Using Adaptive Sparse Grids to Solve High-Dimensional Dynamic Models

• 成果类型: Article
• 署名作者: Brumm, Johannes; Scheidegger, Simon
• 署名单位: Helmholtz Association; Karlsruhe Institute of Technology; University of Zurich
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA12216
• 发表日期: 2017
• 页码: 1575-1612
• 关键词: menu costs; multiproduct firms; interpolation; income; RISK; fluctuations; integration; simulation; credit; shocks

摘要

We present a flexible and scalable method for computing global solutions of high-dimensional 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.