Local (perturbation) methods compute solutions in one point and tend to deliver far lower accuracy levels than global solution methods. We develop a hybrid method that solves for some policy functions locally (using a perturbation method) and that solves for the other policy functions globally...

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...

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 study a class of infinite-horizon nonlinear dynamic economic models in which preferences, technology and laws of motion for exogenous variables can change over time either deterministically or stochastically, according to a Markov process with time-varying transition probabilities, or both....