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## Ramon Marimon and Andrew Scott

Print publication date: 2001

Print ISBN-13: 9780199248278

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0199248273.001.0001

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# Discrete State‐Space Methods for the Study of Dynamic Economies

Chapter:
(p.95) 5 Discrete State‐Space Methods for the Study of Dynamic Economies
Source:
Computational Methods for the Study of Dynamic Economies
Publisher:
Oxford University Press
DOI:10.1093/0199248273.003.0005

A number of numerical methods are discussed for solving dynamic stochastic general equilibrium models that fall within the common category of discrete state‐space methods. These methods can be applied in situations where the state space of the model in question is given by a finite set of discrete points; in these cases the methods provide an ‘exact’ solution to the model in question. However they are frequently applied in situations where the model's state space is continuous in which case the discrete state space can be viewed as an approximation to the continuous state space. Discrete state‐space methods are discussed in the context of two well‐known examples: a simple one‐asset version of Lucas's (1978) consumption‐based asset pricing model and the one‐sector neoclassical growth model. The discussion does not aim to exhaust the list of possible discrete state‐space methods as they are very numerous; rather it describes several examples that illustrate the basic principles involved. The main sections of the chapter describe the basic principles of numerical quadrature underlying most discrete state‐space methods, show how they can be applied in a very straightforward way to problems in which the state space consists entirely of exogenous state variables, and describe methods that can be used when there are endogenous state variables. The last section notes the several files associated with the chapter for use with MATLAB.

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