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

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. However, climate change, long-term economic development, and their interactions are highly uncertain. A thorough empirical analysis of the effects of 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 function and control rules approximations, and reductions of the uncertainty domain. The paper promotes a four stated recursive dynamic programming implementation of the DICE model. Our implementation solves the infinite planning horizon problem for an arbitrary time step. Moreover, we present a closed form continuous time approximation to the exogenous (discretely and inductively defined) processes in DICE and present a Bellman equation for DICE that disentangles risk attitude from the propensity to smooth consumption over time.