IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/33298.html
   My bibliography  Save this paper

Risk Loving and Fat Tails in the Wealth Distribution

Author

Listed:
  • Aloisio Araujo
  • Juan Pablo Gama
  • Timothy J. Kehoe

Abstract

We study the dynamic properties of the wealth distribution in an overlapping generations model with warm-glow bequests and heterogeneous attitudes towards risk. Some dynasties of agents are risk averters, and others are risk lovers. Agents can invest in two types of Lucas trees. The two types of trees are symmetric in the sense that one type has a high return in states where the other has a return of zero. This symmetry allows risk averters to perfectly ensure their future income and eliminates aggregate uncertainty in the model. Furthermore, risk lovers take extreme portfolio positions, which make it easy for us to characterize the evolution of their wealth holdings over time. We show that the model has an equilibrium in which the aggregate wealth distribution converges to a unique invariant distribution. The invariant distribution of wealth of the risk lovers has fat tails for high bequest rates. The existence of fat tails is endogenously generated by the behavior of risk lovers rather than by the exogenous existence of fat tails in the endowments or in the returns of the assets.

Suggested Citation

  • Aloisio Araujo & Juan Pablo Gama & Timothy J. Kehoe, 2024. "Risk Loving and Fat Tails in the Wealth Distribution," NBER Working Papers 33298, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:33298
    Note: EFG
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w33298.pdf
    Download Restriction: Access to the full text is generally limited to series subscribers, however if the top level domain of the client browser is in a developing country or transition economy free access is provided. More information about subscriptions and free access is available at http://www.nber.org/wwphelp.html. Free access is also available to older working papers.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or

