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Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain

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  • Judd, Kenneth L.
  • Maliar, Lilia
  • Maliar, Serguei
  • Valero, Rafael

Abstract

We show how to enhance the performance of a Smolyak method for solving dynamic economic models. First, we propose a more efficient implementation of the Smolyak method for interpolation, 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 that allow us to target higher quality of approximation in some dimensions than in others. Third, we show how to effectively adapt the Smolyak hypercube to a solution domain of a given economic model. Finally, we argue that in large-scale economic applications, a solution algorithm based on Smolyak interpolation has substantially lower expense when it uses derivative-free fixed-point iteration instead of standard time iteration. In the context of one- and multi-agent optimal growth models, we find that the proposed modifications to the conventional Smolyak method lead to substantial increases in accuracy and speed.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 44 (2014)
Issue (Month): C ()
Pages: 92-123

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Handle: RePEc:eee:dyncon:v:44:y:2014:i:c:p:92-123

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Web page: http://www.elsevier.com/locate/jedc

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Keywords: Smolyak method; Sparse grid; Adaptive domain; Projection; Anisotropic grid; High-dimensional problem;

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Cited by:
  1. Julien Albertini & Arthur Poirier, 2014. "Unemployment benefits extensions at the zero lower bound on nominal interest rate," SFB 649 Discussion Papers SFB649DP2014-019, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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