Abstract

http://ssrn.com/abstract=2349281
 
 

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Using Adaptive Sparse Grids to Solve High-Dimensional Dynamic Models


Johannes Brumm


University of Zurich

Simon Scheidegger


University of Zurich

April 15, 2015


Abstract:     
We present a flexible and scalable method for computing global solutions of high-dimensional stochastic dynamic models. Within a time iteration setup, we interpolate policy functions using an adaptive sparse grid algorithm with piecewise multi-linear (hierarchical) basis functions. With increasing dimensions, sparse grids grow much more slowly than standard tensor product grids. In addition, the grid scheme we use is automatically refined locally and can thus capture steep gradients and even non-differentiabilities. To further increase the maximum problem size we can handle, our implementation is fully hybrid parallel: it uses a combination of distributed and shared memory parallelization schemes. This parallelization enables us to efficiently use high-performance computing architectures such as ''CRAY XC30'' at the Swiss National Supercomputing Centre. Numerical experiments show that our algorithm scales up nicely to more than two thousand compute nodes. To demonstrate the performance of our method, we apply it to high-dimensional international real business cycle models with capital adjustment costs and irreversible investment.

Number of Pages in PDF File: 35

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

JEL Classification: C63, C68, F41


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Date posted: November 4, 2013 ; Last revised: April 15, 2015

Suggested Citation

Brumm, Johannes and Scheidegger, Simon, Using Adaptive Sparse Grids to Solve High-Dimensional Dynamic Models (April 15, 2015). Available at SSRN: http://ssrn.com/abstract=2349281 or http://dx.doi.org/10.2139/ssrn.2349281

Contact Information

Johannes Brumm (Contact Author)
University of Zurich ( email )
Rämistrasse 71
Zürich, CH-8006
Switzerland
Simon Scheidegger
University of Zurich ( email )
Rämistrasse 71
Zürich, CH-8006
Switzerland
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