deny policy makers the opportunity to consider low probability, but policy-relevant, outliers. Our presentation is offered as a prototypical example of a method to represent such uncertainties explicitly in an integrated assessment.

Are optimal emissions really optimal - four critical issues for economists in the greenhouse

Although the greenhouse effect is by many considered as one of the most serious environmental problems, several economic studies of the greenhouse effect, most notably Nordhaus's DICE model, suggest that it is optimal to allow the emissions of greenhouse gases (GHG) to increase by a factor of three over the next century. Other studies have found that substantial reductions can be justified on economic grounds. This paper explores into the reasons for these differences and identifies four (partly overlapping) crucial issues that have to be dealt with when analysing the economics of the greenhouse effect: low-probability but catastrophic events; cost evaluation methods; the choice of discount rate; the choice of decision criterion. The paper shows that (i) these aspects are crucial for the policy conclusions drawn from models of the economics of climate change, and that (ii) ethical choices have to be made for each of these issues. This fact needs wider recognition since economics is very often perceived as a value neutral tool that can be used to provide policy makers with “optimal” policies.

How to Decide When Experts Disagree: Uncertainty-Based Choice Rules in Environmental Policy

Environmental economists have traditionally addressed the issue of choice under uncertainty by applying the expected utility hypothesis. When policymakers face a panel of experts with widely divergent beliefs, the problem may more accurately be described as a case of choice under pure uncertainty. Arrow and Hurwicz (1972) demonstrate that rational choice criteria under pure uncertainty will focus on the extremes of the state space, not the midpoint as is typically assumed. Using Nordhaus's DICE model, uncertainty-based choices about global warming policies are evaluated. Linkages to the safe minimum standard and the precautionary principle are also discussed.

Optimal reductions in CO 2 emissions

Current optimizing climate-economy models use CO 2 uptake functions that greatly underestimate both peak atmospheric CO 2 concentrations and the time horizon of elevated CO 2. As a result these models underestiamte potential global warming damages. Here, a more realistic, but practical, carbon cycle parameterization is developed that can be incorporated within an optimizing climate-economy model framework. This method is utilized in conjunction with the DICE model (Nordhaus, 1994) to estimate optimal reductions in CO 2 emissions. The results are shown to be extremely sensitive to the pure rate of time preference, ϱ. For ϱ=3% (Nordhaus' preferred value), our model predicts an optimal CO 2 emission reduction of 13% by the year 2045, as compared to 11% in the original DICE model. But, for ϱ=0% the optimal emissions reduction rises to 79% in the year 2045 and to 97% by the year 2200. We argue that energy policy should be guided by the ϱ=0% results for both economic and ethical reasons. A steady-state analysis performed using the DICE model supports the argument that large fractional reductions in CO 2 emissions should be undertaken.

ASSESSING THE DICE MODEL: UNCERTAINTY ASSOCIATED WITH THE EMISSION AND RETENTION OF GREENHOUSE GASES

Analysis of the DICE model indicates that it contains unsupported assumptions, simple extrapolations, and misspecifications that cause it to understate the rate at which economic activity emits greenhouse gases and the rate at which the atmosphere retains greenhouse gases. The model assumes a world population that is 2 billion people lower than the ’base case' projected by demographers. The model extrapolates a decline in the quantity of greenhouse gases emitted per unit of economic activity that is possible only if there is a structural break in the economic and engineering factors that have determined this ratio over the last century. The model uses a single equation to simulate the rate at which greenhouse gases accumulate in the atmosphere. The forecast for the airborne fraction generated by this equation contradicts forecasts generated by models that represent the physical and chemical processes which determine the movement of carbon from the atmosphere to the ocean. When these unsupported assumptions, simple extrapolations, and misspecifications are remedied with simple fixes, the economic impact of global climate change increases several fold. Similarly, these remedies increase the impact of uncertainty on estimates for the economic impact of global climate change. Together, these results indicate that considerable scientific and economic research is needed before the threat of climate change can be dismissed with any degree of certainty.