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Endogenous Grids in Higher Dimensions: Delaunay Interpolation and Hybrid Methods

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  • Ludwig, Alexander

    ()

  • Schön, Matthias

    (Munich Center for the Economics of Aging (MEA))

Abstract

This paper investigates extensions of the method of endogenous grid-points (ENDGM) introduced by Carroll (2006) to higher dimensions with more than one continuous endogenous state variable. We compare three different categories of algorithms: (i) the conventional method with exogenous grids (EXGM), (ii) the pure method of endogenous grid-points (ENDGM) and (iii) a hybrid method (HEGM). ENDGM comes along with Delaunay interpolation on irregular grids. Comparison of methods is done by evaluating speed and accuracy. We find that HEGM and ENDGM both dominate EXGM. The choice between HEGM and ENDGM depends on the number of dimensions and the number of grid-points in each dimension. With less than 150 grid-points in each dimension ENDGM is faster than HEGM, and vice versa. For a standard choice of 20 to 40 grid-points in each dimension, ENDGM is 1:6 to 1:8 times faster than HEGM.

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Paper provided by Munich Center for the Economics of Aging (MEA) at the Max Planck Institute for Social Law and Social Policy in its series MEA discussion paper series with number 13274.

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Date of creation: 10 Sep 2013
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Handle: RePEc:mea:meawpa:13274

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  1. 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.
  2. Carroll, Christopher D., 2005. "The method of endogenous gridpoints for solving dynamic stochastic optimization problems," CFS Working Paper Series 2005/18, Center for Financial Studies (CFS).
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  7. Yoram Ben-Porath, 1967. "The Production of Human Capital and the Life Cycle of Earnings," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 75, pages 352.
  8. Francisco Barillas & Jesús Fernández-Villaverde, 2006. "A Generalization of the Endogenous Grid Method," Levine's Bibliography 122247000000001200, UCLA Department of Economics.
  9. Hintermaier, Thomas & Koeniger, Winfried, 2010. "The method of endogenous gridpoints with occasionally binding constraints among endogenous variables," Journal of Economic Dynamics and Control, Elsevier, vol. 34(10), pages 2074-2088, October.
  10. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
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