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

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## Abstract

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.

## Keywords

Climate change Uncertainty Integrated assessment DICE Dynamic programming Risk aversion Intertemporal substitution MAGICC Basis Recursive utility## JEL Classification

Q54 Q00 D90 C63## Notes

### Acknowledgments

I thank Larry Karp, Benjamin Crost, Svenn Jensen, Derek Lemoine, David Kelly, Tony Smith, Klaus Keller, Robert Nicholas, Inez Fung, Ujjayant Chakravorty, the referees, and the editor, Jared Carbone. Partial funding by the Giannini Foundation and the National Science Foundation under Grant No. GEO-1240507 on Sustainable Climate Risk Management (SCRiM) is gratefully acknowledged.

## Supplementary material

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