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Using Adaptive Sparse Grids to Solve High-Dimensional Dynamic Models

Johannes Brumm

Karlsruhe Institute of Technology

Simon Scheidegger

University of Zurich

May 22, 2016

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 allows for an efficient use of high-performance computing architectures. To demonstrate the broad applicability of our method, we apply it to two very different dynamic models: First, to high-dimensional international real business cycle models with capital adjustment costs and irreversible investment. Second, to multi-good menu-cost models with temporary sales and economies of scope in price setting.

Number of Pages in PDF File: 36

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

JEL Classification: C63, C68, F41

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Date posted: November 4, 2013 ; Last revised: May 23, 2016

Suggested Citation

Brumm, Johannes and Scheidegger, Simon, Using Adaptive Sparse Grids to Solve High-Dimensional Dynamic Models (May 22, 2016). Available at SSRN: https://ssrn.com/abstract=2349281 or http://dx.doi.org/10.2139/ssrn.2349281

Contact Information

Johannes Brumm (Contact Author)
Karlsruhe Institute of Technology ( email )
Kaiserstraße 12
Karlsruhe, Baden Württemberg 76131
Simon Scheidegger
University of Zurich ( email )
Rämistrasse 71
Zürich, CH-8006
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