Computing equilibria in dynamic models with occasionally binding constraints

Brumm, Johannes; Grill, Michael

doi:10.1016/j.jedc.2013.09.007

Cited by 38 publications

(29 citation statements)

References 18 publications

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“…However, this behavior is not surprising. One has to keep in mind that kinks that appear in our cases [27,28,29].…”

Section: Convergence Of Time Iterationmentioning

confidence: 96%

“…6 In this way, we can adapt to nondifferentiabilities induced by occasionally binding constraints that are common in economic models. While existing methods can adapt very precisely to these nondifferentiabilities [49,27], adaptive sparse grids work in much higher dimensions.…”

Section: Adaptive Sparse Gridsmentioning

confidence: 99%

“…This adaptive grid can better capture the local behavior of functions that have steep gradients or even nondif-70 ferentiabilities. The latter feature naturally arise from occasionally binding constraints which are present in many economic models yet have so far been tractable only in low-dimensional cases [27,28,29].…”

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confidence: 99%

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Scalable high-dimensional dynamic stochastic economic modeling

Brumm

Mikushin

Scheidegger

et al. 2015

Journal of Computational Science

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We present a highly parallelizable and flexible computational method to solve high-dimensional stochastic dynamic economic models. Solving such models often requires the use of iterative methods, like time iteration or dynamic programming. By exploiting the generic iterative structure of this broad class of economic problems, we propose a parallelization scheme that favors hybrid massively parallel computer architectures. Within a parallel nonlinear time iteration framework, we interpolate policy functions partially on GPUs using an adaptive sparse grid algorithm with piecewise linear hierarchical basis functions. GPUs accelerate this part of the computation one order of magnitude thus reducing overall computation time by 50%. The developments in this paper include the use of a fully adaptive sparse grid algorithm and the use of a mixed MPI-Intel TBB-CUDA/Thrust implementation to improve the interprocess communication strategy on massively parallel architectures. Numerical experiments on "Piz Daint" (Cray XC30) at the Swiss National Supercomputing Centre show that high-dimensional international real business cycle models can be efficiently solved in parallel. To our knowledge, this performance on a massively parallel petascale architecture for such nonlinear high-dimensional economic models has not been possible prior to present work. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractWe present a highly parallelizable and flexible computational method to solve highdimensional stochastic dynamic economic models. Solving such models often requires the use of iterative methods, like time iteration or dynamic programming. By exploiting the generic iterative structure of this broad class of economic problems, we propose a parallelization scheme that favors hybrid massively parallel computer architectures.Within a parallel nonlinear time iteration framework, we interpolate policy functions partially on GPUs using an adaptive sparse grid algorithm with piecewise linear hierarchical basis functions. GPUs accelerate this part of the computation one order of magnitude thus reducing overall computation time by 50%. The developments in this paper include the use of a fully adaptive sparse grid algorithm and the use of a mixed MPI-Intel TBB-CUDA/Thrust implementation to improve the interprocess communication strategy on massively parallel architectures. Numerical experiments on "Piz Daint" (Cray XC30) at the Swiss National Supercomputing Centre show that highdimensional international real business cycle models can be efficiently solved in parallel. To our knowledge, this performance on a massively ...

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“…However, this behavior is not surprising. One has to keep in mind that kinks that appear in our cases [27,28,29].…”

Section: Convergence Of Time Iterationmentioning

confidence: 96%

Section: Adaptive Sparse Gridsmentioning

confidence: 99%

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Scalable high-dimensional dynamic stochastic economic modeling

Brumm

Mikushin

Scheidegger

et al. 2015

Journal of Computational Science

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“…[18]). 3 We solve for an equilibrium that is Markov in the physical state of the economy, which is given by the capital stock and the productivity levels of all N countries:…”

Section: Time Iteration Algorithmmentioning

confidence: 99%

“…First, our work is related to papers that develope methods for solving dynamic economic models with occasionally binding constraints (see, e.g. [15,3,9,1]). While these methods are able to match the non-differentiabilities induced by such constraints very precisely for up to three continuous state variables, they are not as flexible and scalable as ours.…”

Section: Introductionmentioning

confidence: 99%

Using Adaptive Sparse Grids to Solve High-Dimensional Dynamic Models

Brumm¹,

Scheidegger²

2017

Econometrica

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We present a flexible and scalable method to compute 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. As the dimensionality increases, sparse grids grow considerably slower than standard tensor product grids. In addition, the grid scheme we use is automatically refined locally and can thus capture steep gradients or even non-differentiabilities. To further increase the maximum problem size we can handle, our implementation is fully hybrid parallel, i.e. using a combination of distributed and shared memory parallelization schemes. This parallelization enables us to efficiently use high-performance computing architectures. Our algorithm scales up nicely to more than one thousand parallel processes. 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.Keywords: Adaptive Sparse Grids, High-Performance Computing, International Real Business Cycles, Occasionally Binding Constraints JEL Classification: C63, C68, F41 * We are very grateful to Felix Kübler for helpful discussions and support. We thank Ken Judd, Karl Schmedders and seminar participants at University of Zürich, Stanford University, University of Chicago, Argonne National Laboratory, and CEF 2013 in Vancouver for valuable comments. Moreover, we thank Xiang Ma for very instructive email discussions regarding the workings of adaptive sparse grids. We are grateful for the support of Olaf Schenk, Antonio Messina and Riccardo Murri concerning HPC related issues. We acknowledge CPU time granted on the University of Zürich's 'Schrödinger' HPC cluster. Johannes Brumm gratefully acknowledges financial support from the ERC.

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Solving Dynamic Portfolio Choice Models in Discrete Time Using Spatially Adaptive Sparse Grids

Schober¹

2018

Lecture Notes in Computational Science and Engineering

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Computing equilibria in dynamic models with occasionally binding constraints

Cited by 38 publications

References 18 publications

Scalable high-dimensional dynamic stochastic economic modeling

Scalable high-dimensional dynamic stochastic economic modeling

Using Adaptive Sparse Grids to Solve High-Dimensional Dynamic Models

Solving Dynamic Portfolio Choice Models in Discrete Time Using Spatially Adaptive Sparse Grids

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