Board of Governors of the Federal Reserve System (US)

Finance and Economics Discussion Series

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

This paper provides a new technique for representing discrete time nonlinear dynamic stochastic time invariant maps. Using this new series representation, the paper augments the usual solution strategy with an additional set of constraints thereby enhancing algorithm 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.

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Gary S. Anderson, *Reliably Computing Nonlinear Dynamic Stochastic Model Solutions: An Algorithm with Error Formulas*, Board of Governors of the Federal Reserve System (US), Finance and Economics Discussion Series 2018-070, 11 Oct 2018.

JEL Classification:

**C63**- Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques**C65**- Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools**C60**- Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General**C62**- Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

Subject headings:

Keywords: Econometric modeling ; Mathematical and quantitative methods

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