Working Paper: NBER ID: w19326
Authors: Kenneth L. Judd; Lilia Maliar; Serguei Maliar; Rafael Valero
Abstract: 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; this allows 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 advocate the use of low-cost fixed-point iteration, instead of conventional time iteration. In the context of one- and multi-agent growth models, we find that the proposed techniques lead to substantial increases in accuracy and speed of a Smolyak-based projection method for solving dynamic economic models.
Keywords: Smolyak method; dynamic economic models; Lagrange interpolation; anisotropic grid; adaptive domain
JEL Codes: C63; C68
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Smolyak method implementation (C69) | accuracy increase (C52) |
| Smolyak method implementation (C69) | speed increase (C69) |
| new method reduces computational costs (C63) | avoiding repeated evaluations of basis functions (C52) |
| anisotropic version of Smolyak method (C49) | better approximation in dimensions (C60) |
| fixed-point iteration (C62) | enhanced computational efficiency (C63) |
| Smolyak method (C69) | reduced residuals in Euler equations (C20) |