Johannes Brumm

Using Adaptive Sparse Grids to Solve High-Dimensional Dynamic Models

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.

Scalable high-dimensional dynamic stochastic economic modeling

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 the best of 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.

Recursive Equilibria in Dynamic Economies With Stochastic Production

In this paper, we prove the existence of recursive equilibria in a dynamic stochastic model with infinitely lived heterogeneous agents, several commodities, and general inter‐ and intratemporal production. We illustrate the usefulness of our result by providing sufficient conditions for the existence of recursive equilibria in heterogeneous agent versions of both the Lucas asset pricing model and the neoclassical stochastic growth model.