A 4-stated DICE: quantitatively addressing uncertainty effects in climate change

We introduce a version of the DICE-2007 model designed for uncertaintyanalysis. DICE is a wide-spread deterministic integrated assessment model of climatechange. Climate change, long-term economic development, and their interactionsare highly uncertain. The quantitative analysis of optimal mitigation policy underuncertainty requires a recursive dynamic programming implementation of integratedassessment 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 functionapproximations, and reductions of the uncertainty domain. The paper promotes astate reduced, recursive dynamic programming implementation of the DICE-2007model. We achieve the reduction by simplifying the carbon cycle and the temperaturedelay equations. We compare our model’s performance and that of the DICE model tothe scientific AOGCM models emulated by MAGICC 6.0 and find that our simplifiedmodel performs equally well as the original DICE model. Our implementation solvesthe infinite planning horizon problem in an arbitrary time step. The paper is thefirst to carefully analyze the quality of the value function approximation using twodifferent types of basis functions and systematically varying the dimension of thebasis. We present the closed form, continuous time approximation to the exogenous(discretely and inductively defined) processes in DICE, and we present a numericallymore efficient re-normalized Bellman equation that, in addition, can disentangle riskattitude from the propensity to smooth consumption over time