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Solving Heterogeneous agent models in Continuous Time with Adaptive Sparse Grids

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  • Du, Zaichuan

Abstract

This paper proposes a new approach to numerically solving a wide class of heterogeneous agent models in continuous time using adaptive sparse grids. I combine the sparse finite difference method with the sparse finite volume method to solve the Hamilton-Jacobian-Bellman equation and Kolmogorov Forward equation, respectively. My algorithm automatically adapts grids and adds local resolutions in regions of the state space where both the value function and the distribution approximation errors remains large. I demonstrate the power of my approach in applications feature high-dimensional state spaces, occasionally binding constraints, lifecycle and overlapping generations.

Suggested Citation

  • Du, Zaichuan, 2024. "Solving Heterogeneous agent models in Continuous Time with Adaptive Sparse Grids," MPRA Paper 121381, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:121381
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    File URL: https://mpra.ub.uni-muenchen.de/121381/1/MPRA_paper_121381.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Huggett, Mark, 1996. "Wealth distribution in life-cycle economies," Journal of Monetary Economics, Elsevier, vol. 38(3), pages 469-494, December.
    3. Adrien Bilal, 2023. "Solving Heterogeneous Agent Models with the Master Equation," NBER Working Papers 31103, National Bureau of Economic Research, Inc.
    4. Young, Eric R., 2010. "Solving the incomplete markets model with aggregate uncertainty using the Krusell-Smith algorithm and non-stochastic simulations," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 36-41, January.
    5. Den Haan, Wouter J. & Judd, Kenneth L. & Juillard, Michel, 2010. "Computational suite of models with heterogeneous agents: Incomplete markets and aggregate uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 1-3, January.
    6. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    heterogeneous agent; mean field game; continuous time; adaptive sparse grids; occasionally binding constraints; overlapping generation; lifecycle;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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