The method of endogenous gridpoints with occasionally binding constraints among endogenous variables

Hintermaier, Thomas; Koeniger, Winfried

doi:10.1016/j.jedc.2010.05.002

Cited by 66 publications

(50 citation statements)

References 25 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%

“…To calculate the M +1 errors at a given point in the state space, we evaluate the terms in (29) to (32) using the computed equilibrium policy function for calculating both today's policy and next period's policy. To generate the statistics on Euler errors reported below we then proceed as follows.…”

Section: Convergence Of Time Iterationmentioning

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: Convergence Of Time Iterationmentioning

confidence: 99%

See 1 more Smart Citation

Scalable high-dimensional dynamic stochastic economic modeling

Brumm

Mikushin

Scheidegger

et al. 2015

Journal of Computational Science

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“…1 Among those, for instance, Barillas and Fernandez-Villaverde (2007) extend the solution method to problems with labor-leisure choice, Hintermaier and Koeniger (2010) and Fella (2014) suggest solution methods for a model with occasionally binding constraints and a decision on durables and non-durables, White (2015) considers the theoretical characterization of EGM with a multi-dimensional setting and under value function iteration. 2 In this paper, we take a different route and develop a method that relies on policy function iteration, namely the Market Resources Method (MRM), paying attention primarily to the solution of problems with labor-leisure choice directly from the first order conditions.…”

Section: Introductionmentioning

confidence: 99%

The Market Resources Method for Solving Dynamic Optimization Problems

Kabukçuoğlu

Martínez‐García

2016

gwp

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“…None of the applied algorithms uses an adaptive grid scheme. A grid structure which is not adaptive, but endogenous, is proposed by Carrol (2006) and extended by Barillas and Fernández-Villaverde (2007), Hintermaier and Koeniger (2010), and Ludwig and Schön (2013). This so called endogenous grid method defines a grid on tomorrow's variables, resulting in an endogenous grid on today's variables.…”

Section: Introductionmentioning

confidence: 99%

Computing equilibria in dynamic models with occasionally binding constraints

Brumm

Grill

2014

Journal of Economic Dynamics and Control

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We propose a method to compute equilibria in dynamic models with several continuous state variables and occasionally binding constraints. These constraints induce non-differentiabilities in policy functions. We develop an interpolation technique that addresses this problem directly: It locates the non-differentiabilities and adds interpolation nodes there. To handle this flexible grid, it uses Delaunay interpolation, a simplicial interpolation technique. Hence, we call this method Adaptive Simplicial Interpolation (ASI). We embed ASI into a time iteration algorithm to compute recursive equilibria in an infinite horizon endowment economy where heterogeneous agents trade in a bond and a stock subject to various trading constraints. We show that this method computes equilibria accurately and outperforms other grid schemes by far. AbstractWe propose a method to compute equilibria in dynamic models with several continuous state variables and occasionally binding constraints. These constraints induce non-differentiabilities in policy functions. We develop an interpolation technique that addresses this problem directly: It locates the non-differentiabilities and adds interpolation nodes there. To handle this flexible grid, it uses Delaunay interpolation, a simplicial interpolation technique. Hence, we call this method Adaptive Simplicial Interpolation (ASI). We embed ASI into a time iteration algorithm to compute recursive equilibria in an infinite horizon endowment economy where heterogeneous agents trade in a bond and a stock subject to various trading constraints. We show that this method computes equilibria accurately and outperforms other grid schemes by far.

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The method of endogenous gridpoints with occasionally binding constraints among endogenous variables

Cited by 66 publications

References 25 publications

Scalable high-dimensional dynamic stochastic economic modeling

Scalable high-dimensional dynamic stochastic economic modeling

The Market Resources Method for Solving Dynamic Optimization Problems

Computing equilibria in dynamic models with occasionally binding constraints

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