Robust Simulation of Global Warming Policies Using the DICE Model

Abstract

I ntegrated assessment models that combine geophysics and economics features are often used to evaluate and compare global warming policies. Because there are typically profound uncertainties in these models, a simulation approach is often used. This approach requires the distribution of the uncertain parameters clearly specified. However, this is typically impossible because there is often a significant amount of ambiguity (e.g., estimation error) in specifying the distribution. In this paper, we adopt the widely used multivariate normal distribution to model the uncertain parameters. However, we assume that the mean vector and covariance matrix of the distribution are within some ambiguity sets. We then show how to find the worst-case performance of a given policy for all distributions constrained by the ambiguity sets. This worst-case performance provides a robust evaluation of the policy. We test our algorithm on a famous integrated model of climate change, known as the Dynamic Integrated Model of Climate and the Economy (DICE model). We find that the DICE model is sensitive to the means and covariance of the parameters. Furthermore, we find that, based on the DICE model, moderately tight environmental policies robustly outperform the no controls policy and the famous aggressive policies proposed by Stern and Gore.

From Integrated to Integrative: Delivering on the Paris Agreement

“…Similarly, the authors of [44] also used outputs from the DICE2007 and MiniCAM (former version of the GCAM) models, and combined economics and decision analysis to implement probabilistic data on energy R&D policy, in response to global climate change and associated risks. Acknowledging the difficulties in estimating the variance and correlations of uncertain parameters used in IAM simulations, Hu et al [45] employed a multivariate normal distribution-based stochastic optimisation model to produce robust policy strategies with the DICE model. Outside the limited scope of deterministic frameworks and scenarios, such methods can, when coupled with modelling activities, provide information about the degree of certainty for selecting specific courses of climate action and eventually reinforce the robustness of policy prescriptions.…”

Robust dual-response optimization

“…Robust approaches are discussed-albeit briefly-not only in discrete-event simulation but also in deterministic simulation if that simulation has uncertain environmental variables. A recent example is Hu et al (2012), who propose a robust climate sim- …”

On how to solve large-scale log-determinant optimization problems

“…It can be regarded as an extension of the qudratic semidefinite programming problem (QSDP) and the log-determinant (Logdet) problem, so it shares the structures of both problems, and it goes without saying that the QP-Logdet problem is considerable. For the QSDP, it is certainly a heart problem in nonlinear semidefinite programming problems, which has been considered by Toh [35], Toh, Tütüncü and Todd [36,37], Zhao [45], Jiang, Sun and Toh [14], etc.. For the Logdet problem, which has a very important application in covariance selection [5] and has been intensively studied over the past several years, including the work of Dahl, Vandenberghe and Roychowdhury [4], d'Aspremont, Banerjee and El Ghaoui [6], Li and Toh [15], Lu [16,17], Lu and Zhang [18], Olsen, Oztoprak, Nocedal and Rennie [24], Scheinberg, Ma and Goldfarb [30], Scheinberg and Rish [31], Toh [34], Wang, Sun and Toh [40], Yang, Sun and Toh [41], Yang, Shen, Wonka, Lu and Ye [43], Yuan [44], etc.. As far as the QP-Logdet problem be concerned, it also arises in many practical applications such as robust simulation of global warming policies [13], speech recognition [39], and so on. Thus the algorithms developed to solve this kind of problems can potentially find wide applications.…”