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A generalized endogenous grid method for non-smooth and non-concave problems

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  • Giulio Fella

    (Queen Mary University of London)

Abstract

This paper extends Carroll's (2006) endogenous grid method and its combination with value function iteration by Barillas and Fernandez-Villaverde (2007) to a class of dynamic programming problems, such as problems with both discrete and continuous choices, in which the value function is non-smooth and non-concave. The method is illustrated using a consumer problem in which the consumer chooses both durable and non-durable consumption subject to a borrowing constraint. The durable choice is discrete and subject to non-convex adjustment costs. The algorithm yields substantial gains in accuracy and computational time relative to value function iteration, the standard solution choice for problems in which the value function is non-smooth or non-concave. (Copyright: Elsevier)

Suggested Citation

  • 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.
    • Handle: RePEc:red:issued:11-275
    DOI: 10.1016/j.red.2013.07.001
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    1. Brant Abbott & Giovanni Gallipoli & Costas Meghir & Giovanni L. Violante, 2013. "Education Policy�and Intergenerational Transfers in Equilibrium," Cowles Foundation Discussion Papers 1887, Cowles Foundation for Research in Economics, Yale University.
    2. Gomes, Joao & Greenwood, Jeremy & Rebelo, Sergio, 2001. "Equilibrium unemployment," Journal of Monetary Economics, Elsevier, vol. 48(1), pages 109-152, August.
    3. Brant Abbott & Giovanni Gallipoli & Costas Meghir & Giovanni L. Violante, 2019. "Education Policy and Intergenerational Transfers in Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 127(6), pages 2569-2624.
    4. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
    5. Jose Luengo-Prado, Maria, 2006. "Durables, nondurables, down payments and consumption excesses," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1509-1539, October.
    6. Edlin, Aaron S. & Shannon, Chris, 1998. "Strict Monotonicity in Comparative Statics," Journal of Economic Theory, Elsevier, vol. 81(1), pages 201-219, July.
    7. Gianluca Violante & Giovanni Gallipoli & Costas Meghir, 2005. "Education Decisions, Equilibrium Policies and Wages Dispersion," 2005 Meeting Papers 522, Society for Economic Dynamics.
    8. Aubhik Khan & Julia K. Thomas, 2008. "Idiosyncratic Shocks and the Role of Nonconvexities in Plant and Aggregate Investment Dynamics," Econometrica, Econometric Society, vol. 76(2), pages 395-436, March.
    9. Carroll, Christopher D., 2006. "The method of endogenous gridpoints for solving dynamic stochastic optimization problems," Economics Letters, Elsevier, vol. 91(3), pages 312-320, June.
    10. Storesletten, Kjetil & Telmer, Christopher I. & Yaron, Amir, 2004. "Consumption and risk sharing over the life cycle," Journal of Monetary Economics, Elsevier, vol. 51(3), pages 609-633, April.
    11. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(3), pages 659-684.
    12. Andrew Clausen & Carlo Strub, 2012. "Envelope theorems for non-smooth and non-concave optimization," ECON - Working Papers 062, Department of Economics - University of Zurich.
    13. John P. Rust, 1989. "A Dynamic Programming Model of Retirement Behavior," NBER Chapters, in: The Economics of Aging, pages 359-404, National Bureau of Economic Research, Inc.
    14. 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.
    15. Barillas, Francisco & Fernandez-Villaverde, Jesus, 2007. "A generalization of the endogenous grid method," Journal of Economic Dynamics and Control, Elsevier, vol. 31(8), pages 2698-2712, August.
    16. Patrick Bajari & Phoebe Chan & Dirk Krueger & Daniel Miller, 2013. "A Dynamic Model Of Housing Demand: Estimation And Policy Implications," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54(2), pages 409-442, May.
    17. Nicholas Bloom, 2009. "The Impact of Uncertainty Shocks," Econometrica, Econometric Society, vol. 77(3), pages 623-685, May.
    18. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    19. 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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    More about this item

    Keywords

    Endogenous grid method; Non-concavity;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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