Value Function Iteration as a Solution Method for the Ramsey Model

  • Value function iteration is one of the Standard tools for the solution of dynamic general equilibrium models if the dimension of the state space is one ore two. We consider three kinds of models: the deterministic and the stochastic growth model and a simple heterogenous agent model. Each model is solved with six different algorithms: (1) simple value function iteration as compared to (2) smart value function iteration neglects the special structure of the problem. (3) Full and (4) modified policy iteration are methods to speed up convergence. (5) linear and (6) cubic interpolation between the grid points are methods that enhance precision and reduce the size of the grid. We evaluate the algorithms with respect to speed and accuracy. Accuracy is defined as the maximum absolute value of the residual of the Euler equation that determines the household’s savings. We demonstrate that the run time of all algorithms can be reduced substantially if the value function is initialized stepwise,Value function iteration is one of the Standard tools for the solution of dynamic general equilibrium models if the dimension of the state space is one ore two. We consider three kinds of models: the deterministic and the stochastic growth model and a simple heterogenous agent model. Each model is solved with six different algorithms: (1) simple value function iteration as compared to (2) smart value function iteration neglects the special structure of the problem. (3) Full and (4) modified policy iteration are methods to speed up convergence. (5) linear and (6) cubic interpolation between the grid points are methods that enhance precision and reduce the size of the grid. We evaluate the algorithms with respect to speed and accuracy. Accuracy is defined as the maximum absolute value of the residual of the Euler equation that determines the household’s savings. We demonstrate that the run time of all algorithms can be reduced substantially if the value function is initialized stepwise, starting on a coarse grid and increasing the number of grid points successively until the desired size is reached. We find that value function iteration with cubic spline interpolation between grid points dominates the other methods if a high level of accuracy is needed.show moreshow less

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Metadaten
Author:Alfred MaußnerGND, Burkhard HeerGND
URN:urn:nbn:de:bvb:384-opus4-380535
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/38053
ISSN:0021-4027
Parent Title (English):Journal of Economics and Statistics
Parent Title (German):Jahrbücher für Nationalökonomie und Statistik
Type:Article
Language:English
Year of first Publication:2011
Publishing Institution:Universität Augsburg
Release Date:2018/02/09
Tag:Howard's Algorithm; Value function iteration; acceleration; cubic interpolation; heterogeneous agents; policy function iteration; stochastic Ramsey model
Volume:231
Issue:4
First Page:494
Last Page:515
Institutes:Wirtschaftswissenschaftliche Fakultät / Volkswirtschaftslehre
Dewey Decimal Classification:3 Sozialwissenschaften / 33 Wirtschaft / 330 Wirtschaft
Licence (German):License LogoDeutsches Urheberrecht