Continuous-Time Methods for Integrated Assessment Models

44 Pages Posted: 8 Sep 2012 Last revised: 6 Sep 2021

See all articles by Yongyang Cai

Yongyang Cai

Ohio State University (OSU); Center for Robust Decisionmaking on Climate & Energy Policy (RDCEP)

Kenneth L. Judd

Stanford University - The Hoover Institution on War, Revolution and Peace; Center for Robust Decisionmaking on Climate & Energy Policy (RDCEP); National Bureau of Economic Research (NBER)

Thomas S. Lontzek

University of Zurich; Center for Robust Decisionmaking on Climate & Energy Policy (RDCEP)

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Date Written: September 2012

Abstract

Continuous 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.

Suggested Citation

Cai, Yongyang and Judd, Kenneth L. and Lontzek, Thomas S., Continuous-Time Methods for Integrated Assessment Models (September 2012). NBER Working Paper No. w18365, Available at SSRN: https://ssrn.com/abstract=2143552

Yongyang Cai (Contact Author)

Ohio State University (OSU) ( email )

Department of Agricultural, Environmental
and Development Economics
Columbus, OH 43210
United States

Center for Robust Decisionmaking on Climate & Energy Policy (RDCEP) ( email )

5735 S. Ellis Street
Chicago, IL 60637
United States

Kenneth L. Judd

Stanford University - The Hoover Institution on War, Revolution and Peace ( email )

Stanford, CA 94305-6010
United States

Center for Robust Decisionmaking on Climate & Energy Policy (RDCEP) ( email )

5735 S. Ellis Street
Chicago, IL 60637
United States

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Thomas S. Lontzek

University of Zurich ( email )

Switzerland

Center for Robust Decisionmaking on Climate & Energy Policy (RDCEP) ( email )

5735 S. Ellis Street
Chicago, IL 60637
United States

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