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Necessity of Hyperbolic Absolute Risk Aversion for the Concavity of Consumption Functions

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  • Alexis Akira Toda

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

  • Alexis Akira Toda, 2020. "Necessity of Hyperbolic Absolute Risk Aversion for the Concavity of Consumption Functions," Papers 2009.13564, arXiv.org, revised Nov 2020.
    • Handle: RePEc:arx:papers:2009.13564
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    1. 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.
    2. Stephen Morris & Andrew Postlewaite, 2020. "Observational Implications of Non-Exponential Discounting," Revue économique, Presses de Sciences-Po, vol. 71(2), pages 313-321.
    3. 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.
    4. 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.
    5. Carroll, Christopher D & Kimball, Miles S, 1996. "On the Concavity of the Consumption Function," Econometrica, Econometric Society, vol. 64(4), pages 981-992, July.
    6. Dan Cao & Iván Werning, 2018. "Saving and Dissaving With Hyperbolic Discounting," Econometrica, Econometric Society, vol. 86(3), pages 805-857, May.
    7. Carroll, Christopher D. & Holm, Martin B. & Kimball, Miles S., 2021. "Liquidity constraints and precautionary saving," Journal of Economic Theory, Elsevier, vol. 195(C).
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    2. Jeanne Commault, 2025. "Heterogeneity in MPC Beyond Liquidity Constraints: The Role of Permanent Earnings," Sciences Po Economics Discussion Papers hal-03870685, HAL.
    3. Liu, Haoyu & Li, Lun, 2023. "On the concavity of consumption function under habit formation," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    4. Charles E. Phelps, 2024. "A user’s guide to economic utility functions," Journal of Risk and Uncertainty, Springer, vol. 69(3), pages 235-280, December.
    5. Ma, Qingyin & Toda, Alexis Akira, 2022. "Asymptotic linearity of consumption functions and computational efficiency," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    6. 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.

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