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Value Function Iteration as a Solution Method for the Ramsey Model

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  • Burkhard Heer

    ()
    (Free University Bolzano-Bozen)

  • Alfred Maußner

    ()
    (University of Augsburg)

Abstract

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.

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Bibliographic Info

Article provided by Justus-Liebig University Giessen, Department of Statistics and Economics in its journal Journal of Economics and Statistics.

Volume (Year): 231 (2011)
Issue (Month): 4 (August)
Pages: 494-515

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Handle: RePEc:jns:jbstat:v:231:y:2011:i:4:p:494-515

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Related research

Keywords: Value function iteration; policy function iteration; Howard’s Algorithm; acceleration; cubic interpolation; stochastic Ramsey model; heterogeneous agents.;

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  1. Lawrence J. Christiano & Jonas D.M. Fisher, 1997. "Algorithms for Solving Dynamic Models with Occasionally Binding Constraints," NBER Technical Working Papers 0218, National Bureau of Economic Research, Inc.
  2. Burkhard Heer & Alfred Maussner, 2004. "Computation of Business Cycle Models: A Comparison of Numerical Methods," CESifo Working Paper Series 1207, CESifo Group Munich.
  3. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
  4. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
  5. Andrés Erosa & Gustavo Ventura, 2000. "On Inflation as a Regressive Consumption Tax," UWO Department of Economics Working Papers 20001, University of Western Ontario, Department of Economics.
  6. S. Boragan Aruoba & Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez, 2003. "Comparing Solution Methods for Dynamic Equilibrium Economies," PIER Working Paper Archive 04-003, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  7. Jess Gaspar & Kenneth L. Judd, 1997. "Solving Large Scale Rational Expectations Models," NBER Technical Working Papers 0207, National Bureau of Economic Research, Inc.
  8. Martin L. Puterman & Moon Chirl Shin, 1978. "Modified Policy Iteration Algorithms for Discounted Markov Decision Problems," Management Science, INFORMS, vol. 24(11), pages 1127-1137, July.
  9. Huggett, Mark, 1993. "The risk-free rate in heterogeneous-agent incomplete-insurance economies," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 953-969.
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