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Approximate and Almost-Exact Aggregation in Dynamic Stochastic Heterogeneous-Agent Models

Author

Listed:
  • Reiter, Michael

    (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria)

Abstract

The paper presents a new method to solve DSGE models with a great number of heterogeneous agents. Using tools from systems and control theory, it is shown how to reduce the dimension of the state and the policy vector so that the reduced model approximates the original model with high precision. The method is illustrated with a stochastic growth model with incomplete markets similar to Krusell and Smith (1998), and with a model of heterogeneous firms with state-dependent pricing. For versions of those models that are nonlinear in individual variables, but linearized in aggregate variables, approximations with 50 to 200 state variables deliver solutions that are precise up to machine precision. The paper also shows how to reduce the state vector even further, with a very small reduction in precision.

Suggested Citation

  • Reiter, Michael, 2010. "Approximate and Almost-Exact Aggregation in Dynamic Stochastic Heterogeneous-Agent Models," Economics Series 258, Institute for Advanced Studies.
    • Handle: RePEc:ihs:ihsesp:258
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    File URL: https://irihs.ihs.ac.at/id/eprint/2021
    File Function: First version, 2010
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    References listed on IDEAS

    as
    1. Fatih Guvenen, 2009. "An Empirical Investigation of Labor Income Processes," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 12(1), pages 58-79, January.
    2. Reiter, Michael & Sveen, Tommy & Weinke, Lutz, 2009. "Lumpy Investment and State-Dependent Pricing in General Equilibrium," Economics Series 239, Institute for Advanced Studies.
    3. 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.
    4. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, April.
    5. Reiter, Michael, 2009. "Solving heterogeneous-agent models by projection and perturbation," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 649-665, March.
    6. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2006. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871525, October.
    7. Ana Castaneda & Javier Diaz-Gimenez & Jose-Victor Rios-Rull, 2003. "Accounting for the U.S. Earnings and Wealth Inequality," Journal of Political Economy, University of Chicago Press, vol. 111(4), pages 818-857, August.
    8. James Costain & Antón Nákov, 2009. "Dynamics of the price distribution in a general model of state-dependent pricing," Working Papers 0831, Banco de España.
    9. Bruce Preston & Mauro Roca, 2007. "Incomplete Markets, Heterogeneity and Macroeconomic Dynamics," NBER Working Papers 13260, National Bureau of Economic Research, Inc.
    10. Benjamin Malin & Dirk Krueger & Felix Kubler, 2007. "Computing Stochastic Dynamic Economic Models with a Large Number of State Variables: A Description and Application of a Smolyak-Collocation Method," NBER Technical Working Papers 0345, National Bureau of Economic Research, Inc.
    11. 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.
    12. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2006. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692083, October.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Reiter Michael & Sveen Tommy & Weinke Lutz, 2023. "Idiosyncratic Shocks, Lumpy Investment and the Monetary Transmission Mechanism," The B.E. Journal of Macroeconomics, De Gruyter, vol. 23(2), pages 1037-1055, June.
    2. Papp, Tamás K. & Reiter, Michael, 2020. "Estimating linearized heterogeneous agent models using panel data," Journal of Economic Dynamics and Control, Elsevier, vol. 115(C).
    3. Boppart, Timo & Krusell, Per & Mitman, Kurt, 2018. "Exploiting MIT shocks in heterogeneous-agent economies: the impulse response as a numerical derivative," Journal of Economic Dynamics and Control, Elsevier, vol. 89(C), pages 68-92.
    4. Zhouzhou Gu & Mathieu Lauri`ere & Sebastian Merkel & Jonathan Payne, 2024. "Global Solutions to Master Equations for Continuous Time Heterogeneous Agent Macroeconomic Models," Papers 2406.13726, arXiv.org.
    5. Reiter, Michael & Sveen, Tommy & Weinke, Lutz, 2013. "Lumpy investment and the monetary transmission mechanism," Journal of Monetary Economics, Elsevier, vol. 60(7), pages 821-834.
    6. Reiter, Michael, 2018. "Comments on “Exploiting MIT shocks in heterogeneous-agent economies: The impulse response as a numerical derivative” by T. Boppart, P. Krusell and K. Mitman," Journal of Economic Dynamics and Control, Elsevier, vol. 89(C), pages 93-99.
    7. 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.
    8. Alisdair McKay, "undated". "Idiosyncratic risk, insurance, and aggregate consumption dynamics: a likelihood perspective," Boston University - Department of Economics - Working Papers Series 2013-013, Boston University - Department of Economics.
    9. Emoto, Masakazu & Sunakawa, Takeki, 2021. "Applying the explicit aggregation algorithm to heterogeneous agent models in continuous time," Economics Letters, Elsevier, vol. 206(C).
    10. Maliar, Lilia & Maliar, Serguei, 2022. "Deep learning classification: Modeling discrete labor choice," Journal of Economic Dynamics and Control, Elsevier, vol. 135(C).
    11. Reiter Michael & Sveen Tommy & Weinke Lutz, 2020. "Agency costs and the monetary transmission mechanism," The B.E. Journal of Macroeconomics, De Gruyter, vol. 20(1), pages 1-11, January.
    12. Michael Reiter, 2019. "Solving Heterogeneous Agent Models with Non-convex Optimization Problems: Linearization and Beyond %," 2019 Meeting Papers 1048, Society for Economic Dynamics.
    13. Maliar, Lilia & Maliar, Serguei & Winant, Pablo, 2021. "Deep learning for solving dynamic economic models," Journal of Monetary Economics, Elsevier, vol. 122(C), pages 76-101.
    14. Reiter, Michael, 2015. "Solving OLG Models with Many Cohorts, Asset Choice and Large Shocks," Economics Series 320, Institute for Advanced Studies.

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    More about this item

    Keywords

    Heterogeneous agents; aggregation; model reduction;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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