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Smolyak Method for Solving Dynamic Economic Models: Lagrange Interpolation, Anisotropic Grid and Adaptive Domain

Kenneth Judd, Lilia Maliar, Serguei Maliar and Rafael Valero ()

No 2013-02, BYU Macroeconomics and Computational Laboratory Working Paper Series from Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory

Abstract: First, we propose a more e¢ cient implementation of the Smolyak method for inter- polation, namely, we show how to avoid costly evaluations of repeated basis functions in the conventional Smolyak formula. Second, we extend the Smolyak method to include anisotropic constructions; this allows us to target higher quality of approximation in some dimensions than in others. Third, we show how to e¤ectively adapt the Smolyak hyper- cube to a solution domain of a given economic model. Finally, we advocate the use of low-cost .xed-point iteration, instead of conventional time iteration. In the context of one- and multi-agent growth models, we .nd that the proposed techniques lead to sub- stantial increases in accuracy and speed of a Smolyak-based projection method for solving dynamic economic models.

Keywords: Intergenerational Risk Sharing; Government Transfer Policies; Aggregate Shocks; Incomplete Markets; Stochastic Simulation (search for similar items in EconPapers)
JEL-codes: C63 C68 (search for similar items in EconPapers)
Pages: 47 pages
Date: 2013-08
New Economics Papers: this item is included in nep-cmp, nep-dge and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (20)

Published as "Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain," in Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 92-123.

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https://docs.google.com/file/d/0B6KGaihAO5TJTU51NVVjcS1udzA/edit First version, 2013 (application/pdf)

Related works:
Journal Article: Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain (2014) Downloads
Working Paper: Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain (2013) Downloads
Working Paper: Smolyak Method for Solving Dynamic Economic Models: Lagrange Interpolation, Anisotropic Grid and Adaptive Domain (2013) Downloads
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