IDEAS home Printed from https://ideas.repec.org/p/red/sed019/151.html

An Impossibility Theorem for Wealth in Heterogeneous-agent Models with Limited Heterogeneity

Author

Listed:
  • John Stachurski

    (Australian National University)

  • Alexis Akira Toda

    (University of California San Diego)

Abstract

It has been conjectured that canonical Bewley-Huggett-Aiyagari heterogeneous-agent models cannot explain the joint distribution of income and wealth. The results stated below verify this conjecture and clarify its implications under very general conditions. We show in particular that if (i) agents are infinitely-lived, (ii) saving is risk-free, and (iii) agents have constant discount factors, then the wealth distribution inherits the tail behavior of income shocks (e.g., light-tailedness or the Pareto exponent). Our restrictions on utility require only that relative risk aversion is bounded, and a large variety of income processes are admitted. Our results show conclusively that it is necessary to go beyond standard models to explain the empirical fact that wealth is heavier-tailed than income. We demonstrate through examples that relaxing any of the above three conditions can generate Pareto tails.

Suggested Citation

  • John Stachurski & Alexis Akira Toda, 2019. "An Impossibility Theorem for Wealth in Heterogeneous-agent Models with Limited Heterogeneity," 2019 Meeting Papers 151, Society for Economic Dynamics.
    • Handle: RePEc:red:sed019:151
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    Other versions of this item:

    Citations

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


    Cited by:

    1. Shenghao Zhu, 2020. "Existence Of Stationary Equilibrium In An Incomplete‐Market Model With Endogenous Labor Supply," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 61(3), pages 1115-1138, August.
    2. Konstantinos Angelopoulos & Spyridon Lazarakis & James Malley, 2019. "The distributional effects of peer and aspirational pressure," Working Papers 2019_06, Business School - Economics, University of Glasgow.
    3. Beare, Brendan K & Toda, Alexis Akira, 2020. "On the emergence of a power law in the distribution of COVID-19 cases," University of California at San Diego, Economics Working Paper Series qt9k5027d0, Department of Economics, UC San Diego.
    4. Ma, Qingyin & Stachurski, John & Toda, Alexis Akira, 2022. "Unbounded dynamic programming via the Q-transform," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    5. Ma, Qingyin & Stachurski, John & Toda, Alexis Akira, 2020. "The income fluctuation problem and the evolution of wealth," Journal of Economic Theory, Elsevier, vol. 187(C).
    6. Sergio Ocampo & Baxter Robinson, 2024. "Computing Longitudinal Moments for Heterogeneous Agent Models," Computational Economics, Springer;Society for Computational Economics, vol. 64(3), pages 1891-1912, September.
    7. Sergio Ocampo & Gueorgui Kambourov & Daphne Chen & Burhanettin Kuruscu & Fatih Guvenen, 2017. "Use It or Lose It: Efficiency Gains from Wealth Taxation," 2017 Meeting Papers 913, Society for Economic Dynamics.
    8. Matthias Krapf, 2023. "Does Income Risk Affect the Wealth Distribution?," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 49(4), pages 475-515, October.
    9. Tjeerd de Vries & Alexis Akira Toda, 2022. "Capital and Labor Income Pareto Exponents Across Time and Space," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 68(4), pages 1058-1078, December.
    10. Toda, Alexis Akira, 2021. "Necessity of hyperbolic absolute risk aversion for the concavity of consumption functions," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    11. Ma, Qingyin & Toda, Alexis Akira, 2022. "Asymptotic linearity of consumption functions and computational efficiency," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    12. Bence Bardóczy, 2024. "HANK Comes of Age: Monetary Policy with Heterogeneous Overlapping Generations," Finance and Economics Discussion Series 2024-052r1, Board of Governors of the Federal Reserve System (U.S.), revised 19 Dec 2025.
    13. Ma, Qingyin & Toda, Alexis Akira, 2021. "A theory of the saving rate of the rich," Journal of Economic Theory, Elsevier, vol. 192(C).
    14. Thomas J. Sargent & John Stachurski, 2024. "Dynamic Programming: Finite States," Papers 2401.10473, arXiv.org.
    15. Schulz, Jan & Weber, Jan David, 2025. "Power laws in socio-economics," BERG Working Paper Series 203, Bamberg University, Bamberg Economic Research Group.
    16. Konstantinos Angelopoulos & Spyridon Lazarakis & Rebecca Mancy & Dorice Agol & Elissaios Papyrakis, 2023. "Resource Risk and the Origins of Inequality: Evidence from a Pastoralist Economy," CESifo Working Paper Series 10611, CESifo.
    17. Joachim Hubmer & Per Krusell & Anthony A. Smith., 2021. "Sources of US Wealth Inequality: Past, Present, and Future," NBER Macroeconomics Annual, University of Chicago Press, vol. 35(1), pages 391-455.
    18. Beare, Brendan K. & Seo, Won-Ki & Toda, Alexis Akira, 2022. "Tail Behavior Of Stopped Lévy Processes With Markov Modulation," Econometric Theory, Cambridge University Press, vol. 38(5), pages 986-1013, October.
    19. Konstantinos Angelopoulos & Spyridon Lazarakis & James Malley, 2019. "The distributional effects of peer and aspirational pressure," Working Papers 2019-06, Business School - Economics, University of Glasgow.
    20. Marcello D’Amato & Christian Di Pietro & Marco M. Sorge, 2024. "Left and right: a tale of two tails of the wealth distribution," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(4), pages 1389-1433, December.
    21. Liu, Haoyu & Li, Lun, 2023. "On the concavity of consumption function under habit formation," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    22. Kaymak, Barıș & Leung, David & Poschke, Markus, 2020. "Accounting for Wealth Concentration in the US," IZA Discussion Papers 13082, Institute of Labor Economics (IZA).
    23. Suzuki, Tomoya, 2021. "Basic income, wealth inequality and welfare: A proposed case in New Zealand," Economic Analysis and Policy, Elsevier, vol. 72(C), pages 118-128.
    24. Robert Kirkby, 2025. "Discretizing earnings dynamics: implications of Gaussian-mixture shocks for life-cycle models," The Japanese Economic Review, Springer, vol. 76(2), pages 493-519, April.

    More about this item

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

    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:red:sed019:151. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Christian Zimmermann (email available below). General contact details of provider: https://edirc.repec.org/data/sedddea.html .

    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.