Center for Robust Decision Making on Climate and Energy Policy

Dynamic Stochastic Integrated model of Climate and Economy (DSICE)

Ken Judd, Yongyang Cai, Thomas Lontzek


  • Ken Judd
  • Yongyang Cai
  • Thomas Lontzek

Cai, Judd, and Lontzek (CJL) used DICE as an initial testing ground for ideas on how to construct stochastic versions of an integrated assessment model.  CJL also substantially improved the computational framework of DICE, replacing the ad hoc discrete-time formulation with a continuous-time model of both climate and economics, and using mathematically valid and efficient methods for solving the resulting system of differential equations. 

Development of DICE-CJL and DSICE

In [13], we construct the continuous time representation of DICE, which we call DICE-CJL, and present mathematical and computational methods for this continuous-time deterministic model. This model, which includes a perfect foresight, forward-looking economic model, is solved using alternative finite difference methods. All verification strategies, such as Richardson extrapolation, indicate that we solve the continuous- time DICE problem with reliable high accuracy. In [14], we introduce a dynamic stochastic integrated model of climate and economy (DSICE), and then use a numerical dynamic programming algorithm which incorporates the ideas and algorithms in [16, 12, 38, 8] to compute its solution with annual time periods over 600 years horizon and stochastic shocks to the economic and climate system. Judd (co-PI) and Cai (postdoc), along with Dr. Thomas Lontzek (postdoc, University of Zurich) have developed DSICE, a dynamic stochastic generalization of the simple and commonly-used policy analysis tool DICE, and are comparing its results to those of the 2007 version of DICE. The results illustrate the limitations of existing policy analysis tools and will help guide our future software development, leading toward implementing dynamic stochastic capabilities in the CIM-EARTH framework. DSICE additions include (1) shocks to economic productivity, as modeled in the dynamic stochastic economics literature, and (2) climate shocks, such as tipping points, with a probability affected by temperature. Multiple shocks, either independent or correlated, are permitted. The model is coded in DPSOL, dynamic programming software developed by Cai and Judd. Judd and Cai (with Lontzek) have improved the computational efficiency of the dynamic programming method by replacing tensor grid methods for approximating the six-dimensional value function with sparse grid methods. In [33], we use the DSICE model to account for abrupt and irreversible climate change, a climate shock in the form of a stochastic tipping point. We investigate the impact of the tipping point externality on optimal mitigation policy. We find that the optimal additional carbon tax in anticipation of a low probability low impact tipping point exhibits a flat profile.