Parallel Extended Path Method for Solving Perfect Foresight Models
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Parallel Extended Path Method for Solving Perfect Foresight Models N. B. Melnikov1,2 · A. P. Gruzdev1 · M. G. Dalton3 · M. Weitzel4 · B. C. O’Neill5 Accepted: 27 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We parallelize the extended path method for solving rational expectations models, and apply it to compute perfect foresight competitive equilibrium for the global economy with multiple goods, regions, industries, and households. At each iteration, first intertemporal variables are updated, then equations for intra-temporal variables are solved in parallel. We compare serial, and parallel, versions of the extended path method in high-performance computing environments based on scenarios with long time horizons that include future populations, economic growth, energy use, and carbon dioxide emissions. Relative to the serial version, the speedup factor for the parallel extended path method grows almost linearly up to about 30 times with 18 cores, and computing times reduced from over 10 h for the serial version down to about 20 min for the parallel version. Keywords Perfect foresight · Intertemporal general equilibrium · Economic growth · Iterative methods · Parallel computing · Energy economics · Climate impacts JEL Classification C63 · D58 · J11 · O13
* N. B. Melnikov [email protected] 1
Lomonosov Moscow State University, Moscow, Russia
2
Central Economics and Mathematics Institute, RAS, Moscow, Russia
3
National Oceanic and Atmospheric Administration, Seattle, WA, USA
4
European Commission, Joint Research Centre, Seville, Spain
5
University of Denver, Denver, CO, USA
13
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1 Introduction Many problems in economics, such as assessing economic impacts from climate policies, require intertemporal general equilibrium models, which describe economic growth due to capital accumulation, technological change and population change. The perfect foresight aspect of dynamic general equilibrium links current and future economic variables, which leads to an infinite system of nonlinear equations. In practice, these infinite-dimensional systems are truncated to finite systems of nonlinear equations. Accounting for regional disaggregation, sectoral detail and household heterogeneity produces large-scale nonlinear systems with a specific block structure, which need robust and efficient solution methods. Parallel computing creates a new class of solution methods, based on whether the serial version is parallelizable. With the rapid growth in multicore processors, substantial benefits from parallelization can now be obtained on a single machine. Moreover, computer clusters are widely available to run large jobs, which provides opportunities to test old yet still useful solution methods for parallelizability. In this paper, we parallelize the extended path method of Fair and Taylor (1983), an early method of solving rational expectations models, which has been largely replaced by dynamic programming, perturbation, or proje
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