02746cam a22003017 4500001000700000003000500007005001700012008004100029100001900070245013700089260006600226490004200292500002000334520122900354530006101583538007201644538003601716690012301752690010101875690010501976690012502081700002102206700002302227710004202250830007702292856003802369856003702407w18365NBER20150707040458.0150707s2012 mau||||fs|||| 000 0 eng d1 aCai, Yongyang.10aContinuous-Time Methods for Integrated Assessment Modelsh[electronic resource] /cYongyang Cai, Kenneth L. Judd, Thomas S. Lontzek. aCambridge, Mass.bNational Bureau of Economic Researchc2012.1 aNBER working paper seriesvno. w18365 aSeptember 2012.3 aContinuous time is a superior representation of both the economic and climate systems that Integrated Assessment Models (IAM) aim to study. Moreover, continuous-time representations are simple to express. Continuous-time models are usually solved by discretizing time, but the quality of a solution is significantly affected by the details of the discretization. The numerical analysis literature offers many reliable methods, and should be used because alternatives derived from "intuition" may be significantly inferior. We take the well-known DICE model as an example. DICE uses 10-year time steps. We first identify the underlying continuous-time model of DICE. Second, we present mathematical and computational methods for transforming continuous-time deterministic perfect foresight models into systems of finite difference equations. While some transformations create finite difference systems that look like a discrete-time dynamical system, the only proper way to view the finite difference system is as an approximation of the continuous-time problem. DICE is an example where the usage of finite difference methods from numerical analysis produces far superior approximations than do simple discrete-time systems. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web. 7aC61 - Optimization Techniques • Programming Models • Dynamic Analysis2Journal of Economic Literature class. 7aC63 - Computational Techniques • Simulation Modeling2Journal of Economic Literature class. 7aD81 - Criteria for Decision-Making under Risk and Uncertainty2Journal of Economic Literature class. 7aQ54 - Climate • Natural Disasters and Their Management • Global Warming2Journal of Economic Literature class.1 aJudd, Kenneth L.1 aLontzek, Thomas S.2 aNational Bureau of Economic Research. 0aWorking Paper Series (National Bureau of Economic Research)vno. w18365.4 uhttp://www.nber.org/papers/w1836541uhttp://dx.doi.org/10.3386/w18365