Numerical Dynamic Programming with Verification and Uncertainty Quantification: An Application to Climate Policy

This paper introduces novel techniques for solving multidimensional dynamic stochastic optimization problems which commonly occur in economics and related disciplines. We (i) present a new efficient method to approximate value functions, (ii) develop an error control scheme that allows us to verify the accuracy of value function iterations, and (iii) quantify the dependence on parameters by computing response surfaces, a basic tool for uncertainty quantification. This is all possible because our effecient use of parallel dynamic programming methods to solve those types of models. As an application of our methodology, we consider a prominent problem in environmental economics—determining the optimal policy for addressing potential adverse impacts of carbon emissions on economic output. Using plausible ranges for several key parameters we obtain an optimal carbon price ranging between $40 and $400 per ton. Our study shows that with the appropriate methods, complex problems of optimal decision making under various types of uncertainties can be addressed, and decisively refutes the pessimism one often hears about the possibility of solving such models. ∗Ohio State University †Hoover Institution, Stanford University & NBER, kennethjudd@mac.com.