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A Generalized Endogenous Grid Method for Models with the Option to Default

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  • Jang, Youngsoo
  • Lee, Soyoung
Abstract
We develop an endogenous grid method for models with the option to default in which price schedules are endogenously determined in equilibrium and depend on individuals’ states. The algorithm has noticeable computational benefits in efficiency and accuracy. We obtain these computational benefits by combining Fella’s (2014) identification for non-concave regions with our algorithm that numerically searches for risky borrowing limits. These two procedures identify the region of solution sets to which Carroll’s (2006) endogenous grid method is applicable. To demonstrate the method, we apply our method to Nakajima and Rios-Rull’s(2014) model. In terms of computation time, this method is seven to twenty-seven times faster than the conventional grid search method. Moreover, various types of accuracy tests indicate that our method yields more accurate results than the grid search method.

Suggested Citation

  • Jang, Youngsoo & Lee, Soyoung, 2019. "A Generalized Endogenous Grid Method for Models with the Option to Default," MPRA Paper 95721, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:95721
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    References listed on IDEAS

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    1. Juan Carlos Hatchondo & Leonardo Martinez & Horacio Sapriza, 2010. "Quantitative properties of sovereign default models: solution methods," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 13(4), pages 919-933, October.
    2. Makoto Nakajima & José-Víctor Ríos-Rull, 2014. "Credit, Bankruptcy, and Aggregate Fluctuations," NBER Working Papers 20617, National Bureau of Economic Research, Inc.
    3. Druedahl, Jeppe & Jørgensen, Thomas Høgholm, 2017. "A general endogenous grid method for multi-dimensional models with non-convexities and constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 74(C), pages 87-107.
    4. Arellano, Cristina & Maliar, Lilia & Maliar, Serguei & Tsyrennikov, Viktor, 2016. "Envelope condition method with an application to default risk models," Journal of Economic Dynamics and Control, Elsevier, vol. 69(C), pages 436-459.
    5. 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.
    6. 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.
    7. 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.
    8. Aubhik Khan, 2016. "Aggregate Fluctuations in a Quantitative Overlapping Generations Economy with Unemployment Risk," 2016 Meeting Papers 1468, Society for Economic Dynamics.
    9. Cristina Arellano, 2008. "Default Risk and Income Fluctuations in Emerging Economies," American Economic Review, American Economic Association, vol. 98(3), pages 690-712, June.
    10. Juan Carlos Hatchondo & Leonardo Martinez & Horacio Sapriza, 2010. "Quantitative properties of sovereign default models: solution methods matter," Working Paper 10-04, Federal Reserve Bank of Richmond.
    11. Clausen, Andrew & Strub, Carlo, 2020. "Reverse Calculus and nested optimization," Journal of Economic Theory, Elsevier, vol. 187(C).
    12. 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.
    13. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
    14. Fedor Iskhakov & Thomas H. Jørgensen & John Rust & Bertel Schjerning, 2017. "The endogenous grid method for discrete‐continuous dynamic choice models with (or without) taste shocks," Quantitative Economics, Econometric Society, vol. 8(2), pages 317-365, July.
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    More about this item

    Keywords

    Endogenous grid method; Default; Bankruptcy;
    All these keywords.

    JEL classification:

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

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