Reliably Computing Nonlinear Dynamic Stochastic Model Solutions: An Algorithm with Error Formulas

Abstract

This paper provides a new technique for representing discrete time nonlinear dynamic stochastic time invariant maps. Using this new series representation, the paper shows how to augment a solution strategy based on projection methods with an additional set of constraints thereby enhancing its reliability. The paper also provides general formulas for evaluating the accuracy of proposed solutions. The technique can readily accommodate models with occasionally binding constraints and regime switching. The algorithm uses Smolyak polynomial function approximation in a way which makes it possible to exploit a high degree of parallelism.