IDEAS home Printed from https://ideas.repec.org/a/spr/jopoec/v35y2022i3d10.1007_s00148-021-00824-7.html
   My bibliography  Save this article

Hyperbolic discounting in an intergenerational model with altruistic parents

Author

Listed:
  • Jia Cao

    (Renmin University of China)

  • Minghao Li

    (New Mexico State University)

Abstract

Hyperbolic utility discounting has emerged as a leading alternative to exponential discounting because it can explain time-inconsistent behaviors. Intuitively, hyperbolic discounting should play a crucial role in intergenerational models characterized by intertemporal trade-offs. In this paper, we incorporate hyperbolic discounting into a dynamic model in which parents are altruistic towards their children. Agents live for four periods and choose levels of consumption, fertility, investment in their children’s human capital, and bequests to maximize discounted utility. In the steady state, hyperbolic discounting decreases fertility, increases human capital investment, and shifts consumption towards younger ages. These effects are more pronounced in the time-consistent problem (in which agents cannot commit to a course of action) than in the commitment problem, which can be interpreted as realized and intended actions, respectively. The preference-based discrepancy between intended fertility and realized fertility has important implications for the empirical literature that compares the two.

Suggested Citation

  • Jia Cao & Minghao Li, 2022. "Hyperbolic discounting in an intergenerational model with altruistic parents," Journal of Population Economics, Springer;European Society for Population Economics, vol. 35(3), pages 989-1005, July.
    • Handle: RePEc:spr:jopoec:v:35:y:2022:i:3:d:10.1007_s00148-021-00824-7
    DOI: 10.1007/s00148-021-00824-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00148-021-00824-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00148-021-00824-7?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Christine A. Bachrach & S. Philip Morgan, 2013. "A Cognitive–Social Model of Fertility Intentions," Population and Development Review, The Population Council, Inc., vol. 39(3), pages 459-485, September.
    2. Isabel Günther & Kenneth Harttgen, 2016. "Desired Fertility and Number of Children Born Across Time and Space," Demography, Springer;Population Association of America (PAA), vol. 53(1), pages 55-83, February.
    3. Wigniolle, Bertrand, 2013. "Fertility in the absence of self-control," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 71-86.
    4. Pritchett, Lant H. & DEC, 1994. "Desired fertility and the impact of population policies," Policy Research Working Paper Series 1273, The World Bank.
    5. Matthew Rabin & Ted O'Donoghue, 1999. "Doing It Now or Later," American Economic Review, American Economic Association, vol. 89(1), pages 103-124, March.
    6. Oded Galor & Joseph Zeira, 1993. "Income Distribution and Macroeconomics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(1), pages 35-52.
    7. Gary S. Becker & H. Gregg Lewis, 1974. "Interaction between Quantity and Quality of Children," NBER Chapters, in: Economics of the Family: Marriage, Children, and Human Capital, pages 81-90, National Bureau of Economic Research, Inc.
    8. Matthias Doepke & Michèle Tertilt, 2018. "Women's Empowerment, the Gender Gap in Desired Fertility, and Fertility Outcomes in Developing Countries," AEA Papers and Proceedings, American Economic Association, vol. 108, pages 358-362, May.
    9. Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
    10. Gary S. Becker & Robert J. Barro, 1988. "A Reformulation of the Economic Theory of Fertility," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 103(1), pages 1-25.
    11. Diamond, Peter & Koszegi, Botond, 2003. "Quasi-hyperbolic discounting and retirement," Journal of Public Economics, Elsevier, vol. 87(9-10), pages 1839-1872, September.
    12. Wang, Mei & Rieger, Marc Oliver & Hens, Thorsten, 2016. "How time preferences differ: Evidence from 53 countries," Journal of Economic Psychology, Elsevier, vol. 52(C), pages 115-135.
    13. Ikeda, Shinsuke & Kang, Myong-Il & Ohtake, Fumio, 2010. "Hyperbolic discounting, the sign effect, and the body mass index," Journal of Health Economics, Elsevier, vol. 29(2), pages 268-284, March.
    14. Matthias Wrede, 2011. "Hyperbolic discounting and fertility," Journal of Population Economics, Springer;European Society for Population Economics, vol. 24(3), pages 1053-1070, July.
    15. Eva Beaujouan & Caroline Berghammer, 2019. "The Gap Between Lifetime Fertility Intentions and Completed Fertility in Europe and the United States: A Cohort Approach," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 38(4), pages 507-535, August.
    16. Dan Cao & Iván Werning, 2018. "Saving and Dissaving With Hyperbolic Discounting," Econometrica, Econometric Society, vol. 86(3), pages 805-857, May.
    17. van der Pol, Marjon & Cairns, John, 2002. "A comparison of the discounted utility model and hyperbolic discounting models in the case of social and private intertemporal preferences for health," Journal of Economic Behavior & Organization, Elsevier, vol. 49(1), pages 79-96, September.
