First, we propose a more e¢ cient implementation of the Smolyak method for inter- polation, 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...

We propose a novel methodology for evaluating the accuracy of numerical solutions to dynamic economic models. Specifically, we construct a lower bound on the size of approximation errors. A small lower bound on errors is a necessary condition for accuracy: If a lower error bound is unacceptably...

We develop an envelope condition method (ECM) for dynamic programming problems –a tractable alternative to expensive conventional value function iteration. ECM has two novel features: First, to reduce the cost, ECM replaces expensive backward iteration on Bellman equation with relatively...

We characterize and demonstrate a solution method for an optimal commodity (sales) tax problem consisting of multiple goods, heterogeneous agents, and a nonconvex policy maker optimization problem. Our approach allows for more dimensions of heterogeneity than has been previously possible,...