High-Dimensional Dynamic Stochastic Model Representation

27 Pages Posted: 11 Jun 2020

See all articles by Aryan Eftekhari

Aryan Eftekhari

Università della Svizzera italiana - Institute of Computational Science

Simon Scheidegger

University of Lausanne - School of Economics and Business Administration (HEC-Lausanne)

Date Written: May 17, 2020

Abstract

We propose a generic and scalable method for computing global solutions of nonlinear, high-dimensional dynamic stochastic economic models. First, within an MPI–TBB parallel time-iteration framework, we approximate economic policy functions using an adaptive, high-dimensional model representation scheme, combined with adaptive sparse grids. With increasing dimensions, the number of points in this efficiently-chosen combination of low-dimensional grids grows much more slowly than standard tensor product grids, sparse grids, or even adaptive sparse grids. Moreover, the adaptivity within the individual component functions adds an additional layer of sparsity, since grid points are added only where they are most needed — that is to say, in regions of the computational domain with steep gradients or at non-differentiabilities. Second, we introduce a performant vectorization scheme of the interpolation compute kernel. Third, we validate our claims with numerical experiments conducted on “Piz Daint" (Cray XC50) at the Swiss National Super-computing Center. We observe significant speedups over the state-of-the-art techniques, and almost ideal strong scaling up to at least 1, 000 compute nodes. Fourth, to demonstrate the broad applicability of our method, we compute global solutions to two different versions of a dynamic stochastic economic model: a high-dimensional international real business cycle model with capital adjustment costs, and with or without irreversible investment. We solve these models up to 300 continuous state variables globally.

Keywords: Generalized ANOVA, Dimensional Decomposition, High-Dimensional Model Representation, Adaptive Sparse Grids, High-Performance Computing, International Real Business Cycles, Occasionally Binding Constraints

JEL Classification: C63, E30, F44

Suggested Citation

Eftekhari, Aryan and Scheidegger, Simon, High-Dimensional Dynamic Stochastic Model Representation (May 17, 2020). Available at SSRN: https://ssrn.com/abstract=3603294 or http://dx.doi.org/10.2139/ssrn.3603294

Aryan Eftekhari

Università della Svizzera italiana - Institute of Computational Science ( email )

Via Giuseppe Buffi 13
Lugano, Ticino 6900
Switzerland

Simon Scheidegger (Contact Author)

University of Lausanne - School of Economics and Business Administration (HEC-Lausanne) ( email )

Unil Dorigny, Batiment Internef
Lausanne, 1015
Switzerland

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