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Endogenous Grids in Higher Dimensions: Delaunay Interpolation and Hybrid Methods

  • Ludwig, Alexander

    ()

  • Schön, Matthias

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

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. Christopher Carroll, 2005. "The Method of Endogenous Gridpoints for Solving Dynamic Stochastic Optimization Problems," Economics Working Paper Archive 520, The Johns Hopkins University,Department of Economics.
  2. Krueger, Dirk & Ludwig, Alexander, 2006. "On the Consequences of Demographic Change for Rates of Return to Capital, and the Distribution of Wealth and Welfare," CEPR Discussion Papers 5834, C.E.P.R. Discussion Papers.
  3. Brumm, Johannes & Grill, Michael, 2014. "Computing equilibria in dynamic models with occasionally binding constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 142-160.
  4. Robert E. Hall & Charles I. Jones, 2005. "The value of life and the rise in health spending," Proceedings, Federal Reserve Bank of San Francisco.
  5. 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.
  6. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
  7. John Rust & Bertel Schjerning & Fedor Iskhakov, 2012. "A generalized endogenous grid method for discrete-continuous choice," 2012 Meeting Papers 1162, Society for Economic Dynamics.
  8. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, June.
  9. Yoram Ben-Porath, 1967. "The Production of Human Capital and the Life Cycle of Earnings," Journal of Political Economy, University of Chicago Press, vol. 75, pages 352.
  10. Francisco Barillas & Jesús Fernández-Villaverde, 2006. "A Generalization of the Endogenous Grid Method," Levine's Bibliography 122247000000001200, UCLA Department of Economics.
  11. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
  12. Michael Grill & Johannes Brumm, 2010. "Computing Equilibria in Dynamic Models with Occasionally Binding Constraints," 2010 Meeting Papers 695, Society for Economic Dynamics.
  13. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
  14. Paul Klein & Marek Kapicka, 2011. "Consumption risk sharing under private information when earnings are persistent," 2011 Meeting Papers 247, Society for Economic Dynamics.
  15. Giulio Fella, 2014. "A generalized endogenous grid method for non-smooth and non-concave problems," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(2), pages 329-344, April.
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