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Value Function Iteration as a Solution Method for the Ramsey Model

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  • Burkhard Heer
  • Alfred Maussner

Abstract

Value function iteration is one of the standard tools for the solution of the Ramsey model. We compare six different ways of value function iteration with regard to speed and precision. We find that value function iteration with cubic spline interpolation between grid points dominates the other methods in most cases. For the initialization of the value function over a fine grid, modified policy function iteration over a coarse grid and subsequent linear interpolation between the grid points provides a very efficient way to reduce computational time.

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File URL: http://www.cesifo-group.de/portal/page/portal/DocBase_Content/WP/WP-CESifo_Working_Papers/wp-cesifo-2008/wp-cesifo-2008-04/cesifo1_wp2278.pdf
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Bibliographic Info

Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 2278.

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Date of creation: 2008
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Handle: RePEc:ces:ceswps:_2278

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Keywords: value function iteration; policy function iteration; Howard’s algorithm; acceleration; cubic interpolation; stochastic Ramsey model;

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  1. Jess Gaspar & Kenneth L. Judd, 1997. "Solving Large Scale Rational Expectations Models," NBER Technical Working Papers 0207, National Bureau of Economic Research, Inc.
  2. Erosa, Andres & Ventura, Gustavo, 2002. "On inflation as a regressive consumption tax," Journal of Monetary Economics, Elsevier, vol. 49(4), pages 761-795, May.
  3. 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.
  4. S. B. Aruoba & Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2005. "Comparing Solution Methods for Dynamic Equilibrium Economies," Levine's Bibliography 122247000000000855, UCLA Department of Economics.
  5. Burkhard Heer & Alfred Maussner, 2004. "Computation of Business Cycle Models: A Comparison of Numerical Methods," CESifo Working Paper Series 1207, CESifo Group Munich.
  6. 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.
  7. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
  8. Martin L. Puterman & Moon Chirl Shin, 1978. "Modified Policy Iteration Algorithms for Discounted Markov Decision Problems," Management Science, INFORMS, INFORMS, vol. 24(11), pages 1127-1137, July.
  9. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
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