Numerical Solution Methods

Alfonso Novales, Esther Fernández and Jesus Ruiz

Chapter 5 in Economic Growth, 2022, pp 213-278 from Springer

Abstract: Abstract We start by considering the stochastic optimal growth model of Chap. 4 , without taxes, explaining the construction of linear and log-linear approximations. Different solution methods are described: the Blanchard and Kahn approach, Uhlig’s method of undetermined coefficients, and Sims’ method based on an eigenvalue–eigenvector decomposition. We pay special attention to characterizing stability. We explain their practical implementation and discuss some of the results obtained. After that, we implement the same methods to solve the stochastic optimal growth model under different tax specifications and discuss some policy issues. The chapter closes with nonlinear solution methods, such as Marcet’s Parameterized Expectations and Projection methods. We apply them to the standard Cass–Koopmans growth model and provide MATLAB programs for their implementation.

Keywords: Conditional expectation; Stability conditions; Linear-quadratic approximation; Blanchard and Kahn method; Method of undetermined coefficients; Eigenvalue–eigenvector decomposition; Parameterized expectations method; Projection methods; Simulation (search for similar items in EconPapers)
Date: 2022
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Chapter: Numerical Solution Methods (2014)
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DOI: 10.1007/978-3-662-63982-5_5

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