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Parallel Extended Path Method for Solving Perfect Foresight Models

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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.

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Notes

  1. Use of block Jacobi preconditioning was demonstrated with blocks corresponding to one or several consecutive time periods.

  2. Household preferences change over time and are mainly driven by demographic and income changes (Dalton et al. 2008; Melnikov et al. 2012; O’Neill et al. 2012). Allowing multiple household types within each region relaxes the representative household assumption, which adds substantial computing costs to the solution in terms of many more variables, including an additional state variable for each household type. For O’Neill et al. (2010a), it was not numerically feasible to allow multiple household types within each of the 9 regions. However, household heterogeneity can be an important factor in macroeconomic models (Heathcote et al. 2009), and there is growing interest in the effects of heterogeneity (Kaplan and Violante 2018). The solution method in this paper can accommodate multiple household types within each region.

  3. Technical change is described using separate productivity coefficients in the CES production functions that change exogenously over time for each input of each production function in the model (Dalton et al. 2008).

  4. For \(A_X^{OPR}\) this also includes OPR used in the land nest, \(A_X^{S} A_S^{OPR}\).

  5. In practice one can choose the relaxation factors small enough to insure convergence, but a large number of iterations can be required to achieve prescribed tolerance level.

  6. We use Intel Fortran compilers (for performance evaluation, see Tian et al. 2002).

  7. By the speedup we mean the ratio of the parallel execution time on several processors to the execution time on a single processor. Generally there is some overhead in the parallel algorithm not present in the serial one due to various aspects of parallelization.

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Acknowledgements

Much of B.C.O.'s contribution was made while employed at the U.S. National Center for Atmospheric Research (NCAR). N.B.M. gratefully acknowledges the hospitality of the Integrated Assessment Modeling group within Climate and Global Dynamics Laboratory at NCAR. The research was carried out using the equipment of the shared research facilities of high-performance computing (HPC) resources at Lomonosov Moscow State University and HPC support from Cheyenne (https://doi.org/10.5065/D6RX99HX) provided by NCAR’s Computational and Information Systems Laboratory, sponsored by the U.S. National Science Foundation. We are grateful to R. Loft for useful discussions of the results obtained at Cheyenne. The views expressed are purely those of the authors and may not in any circumstances be regarded as stating an official position of the European Commission. We thank the referees for useful comments, which allowed us to improve the manuscript.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    N. B. Melnikov & A. P. Gruzdev

  2. Central Economics and Mathematics Institute, RAS, Moscow, Russia

    N. B. Melnikov

  3. National Oceanic and Atmospheric Administration, Seattle, WA, USA

    M. G. Dalton

  4. European Commission, Joint Research Centre, Seville, Spain

    M. Weitzel

  5. University of Denver, Denver, CO, USA

    B. C. O’Neill

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  1. N. B. Melnikov
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  2. A. P. Gruzdev
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  3. M. G. Dalton
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  4. M. Weitzel
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  5. B. C. O’Neill
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Correspondence to N. B. Melnikov.

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Appendix

Appendix

Table 3 List of regions in the iPETS model
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Table 4 List of sectors in the iPETS model
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Melnikov, N.B., Gruzdev, A.P., Dalton, M.G. et al. Parallel Extended Path Method for Solving Perfect Foresight Models. Comput Econ 58, 517–534 (2021). https://doi.org/10.1007/s10614-020-10044-y

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