    18. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 443-478.
    19. Alicia Adsera, 2006. "An Economic Analysis of the Gap Between Desired and Actual Fertility: The Case of Spain," Review of Economics of the Household, Springer, vol. 4(1), pages 75-95, March.
    20. Paul A. Samuelson, 1937. "A Note on Measurement of Utility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 4(2), pages 155-161.
    21. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 185-199.
    22. Elizabeth Thomson & Elaine McDonald & Larry Bumpass, 1990. "Fertility desires and fertility: Hers, his, and theirs," Demography, Springer;Population Association of America (PAA), vol. 27(4), pages 579-588, November.
    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. Galizzi, Matteo M. & Miraldo, Marisa & Stavropoulou, Charitini & van der Pol, Marjon, 2016. "Doctor–patient differences in risk and time preferences: A field experiment," Journal of Health Economics, Elsevier, vol. 50(C), pages 171-182.
    2. Drouhin, Nicolas, 2020. "Non-stationary additive utility and time consistency," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 1-14.
    3. Jean-Pierre Drugeon & Bertrand Wigniolle, 2021. "On Markovian collective choice with heterogeneous quasi-hyperbolic discounting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(4), pages 1257-1296, November.
    4. Matthias Wrede, 2011. "Hyperbolic discounting and fertility," Journal of Population Economics, Springer;European Society for Population Economics, vol. 24(3), pages 1053-1070, July.
    5. Schaewitz, Johannes & Wang, Mei & Rieger, Marc Oliver, 2022. "Culture and Institutions: Long-lasting effects of communism on risk and time preferences of individuals in Europe," Journal of Economic Behavior & Organization, Elsevier, vol. 202(C), pages 785-829.
    6. Han Bleichrodt & Yu Gao & Kirsten I. M. Rohde, 2016. "A measurement of decreasing impatience for health and money," Journal of Risk and Uncertainty, Springer, vol. 52(3), pages 213-231, June.
    7. Weinschenk, Philipp, 2021. "On the benefits of time-inconsistent preferences," Journal of Economic Behavior & Organization, Elsevier, vol. 182(C), pages 185-195.
    8. Lades, Leonhard K., 2012. "Towards an incentive salience model of intertemporal choice," Journal of Economic Psychology, Elsevier, vol. 33(4), pages 833-841.
    9. Jindrich Matousek & Tomas Havranek & Zuzana Irsova, 2022. "Individual discount rates: a meta-analysis of experimental evidence," Experimental Economics, Springer;Economic Science Association, vol. 25(1), pages 318-358, February.
    10. Uttara Balakrishnan & Johannes Haushofer & Pamela Jakiela, 2020. "How soon is now? Evidence of present bias from convex time budget experiments," Experimental Economics, Springer;Economic Science Association, vol. 23(2), pages 294-321, June.
    11. Tyson, Christopher J., 2008. "Management of a capital stock by Strotz's naive planner," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2214-2239, July.
    12. Wigniolle, Bertrand, 2013. "Fertility in the absence of self-control," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 71-86.
    13. Palenik Marcin, 2021. "The effect of uncertainty on negative discounting," International Journal of Management and Economics, Warsaw School of Economics, Collegium of World Economy, vol. 57(4), pages 287-298, December.
    14. George Ainslie, 2012. "Pure hyperbolic discount curves predict “eyes open” self-control," Theory and Decision, Springer, vol. 73(1), pages 3-34, July.
    15. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2022. "Time-consistent equilibria in dynamic models with recursive payoffs and behavioral discounting," Journal of Economic Theory, Elsevier, vol. 204(C).
    16. Musau, Andrew, 2009. "Modeling Alternatives to Exponential Discounting," MPRA Paper 16416, University Library of Munich, Germany.
    17. Bård Harstad, 2013. "Investment Policy for Time-Inconsistent Discounters," CESifo Working Paper Series 4546, CESifo.
    18. Tim Friehe & Christoph Rößler & Xiaoge Dong, 2020. "Liability for Third-Party Harm When Harm-Inflicting Consumers Are Present Biased," American Law and Economics Review, Oxford University Press, vol. 22(1), pages 75-104.
    19. Andrew Musau, 2014. "Hyperbolic discount curves: a reply to Ainslie," Theory and Decision, Springer, vol. 76(1), pages 9-30, January.
    20. Miranda, Alfonso & Trivedi, Pravin K., 2020. "Econometric Models of Fertility," IZA Discussion Papers 13357, Institute of Labor Economics (IZA).

    More about this item

    Keywords

    Hyperbolic discounting; Fertility; Human capital; Intergenerational model;
    All these keywords.

    JEL classification:

    • J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends, Macroeconomic Effects, and Forecasts
    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education
    • D14 - Microeconomics - - Household Behavior - - - Household Saving; Personal Finance
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    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:spr:jopoec:v:35:y:2022:i:3:d:10.1007_s00148-021-00824-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.