IDEAS home Printed from https://ideas.repec.org/p/kyo/wpaper/636.html
   My bibliography  Save this paper

Complete Monotonicity of the Representative Consumer's Discount Factor

Author

Listed:
  • Chiaki Hara

    (Institute of Economic Research, Kyoto University)

Abstract

A univariate real-valued function is said to be completely monotone if it takes positive values and alternate the signs of its higher order derivatives, starting from everywhere negative first derivatives. We prove that the representative consumer's discount factor of a continuous-time economy under uncertainty is a power function of some completely monotone function of time satisfying certain boundary conditions if and only if it may be derived from a group of consumers having constant and equal relative risk aversion, and constant and yet possibly unequal discount rates.

Suggested Citation

  • Chiaki Hara, 2007. "Complete Monotonicity of the Representative Consumer's Discount Factor," KIER Working Papers 636, Kyoto University, Institute of Economic Research.
    • Handle: RePEc:kyo:wpaper:636
    as

    Download full text from publisher

    File URL: http://www.kier.kyoto-u.ac.jp/DP/DP636.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Townsend, Robert M, 1994. "Risk and Insurance in Village India," Econometrica, Econometric Society, vol. 62(3), pages 539-591, May.
    2. Hara, Chiaki & Huang, James & Kuzmics, Christoph, 2007. "Representative consumer's risk aversion and efficient risk-sharing rules," Journal of Economic Theory, Elsevier, vol. 137(1), pages 652-672, November.
    3. Ogaki, Masao & Zhang, Qiang, 2001. "Decreasing Relative Risk Aversion and Tests of Risk Sharing," Econometrica, Econometric Society, vol. 69(2), pages 515-526, March.
    4. Chiaki Hara, 2006. "Heterogeneous Risk Attitudes In A Continuous‐Time Model," The Japanese Economic Review, Japanese Economic Association, vol. 57(3), pages 377-405, September.
    5. Hara, Chiaki & 原, 千秋 & ハラ, チアキ, 2008. "Heterogeneous Impatience in a Continuous-Time Model," PIE/CIS Discussion Paper 396, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
    6. Maurizio Mazzocco & Shiv Saini, 2012. "Testing Efficient Risk Sharing with Heterogeneous Risk Preferences," American Economic Review, American Economic Association, vol. 102(1), pages 428-468, February.
    7. Robert B. Barsky & F. Thomas Juster & Miles S. Kimball & Matthew D. Shapiro, 1997. "Preference Parameters and Behavioral Heterogeneity: An Experimental Approach in the Health and Retirement Study," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 537-579.
    8. Christian Gollier & Richard Zeckhauser, 2005. "Aggregation of Heterogeneous Time Preferences," Journal of Political Economy, University of Chicago Press, vol. 113(4), pages 878-896, August.
    9. Maurizio Mazzocco & Shiv Saini, 2006. "Testing Efficient Risk Sharing with Heterogeneous Risk Preferences: Semi-parametric Tests with an Application to Village Economies," 2006 Meeting Papers 108, Society for Economic Dynamics.
    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. Chiaki Hara, 2019. "Heterogeneous Impatience of Individual Consumers and Decreasing Impatience of the Representative Consumer," KIER Working Papers 1009, Kyoto University, Institute of Economic Research.
    2. Hara, Chiaki & 原, 千秋 & ハラ, チアキ, 2008. "Heterogeneous Impatience in a Continuous-Time Model," PIE/CIS Discussion Paper 396, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
    3. Arai, Takuji & Asano, Takao & Nishide, Katsumasa, 2019. "Optimal initial capital induced by the optimized certainty equivalent," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 115-125.
    4. Chiaki Hara & Kenjiro Hirata, 2015. "Dynamic Inconsistency in Pension Fund Management," KIER Working Papers 916, Kyoto University, Institute of Economic Research.
    5. Christopher P. Chambers & Federico Echenique, 2020. "The Pareto Comparisons of a Group of Exponential Discounters," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 622-640, May.
    6. Ebert, Sebastian & Wei, Wei & Zhou, Xun Yu, 2020. "Weighted discounting—On group diversity, time-inconsistency, and consequences for investment," Journal of Economic Theory, Elsevier, vol. 189(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. Chiaki Hara, 2006. "Heterogeneous Risk Attitudes In A Continuous‐Time Model," The Japanese Economic Review, Japanese Economic Association, vol. 57(3), pages 377-405, September.