    for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Manuel S. Santos & Michael Woodford, 1997. "Rational Asset Pricing Bubbles," Econometrica, Econometric Society, vol. 65(1), pages 19-58, January.
    2. Benhabib, Jess & Bisin, Alberto & Zhu, Shenghao, 2016. "The Distribution Of Wealth In The Blanchard–Yaari Model," Macroeconomic Dynamics, Cambridge University Press, vol. 20(2), pages 466-481, March.
    3. Kehoe, Timothy J & Levine, David K, 2001. "Liquidity Constrained Markets versus Debt Constrained Markets," Econometrica, Econometric Society, vol. 69(3), pages 575-598, May.
    4. Jess Benhabib & Alberto Bisin & Shenghao Zhu, 2011. "The Distribution of Wealth and Fiscal Policy in Economies With Finitely Lived Agents," Econometrica, Econometric Society, vol. 79(1), pages 123-157, January.
    5. Toda, Alexis Akira, 2019. "Wealth distribution with random discount factors," Journal of Monetary Economics, Elsevier, vol. 104(C), pages 101-113.
    6. Thomas Piketty & Emmanuel Saez, 2014. "Inequality in the long run," Post-Print halshs-01053609, HAL.
    7. Kihlstrom, Richard E & Laffont, Jean-Jacques, 1979. "A General Equilibrium Entrepreneurial Theory of Firm Formation Based on Risk Aversion," Journal of Political Economy, University of Chicago Press, vol. 87(4), pages 719-748, August.
    8. Peter H. Lindert & Jeffrey G. Williamson, 2016. "Unequal Gains: American Growth and Inequality since 1700," Economics Books, Princeton University Press, edition 1, number 10670.
    9. Matthias Birkner & Niklas Scheuer & Klaus Wälde, 2023. "The dynamics of Pareto distributed wealth in a small open economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 607-644, August.
    10. Aloisio Araujo & Alain Chateauneuf & Juan Pablo Gama & Rodrigo Novinski, 2018. "General Equilibrium With Uncertainty Loving Preferences," Econometrica, Econometric Society, vol. 86(5), pages 1859-1871, September.
    11. Andreoni, James, 1989. "Giving with Impure Altruism: Applications to Charity and Ricardian Equivalence," Journal of Political Economy, University of Chicago Press, vol. 97(6), pages 1447-1458, December.
    12. Toda, Alexis Akira, 2014. "Incomplete market dynamics and cross-sectional distributions," Journal of Economic Theory, Elsevier, vol. 154(C), pages 310-348.
    13. Jing Wan & Shenghao Zhu, 2019. "Bequests, estate taxes, and wealth distributions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(1), pages 179-210, February.
    14. Timothy J. Kehoe & David K. Levine, 1993. "Debt-Constrained Asset Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(4), pages 865-888.
    15. Debraj Ray, 2006. "On the dynamics of inequality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(2), pages 291-306, October.
    16. Benhabib, Jess & Bisin, Alberto & Zhu, Shenghao, 2015. "The wealth distribution in Bewley economies with capital income risk," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 489-515.
    17. Émilien Gouin‐Bonenfant & Alexis Akira Toda, 2023. "Pareto extrapolation: An analytical framework for studying tail inequality," Quantitative Economics, Econometric Society, vol. 14(1), pages 201-233, January.
    18. Dutta, Jayasri & Michel, Philippe, 1998. "The Distribution of Wealth with Imperfect Altruism," Journal of Economic Theory, Elsevier, vol. 82(2), pages 379-404, October.
    19. repec:hal:pseose:halshs-01053609 is not listed on IDEAS
    20. Shenghao Zhu, 2019. "A Becker–Tomes model with investment risk," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(4), pages 951-981, June.
    21. Hernandez D., Alejandro & Santos, Manuel S., 1996. "Competitive Equilibria for Infinite-Horizon Economies with Incomplete Markets," Journal of Economic Theory, Elsevier, vol. 71(1), pages 102-130, October.
    22. Makoto Nirei & Wataru Souma, 2007. "A Two Factor Model Of Income Distribution Dynamics," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 53(3), pages 440-459, September.
    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. 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.
    2. Stachurski, John & Toda, Alexis Akira, 2019. "An impossibility theorem for wealth in heterogeneous-agent models with limited heterogeneity," Journal of Economic Theory, Elsevier, vol. 182(C), pages 1-24.
    3. Shuhei Aoki & Makoto Nirei, 2014. "Zipf's Law, Pareto's Law, and the Evolution of Top Incomes in the U.S," Working Papers e074, Tokyo Center for Economic Research.
    4. Toda, Alexis Akira, 2019. "Wealth distribution with random discount factors," Journal of Monetary Economics, Elsevier, vol. 104(C), pages 101-113.
    5. Matthias Birkner & Niklas Scheuer & Klaus Wälde, 2023. "The dynamics of Pareto distributed wealth in a small open economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 607-644, August.
    6. Shuhei Aoki & Makoto Nirei, 2016. "Pareto Distribution of Income in Neoclassical Growth Models," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 20, pages 25-42, April.
    7. Emilien Gouin-Bonenfant & Alexis Akira Toda, 2019. "Pareto Extrapolation: Bridging Theoretical and Quantitative Models of Wealth Inequality," 2019 Meeting Papers 152, Society for Economic Dynamics.
    8. 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).
    9. repec:cdl:ucsdec:qt5n29f260 is not listed on IDEAS
    10. repec:cdl:ucsdec:qt90n2h2bb is not listed on IDEAS
    11. Dan Cao & Wenlan Luo, 2017. "Persistent Heterogeneous Returns and Top End Wealth Inequality," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 26, pages 301-326, October.
    12. Mariacristina De Nardi & Giulio Fella, 2017. "Saving and Wealth Inequality," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 26, pages 280-300, October.
    13. Berenice Anne Neumann & Niklas Scheuer, 2024. "The Impact of Bequest Taxation on Wealth Inequality - Theory and Evidence," Research Papers in Economics 2024-05, University of Trier, Department of Economics.
    14. Yang, Xiaoliang & Zhou, Peng, 2022. "Wealth inequality and social mobility: A simulation-based modelling approach," Journal of Economic Behavior & Organization, Elsevier, vol. 196(C), pages 307-329.
    15. repec:cdl:ucsdec:qt9k5027d0 is not listed on IDEAS
    16. Bejan, Camelia & Bidian, Florin, 2010. "Limited enforcement, bubbles and trading in incomplete markets," MPRA Paper 36819, University Library of Munich, Germany, revised 20 Feb 2012.
    17. Shuhei Aoki & Makoto Nirei, 2017. "Zipf's Law, Pareto's Law, and the Evolution of Top Incomes in the United States," American Economic Journal: Macroeconomics, American Economic Association, vol. 9(3), pages 36-71, July.
    18. Emma Moreno-García & Juan Torres-Martínez, 2012. "Equilibrium existence in infinite horizon economies," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 11(2), pages 127-145, August.
    19. Fernández-Villaverde, Jesús & Levintal, Oren, 2024. "The Distributional Effects of Asset Returns," CEPR Discussion Papers 18855, C.E.P.R. Discussion Papers.
    20. Martins-da-Rocha, Victor Filipe & Vailakis, Yiannis, 2010. "Competitive equilibria in infinite-horizon collateralized economies with default penalties," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 703, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    21. Khieu, Hoang & Wälde, Klaus, 2023. "Capital income risk and the dynamics of the wealth distribution," Economic Modelling, Elsevier, vol. 122(C).
    22. 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.
    23. Azariadis, Costas & Kaas, Leo, 2007. "Asset price fluctuations without aggregate shocks," Journal of Economic Theory, Elsevier, vol. 136(1), pages 126-143, September.

    More about this item

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets

    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:nbr:nberwo:33298. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.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.