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Using Adaptive Sparse Grids to Solve High-Dimensional Dynamic Models

37 Pages Posted: 4 Nov 2013 Last revised: 25 May 2017

Johannes Brumm

Karlsruhe Institute of Technology

Simon Scheidegger

University of Zurich; Stanford University - The Hoover Institution on War, Revolution and Peace

Date Written: May 22, 2017

Abstract

We present a flexible and scalable method for computing global solutions of high-dimensional stochastic dynamic models. Within a time iteration or value function iteration setup, we interpolate functions using an adaptive sparse grid algorithm. With increasing dimensions, sparse grids grow much more slowly than standard tensor product grids. Moreover, adaptivity adds a second layer of sparsity, as grid points are added only where they are most needed, for instance in regions with steep gradients or at non-differentiabilities. To further speed up the solution process, our implementation is fully hybrid parallel, combining distributed and shared memory parallelization paradigms, and thus permits an efficient use of high-performance computing architectures. To demonstrate the broad applicability of our method, we solve two very different types of dynamic models: first, high-dimensional international real business cycle models with capital adjustment costs and irreversible investment; second, multiproduct menu-cost models with temporary sales and economies of scope in price setting.

Keywords: Adaptive Sparse Grids, High-Performance Computing, International Real Business Cycles, Menu Costs, Occasionally Binding Constraints

JEL Classification: C63, E30, F44

Suggested Citation

Brumm, Johannes and Scheidegger, Simon, Using Adaptive Sparse Grids to Solve High-Dimensional Dynamic Models (May 22, 2017). Available at SSRN: https://ssrn.com/abstract=2349281 or http://dx.doi.org/10.2139/ssrn.2349281

Johannes Brumm (Contact Author)

Karlsruhe Institute of Technology ( email )

Kaiserstraße 12
Karlsruhe, Baden Württemberg 76131
Germany

Simon Scheidegger

University of Zurich ( email )

Rämistrasse 71
Zürich, CH-8006
Switzerland

Stanford University - The Hoover Institution on War, Revolution and Peace ( email )

Stanford, CA 94305-6010
United States

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