IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v94y2021ics0304406820301373.html
   My bibliography  Save this article

Necessity of hyperbolic absolute risk aversion for the concavity of consumption functions

Author

Listed:
  • Toda, Alexis Akira

Abstract

Carroll and Kimball (1996) have shown that, in the class of utility functions that are strictly increasing, strictly concave, and have nonnegative third derivatives, hyperbolic absolute risk aversion (HARA) is sufficient for the concavity of consumption functions in general consumption-saving problems. This paper shows that HARA is necessary, implying the concavity of consumption is not a robust prediction outside the HARA class.

Suggested Citation

  • Toda, Alexis Akira, 2021. "Necessity of hyperbolic absolute risk aversion for the concavity of consumption functions," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    • Handle: RePEc:eee:mateco:v:94:y:2021:i:c:s0304406820301373
    DOI: 10.1016/j.jmateco.2020.102460
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406820301373
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2020.102460?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. Gong, Liutang & Zhong, Ruquan & Zou, Heng-fu, 2012. "On the concavity of the consumption function with the time varying discount rate," Economics Letters, Elsevier, vol. 117(1), pages 99-101.
    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. Carroll, Christopher D. & Holm, Martin B. & Kimball, Miles S., 2021. "Liquidity constraints and precautionary saving," Journal of Economic Theory, Elsevier, vol. 195(C).
    4. Carroll, Christopher D & Kimball, Miles S, 1996. "On the Concavity of the Consumption Function," Econometrica, Econometric Society, vol. 64(4), pages 981-992, July.
    5. Dan Cao & Iván Werning, 2018. "Saving and Dissaving With Hyperbolic Discounting," Econometrica, Econometric Society, vol. 86(3), pages 805-857, May.
    6. Shin-Ichi Nishiyama & Ryo Kato, 2011. "On the Concavity of the Consumption Function with a Quadratic Utility under Liquidity Constraints," TERG Discussion Papers 274, Graduate School of Economics and Management, Tohoku University.
    7. Stephen Morris & Andrew Postlewaite, 2020. "Observational Implications of Non-Exponential Discounting," Revue économique, Presses de Sciences-Po, vol. 71(2), pages 313-321.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. 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.
    2. Jeanne Commault, 2024. "Heterogeneity in MPC Beyond Liquidity Constraints: The Role of Permanent Earnings," Working Papers hal-03870685, HAL.
    3. Ma, Qingyin & Toda, Alexis Akira, 2022. "Asymptotic linearity of consumption functions and computational efficiency," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    4. Liu, Haoyu & Li, Lun, 2023. "On the concavity of consumption function under habit formation," Journal of Mathematical Economics, Elsevier, vol. 106(C).

    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. Broer, Tobias, 2020. "Consumption insurance over the business cycle," CEPR Discussion Papers 14579, C.E.P.R. Discussion Papers.
    2. Liu, Haoyu & Li, Lun, 2023. "On the concavity of consumption function under habit formation," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    3. Giovanni L. Violante & Greg Kaplan, 2022. "The Marginal Propensity to Consume in Heterogeneous Agent Models," Annual Review of Economics, Annual Reviews, vol. 14(1), pages 747-775, August.
    4. Mark Huggett, 2004. "Precautionary Wealth Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 769-781.
    5. Alfonso Palacio Vera, 2008. "The "New consensus"and the Post-Keynesian approach to the analysis of liquidity traps," Documentos de trabajo de la Facultad de Ciencias Económicas y Empresariales 08-03, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales.
    6. Carroll, Christopher D., 2009. "Precautionary saving and the marginal propensity to consume out of permanent income," Journal of Monetary Economics, Elsevier, vol. 56(6), pages 780-790, September.
    7. Joachim Hubmer & Per Krusell & Anthony A. Smith Jr., 2020. "Sources of US Wealth Inequality: Past, Present, and Future," NBER Chapters, in: NBER Macroeconomics Annual 2020, volume 35, pages 391-455, National Bureau of Economic Research, Inc.
    8. Emilio Fernandez-Corugedo, 2002. "Soft liquidity constraints and precautionary saving," Bank of England working papers 158, Bank of England.
    9. Clare Kelly & Gauthier Lanot, 2003. "Analytical Results for a Model of Periodic Consumption," Keele Economics Research Papers KERP 2003/01, Centre for Economic Research, Keele University.
    10. Maude Toussaint‐Comeau, 2021. "Liquidity constraints and debts: Implications for the saving behavior of the middle class," Contemporary Economic Policy, Western Economic Association International, vol. 39(3), pages 479-493, July.
    11. Ma, Qingyin & Toda, Alexis Akira, 2022. "Asymptotic linearity of consumption functions and computational efficiency," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    12. Raül Santaeulàlia-Llopis & Yu Zheng, 2018. "The Price of Growth: Consumption Insurance in China 1989–2009," American Economic Journal: Macroeconomics, American Economic Association, vol. 10(4), pages 1-35, October.
    13. Savoia, Ettore, 2023. "The effects of labor income risk heterogeneity on the marginal propensity to consume," Working Paper Series 2866, European Central Bank.
    14. D'Orazio, Paola, 2019. "Income inequality, consumer debt, and prudential regulation: An agent-based approach to study the emergence of crises and financial instability," Economic Modelling, Elsevier, vol. 82(C), pages 308-331.
    15. Helge Braun & Winfried Koeniger, 2007. "On the role of market insurance in a dynamic model," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 32(1), pages 61-90, June.
    16. Lee, Jeong-Joon & Sawada, Yasuyuki, 2010. "Precautionary saving under liquidity constraints: Evidence from rural Pakistan," Journal of Development Economics, Elsevier, vol. 91(1), pages 77-86, January.
    17. Cao, Dan, 2020. "Recursive equilibrium in Krusell and Smith (1998)," Journal of Economic Theory, Elsevier, vol. 186(C).
    18. James Feigenbaum, 2005. "Heterogeneity vs Uncertainty in Anticipation of a Borrowing Constraint," Working Paper 230, Department of Economics, University of Pittsburgh, revised Jan 2005.
    19. Ma, Qingyin & Toda, Alexis Akira, 2021. "A theory of the saving rate of the rich," Journal of Economic Theory, Elsevier, vol. 192(C).
    20. El Anshasy, Amany A. & Bradley, Michael D., 2012. "Oil prices and the fiscal policy response in oil-exporting countries," Journal of Policy Modeling, Elsevier, vol. 34(5), pages 605-620.

    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:eee:mateco:v:94:y:2021:i:c:s0304406820301373. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    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.