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

B-Tier
Journal: Journal of Economic Dynamics and Control
Year: 2014
Volume: 44
Issue: C
Pages: 92-123

Score contribution per author:

0.503 = (α=2.01 / 4 authors) × 1.0x B-tier

α: calibrated so average coauthorship-adjusted count equals average raw count

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.

Technical Details

RePEc Handle
repec:eee:dyncon:v:44:y:2014:i:c:p:92-123
Journal Field
Macro
Author Count
4
Added to Database
2026-01-25