Using Adaptive Sparse Grids to Solve High-Dimensional Dynamic Models

Johannes Brumm; Simon Scheidegger

doi:10.3982/ecta12216

Econometrica Vol. 85 No. 5 2017

Using Adaptive Sparse Grids to Solve High-Dimensional Dynamic Models

Johannes Brumm^{1,2,3,4,5,6,7,8,9,10,11}; Simon Scheidegger^{1,2,3,4,5,6,7,8,9,10,11}

¹ Karlsruhe Institute of Technology · ² Goethe University Frankfurt · ³ University of Geneva · ⁴ University of Copenhagen · ⁵ Argonne National Laboratory · ⁶ University of Bonn · ⁷ University of Zurich · ⁸ Cornell University · ⁹ University of Chicago · ¹⁰ Economie Publique · ¹¹ Institute of Finance and Banking

Abstract

We present a flexible and scalable method for computing global solutions of highdimensional 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 nondifferentiabilities.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.

DOI: 10.3982/ecta12216
Volume: 85
Issue: 5
Pages: 1575-1612
Language: en
Sources: bibtex:phds-export.bib openalex crossref

Using Adaptive Sparse Grids to Solve High-Dimensional Dynamic Models

Abstract

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