    2. Marina Pavan & Aldo Colussi, 2008. "Assessing the Impact of Public Transfers on Private Risk Sharing Arrangements. Evidence from a Randomized Experiment in Mexico," Working Papers 200807, Geary Institute, University College Dublin.
    3. Jaramillo, Fernando & Kempf, Hubert & Moizeau, Fabien, 2015. "Heterogeneity and the formation of risk-sharing coalitions," Journal of Development Economics, Elsevier, vol. 114(C), pages 79-96.
    4. Árpád Ábrahám & Sarolta Laczó, 2018. "Efficient Risk Sharing with Limited Commitment and Storage," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(3), pages 1389-1424.
    5. Tobias Broer & Tessa Bold, 2015. "Risk-Sharing in Village Economies Revisited," 2015 Meeting Papers 1232, Society for Economic Dynamics.
    6. Sawada, Yasuyuki & Nakata, Hiroyuki & Kotera, Tomoaki, 2017. "Self-Production, Friction, and Risk Sharing against Disasters: Evidence from a Developing Country," World Development, Elsevier, vol. 94(C), pages 27-37.
    7. Hara, Chiaki & Huang, James & Kuzmics, Christoph, 2007. "Representative consumer's risk aversion and efficient risk-sharing rules," Journal of Economic Theory, Elsevier, vol. 137(1), pages 652-672, November.
    8. Hara, Chiaki & 原, 千秋 & ハラ, チアキ, 2008. "Heterogeneous Impatience in a Continuous-Time Model," PIE/CIS Discussion Paper 396, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
    9. Hillesland, Marya, 2019. "Gender differences in risk behavior: An analysis of asset allocation decisions in Ghana," World Development, Elsevier, vol. 117(C), pages 127-137.
    10. Dercon, Stefan & Bold, Tessa, 2014. "Insurance companies of the poor," CEPR Discussion Papers 10278, C.E.P.R. Discussion Papers.
    11. Sam Schulhofer-Wohl, 2011. "Heterogeneity and Tests of Risk Sharing," Journal of Political Economy, University of Chicago Press, vol. 119(5), pages 925-958.
    12. Sergio Sousa, 2010. "Small-scale changes in wealth and attitudes toward risk," Discussion Papers 2010-11, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    13. Renaud Bourlès & Yann Bramoullé & Eduardo Perez‐Richet, 2017. "Altruism in Networks," Econometrica, Econometric Society, vol. 85, pages 675-689, March.
    14. Pierre Dubois & Bruno Jullien & Thierry Magnac, 2008. "Formal and Informal Risk Sharing in LDCs: Theory and Empirical Evidence," Econometrica, Econometric Society, vol. 76(4), pages 679-725, July.
    15. Laurent E. Calvet & Paolo Sodini, 2014. "Twin Picks: Disentangling the Determinants of Risk-Taking in Household Portfolios," Journal of Finance, American Finance Association, vol. 69(2), pages 867-906, April.
    16. Nagayasu, Jun, 2012. "The threshold consumption correlation-based approach to international capital mobility: Evidence from advanced and developing countries," Structural Change and Economic Dynamics, Elsevier, vol. 23(3), pages 256-263.
    17. Goh, Chor-ching & Kang, Sung Jin & Sawada, Y asuyuki, 2005. "How did Korean households cope with negative shocks from the financial crisis?," Journal of Asian Economics, Elsevier, vol. 16(2), pages 239-254, April.
    18. Bandiera, Oriana & Gulesci, Selim & Rasul, Imran & Burgess, Robin, 2009. "Community networks and poverty reduction programmes: evidence from Bangladesh," LSE Research Online Documents on Economics 58054, London School of Economics and Political Science, LSE Library.
    19. Satya R. Chakravarty & Nachiketa Chattopadhyay & Jacques Silber & Guanghua Wan, 2016. "Measuring the impact of vulnerability on the number of poor: a new methodology with empirical illustrations," Chapters, in: Jacques Silber & Guanghua Wan (ed.), The Asian ‘Poverty Miracle’, chapter 4, pages 84-117, Edward Elgar Publishing.
    20. Yasuyuki Sawada, 2017. "Disasters, Household Decisions, and Insurance Mechanisms: A Review of Evidence and a Case Study from a Developing Country in Asia," Asian Economic Policy Review, Japan Center for Economic Research, vol. 12(1), pages 18-40, January.

    More about this item

    Keywords

    Complete monotonicity; discount factor; discount rate; representative consumer; expected utility; time additivity; relative risk aversion; Bernstein's theorem.;
    All these keywords.

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    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:kyo:wpaper:636. 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: Makoto Watanabe (email available below). General contact details of provider: https://edirc.repec.org/data/iekyojp.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.