First, we propose a more efficient implementation of the Smolyak method for interpolation, namely, we show how to avoid costly evaluations of repeated basis functions in the conventional Smolyak formula. Second, we extend the Smolyak method to include anisotropic constructions; this allows us to...

We introduce a computational technique- precomputation of integrals - that makes it possible to construct conditional expectation functions in dynamic stochastic models in the initial stage of a solution procedure. This technique is very general: it works for a broad class of approximating...

First, we propose a more efficient implementation of the Smolyak method for interpolation, namely, we show how to avoid costly evaluations of repeated basis functions in the conventional Smolyak formula. Second, we extend the Smolyak method to include anisotropic constructions; this allows us to...

First, we propose a more efficient implementation of the Smolyak method for interpolation, namely, we show how to avoid costly evaluations of repeated basis functions in the conventional Smolyak formula. Second, we extend the Smolyak method to include anisotropic constructions; this allows us to...

We develop numerically stable and accurate stochastic simulation approaches for solving dynamic economic models. First, instead of standard least-squares approximation methods, we examine a variety of alternatives, including least- squares methods using singular value decomposition and Tikhonov...

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,...

We introduce an envelope condition method (ECM) for solving dynamic programming problems. ECM iterates on the Bellman equation forward and is much faster than conventional value function methods that iterate backward. In the studied examples, ECM is comparable in accuracy and cost to Carroll's...