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Solving the incomplete markets model with aggregate uncertainty using parameterized cross-sectional distributions

Author

Listed:
  • Yann Algan

    (Sciences Po - Sciences Po)

  • Olivier Allais

    (ALISS - Alimentation et sciences sociales - INRA - Institut National de la Recherche Agronomique)

  • Wouter J den Haan

    (Department of Economics - UvA - University of Amsterdam [Amsterdam] = Universiteit van Amsterdam)

Abstract

This note describes how the incomplete markets model with aggregate uncertainty in Den Haan et al. [Comparison of solutions to the incomplete markets model with aggregate uncertainty. Journal of Economic Dynamics and Control, this issue] is solved using standard quadrature and projection methods. This is made possible by linking the aggregate state variables to a parameterized density that describes the cross-sectional distribution. A simulation procedure is used to find the best shape of the density within the class of approximating densities considered. This note compares several simulation procedures in which there is—as in the model—no cross-sectional sampling variation.

Suggested Citation

  • Yann Algan & Olivier Allais & Wouter J den Haan, 2010. "Solving the incomplete markets model with aggregate uncertainty using parameterized cross-sectional distributions," SciencePo Working papers Main hal-02662044, HAL.
    • Handle: RePEc:hal:spmain:hal-02662044
    DOI: 10.1016/j.jedc.2009.03.010
    Note: View the original document on HAL open archive server: https://hal.inrae.fr/hal-02662044v1
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    References listed on IDEAS

    as
    1. Jonathan Heathcote, 2005. "Fiscal Policy with Heterogeneous Agents and Incomplete Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(1), pages 161-188.
    2. Christiano, Lawrence J. & Fisher, Jonas D. M., 2000. "Algorithms for solving dynamic models with occasionally binding constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 24(8), pages 1179-1232, July.
    3. Den Haan, Wouter J., 1997. "Solving Dynamic Models With Aggregate Shocks And Heterogeneous Agents," Macroeconomic Dynamics, Cambridge University Press, vol. 1(2), pages 355-386, June.
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    5. José-Víctor Ríos-Rull, 1997. "Computation of equilibria in heterogeneous agent models," Staff Report 231, Federal Reserve Bank of Minneapolis.
    6. Algan, Yann & Allais, Olivier & Den Haan, Wouter J., 2008. "Solving heterogeneous-agent models with parameterized cross-sectional distributions," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 875-908, March.
    7. 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.
    8. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, April.
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    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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    Cited by:

    1. Den Haan, Wouter J. & Rendahl, Pontus, 2010. "Solving the incomplete markets model with aggregate uncertainty using explicit aggregation," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 69-78, January.
    2. Vasco M. Carvalho & Basile Grassi, 2019. "Large Firm Dynamics and the Business Cycle," American Economic Review, American Economic Association, vol. 109(4), pages 1375-1425, April.
    3. Juan M. Morelli & Pablo Ottonello & Diego J. Perez, 2022. "Global Banks and Systemic Debt Crises," Econometrica, Econometric Society, vol. 90(2), pages 749-798, March.
    4. Mordecai Kurz & Maurizio Motolese & Giulia Piccillo & Howei Wu, 2015. "Monetary Policy with Diverse Private Expectations," Discussion Papers 15-004, Stanford Institute for Economic Policy Research.
    5. Andrei Jirnyi & Vadym Lepetyuk, 2011. "A reinforcement learning approach to solving incomplete market models with aggregate uncertainty," Working Papers. Serie AD 2011-21, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    6. Den Haan, Wouter J., 2010. "Assessing the accuracy of the aggregate law of motion in models with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 79-99, January.
    7. Bayer, Christian & Luetticke, Ralph, 2018. "Solving heterogeneous agent models in discrete time with many idiosyncratic states by perturbation methods," CEPR Discussion Papers 13071, C.E.P.R. Discussion Papers.
    8. Jesús Fernández‐Villaverde & Samuel Hurtado & Galo Nuño, 2023. "Financial Frictions and the Wealth Distribution," Econometrica, Econometric Society, vol. 91(3), pages 869-901, May.
    9. Adrien Auclert & Bence Bardóczy & Matthew Rognlie & Ludwig Straub, 2021. "Using the Sequence‐Space Jacobian to Solve and Estimate Heterogeneous‐Agent Models," Econometrica, Econometric Society, vol. 89(5), pages 2375-2408, September.
    10. Michael C. Hatcher & Eric M. Scheffel, 2016. "Solving the Incomplete Markets Model in Parallel Using GPU Computing and the Krusell–Smith Algorithm," Computational Economics, Springer;Society for Computational Economics, vol. 48(4), pages 569-591, December.
    11. Pichler, Paul, 2011. "Solving the multi-country Real Business Cycle model using a monomial rule Galerkin method," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 240-251, February.
    12. Den Haan, Wouter J., 2010. "Comparison of solutions to the incomplete markets model with aggregate uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 4-27, January.
    13. Takeki Sunakawa, 2020. "Applying the Explicit Aggregation Algorithm to Heterogeneous Macro Models," Computational Economics, Springer;Society for Computational Economics, vol. 55(3), pages 845-874, March.
    14. Chipeniuk, Karsten O. & Katz, Nets Hawk & Walker, Todd B., 2022. "Households, auctioneers, and aggregation," European Economic Review, Elsevier, vol. 141(C).
    15. Wouter Den Haan & Pontus Rendahl & Markus Riegler, 2015. "Unemployment (Fears) and Deflationary Spirals," Discussion Papers 1521, Centre for Macroeconomics (CFM).
    16. Karsten O. Chipeniuk, 2020. "Optimal Grid Selection for the Numerical Solution of Dynamic Stochastic Optimization Problems," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 883-928, December.
    17. Emoto, Masakazu & Sunakawa, Takeki, 2021. "Applying the explicit aggregation algorithm to heterogeneous agent models in continuous time," Economics Letters, Elsevier, vol. 206(C).
    18. Ivo Bakota, 2023. "Market Clearing and Krusell-Smith Algorithm in an Economy with Multiple Assets," Computational Economics, Springer;Society for Computational Economics, vol. 62(3), pages 1007-1045, October.

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    More about this item

    Keywords

    PROJECTION METHODS; Numerical Solutions; Projection Methods; Simulations; NUMERICAL SOLUTIONS; SIMULATIONS;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets

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