Maliar, L. and S. Maliar
Handbook of Computational Economics – Volume 3, Chapter 7 (2014), 325-477

Keywords: High dimensions; Large scale; Projection; Perturbation; Stochastic simulation; Value function iteration; Endogenous grid; Envelope condition; Smolyak; ε-distinguishable set; Curse of dimensionality; Precomputation; Manifold; Parallel computation; Supercomputers.

Abstract: We survey numerical methods that are tractable in dynamic economic models with a finite, large number of continuous state variables. (Examples of such models are new Keynesian models, life-cycle models, heterogeneous agents models, asset pricing models, multisector models, multicountry models, and climate change models.) First, we describe the ingredients that help us to reduce the cost of global solution methods. These are efficient nonproduct techniques for interpolating and approximating functions (Smolyak, stochastic simulation, and ε-distinguishable set grids), accurate low-cost monomial integration formulas, derivative-free solvers, and numerically stable regression methods. Second, we discuss endogenous grid and envelope condition methods that reduce the cost and increase accuracy of value function iteration. Third, we show precomputation techniques that construct solution manifolds for some models’ variables outside the main iterative cycle. Fourth, we review techniques that increase the accuracy of perturbation methods: a change of variables and a hybrid of local and global solutions. Finally, we show examples of parallel computation using multiple CPUs and GPUs including applications on a supercomputer. We illustrate the performance of the surveyed methods using a multi-agent model. Many codes are publicly available.