IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2510.26065.html

Price Levels in Heterogeneous-Agent Models

Author

Listed:
  • Felix Hofer

Abstract

We study a model of the Fiscal Theory of the Price Level (FTPL) in a Bewley-Huggett-Aiyagari framework with heterogeneous agents. The model is set in continuous time, and ex post heterogeneity arises due to idiosyncratic, uninsurable income shocks. Such models have a natural interpretation as mean-field games, introduced by Huang, Caines, and Malham\'e and by Lasry and Lions. We highlight this connection and discuss the existence and multiplicity of stationary equilibria in models with and without capital. Our focus is on the mathematical analysis, and we prove the existence of two equilibria in which the government runs constant primary deficits, which in turn implies the existence of multiple price levels.

Suggested Citation

  • Felix Hofer, 2025. "Price Levels in Heterogeneous-Agent Models," Papers 2510.26065, arXiv.org.
    • Handle: RePEc:arx:papers:2510.26065
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2510.26065
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bayer, Christian & Rendall, Alan D. & Wälde, Klaus, 2019. "The invariant distribution of wealth and employment status in a small open economy with precautionary savings," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 17-37.
    2. Achdou, Yves & Han, Jiequn & Lasry, Jean Michel & Lions, Pierre Louis & Moll, Ben, 2022. "Income and wealth distribution in macroeconomics: a continuous-time approach," LSE Research Online Documents on Economics 107422, London School of Economics and Political Science, LSE Library.
    3. Mao Fabrice Djete & Dylan Possamaï & Xiaolu Tan, 2022. "McKean–Vlasov Optimal Control: Limit Theory and Equivalence Between Different Formulations," Mathematics of Operations Research, INFORMS, vol. 47(4), pages 2891-2930, November.
    4. Cherrier, Beatrice & Duarte, Pedro Garcia & Saïdi, Aurélien, 2023. "Household heterogeneity in macroeconomic models: A historical perspective," European Economic Review, Elsevier, vol. 158(C).
    5. Markus K. Brunnermeier & Sebastian A. Merkel & Yuliy Sannikov, 2020. "The Fiscal Theory of Price Level with a Bubble," NBER Working Papers 27116, National Bureau of Economic Research, Inc.
    6. Kaplan, Greg & Nikolakoudis, Georgios & Violante, Giovanni, 2023. "Price Level and Inflation Dynamics in Heterogeneous Agent Economies," CEPR Discussion Papers 18260, C.E.P.R. Discussion Papers.
    7. Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lionse & Benjamin Moll, 2022. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(1), pages 45-86.
    8. 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.
    9. Sun, Yeneng, 2006. "The exact law of large numbers via Fubini extension and characterization of insurable risks," Journal of Economic Theory, Elsevier, vol. 126(1), pages 31-69, January.
    10. Huggett, Mark, 1993. "The risk-free rate in heterogeneous-agent incomplete-insurance economies," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 953-969.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ruitu Xu & Yifei Min & Tianhao Wang & Zhaoran Wang & Michael I. Jordan & Zhuoran Yang, 2023. "Finding Regularized Competitive Equilibria of Heterogeneous Agent Macroeconomic Models with Reinforcement Learning," Papers 2303.04833, arXiv.org.
    2. Li, Mingzhe, 2025. "A Theory of Portfolio Choice for Heterogeneous Investors," MPRA Paper 126642, University Library of Munich, Germany, revised 29 Oct 2025.
    3. Keyvan Eslami & Thomas Phelan, 2025. "The Art of Temporal Approximation: An Investigation into Numerical Solutions to Discrete- and Continuous-Time Problems in Economics," Computational Economics, Springer;Society for Computational Economics, vol. 65(3), pages 1505-1547, March.
    4. Andrew Lyasoff, 2023. "The Time-Interlaced Self-Consistent Master System of Heterogeneous-Agent Models," Papers 2303.12567, arXiv.org, revised May 2025.
    5. Dirk Krueger & Harald Uhlig, 2022. "Neoclassical Growth with Limited Commitment," NBER Working Papers 30518, National Bureau of Economic Research, Inc.
    6. Frederick Ploeg, 2023. "Fiscal Costs of Climate Policies: Role of Tax, Political, and Behavioural Distortions," De Economist, Springer, vol. 171(2), pages 119-137, June.
    7. Toda, Alexis Akira & Walsh, Kieran James, 2024. "Recent advances on uniqueness of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    8. Marta Grzeskiewicz, 2025. "Solving Heterogeneous Agent Models with Physics-informed Neural Networks," Papers 2511.20283, arXiv.org.
    9. Chenxin Zhang & Yujie Yang & Wenwen Hou, 2025. "Trade Friction in Two-Country HANK with Financial Friction," Computational Economics, Springer;Society for Computational Economics, vol. 65(1), pages 365-394, January.
    10. Central Reserve Bank of Peru, 2025. "Heterogeneity considerations in monetary policy design: the case of Peru," BIS Papers chapters, in: Bank for International Settlements (ed.), How can central banks take account of differences across households and firms for monetary policy?, volume 127, pages 225-242, Bank for International Settlements.
    11. Keyvan Eslami & Tom Phelan, 2023. "The Art of Temporal Approximation An Investigation into Numerical Solutions to Discrete and Continuous-Time Problems in Economics," Working Papers 23-10, Federal Reserve Bank of Cleveland.
    12. Dmitriy Sergeyev & Chen Lian & Yuriy Gorodnichenko, 2023. "The Economics of Financial Stress," NBER Working Papers 31285, National Bureau of Economic Research, Inc.
    13. Toda, Alexis Akira, 2019. "Wealth distribution with random discount factors," Journal of Monetary Economics, Elsevier, vol. 104(C), pages 101-113.
    14. Schesch, Constantin, 2024. "Pseudospectral methods for continuous-time heterogeneous-agent models," Journal of Economic Dynamics and Control, Elsevier, vol. 163(C).
    15. Alexandre Gaillard & Christian Hellwig & Philipp Wangner & Nicolas Werquin, 2023. "Consumption, Wealth, and Income Inequality: A Tale of Tails," Working Paper Series WP 2023-43, Federal Reserve Bank of Chicago.
    16. Luo, Yulei & Nie, Jun & Wang, Gaowang & Young, Eric R., 2017. "Rational inattention and the dynamics of consumption and wealth in general equilibrium," Journal of Economic Theory, Elsevier, vol. 172(C), pages 55-87.
    17. Luo, Yulei & Nie, Jun & Wang, Gaowang & Young, Eric, 2014. "What We Don't Know Doesn't Hurt Us: Rational Inattention and the Permanent Income Hypothesis in General Equilibrium," MPRA Paper 59182, University Library of Munich, Germany.
    18. Jordan Roulleau-Pasdeloup, 2025. "Explicit Consumption Functions with Borrowing Constraints: a Continuous Time Approach," Papers 2511.03452, arXiv.org.
    19. Hashimzade, Nigar & Kirsanov, Oleg & Kirsanova, Tatiana, 2023. "Distributional effects of endogenous discounting," Mathematical Social Sciences, Elsevier, vol. 122(C), pages 1-6.
    20. Christopher Sandmann & Nicolas Bonneton, 2023. "Existence of a Non-Stationary Equilibrium in Search-And-Matching Models: TU and NTU," CRC TR 224 Discussion Paper Series crctr224_2023_427v2, University of Bonn and University of Mannheim, Germany, revised Feb 2025.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2510.26065. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.