IDEAS home Printed from https://ideas.repec.org/p/pen/papers/18-020.html
   My bibliography  Save this paper

Stochastic Impatience and the Separation of Time and Risk Preferences

Author

Listed:
  • David Dillenberger

    (Department of Economics, University of Pennsylvania)

  • Daniel Gottlieb

    (Department of Economics, Washington University in St. Louis)

  • Pietro Ortoleva

    (Department of Economics, Princeton University)

Abstract

We study how the separation between time and risk preferences relates to a new behavioral property that generalizes impatience to stochastic environments: Stochastic Impatience. We show that Stochastic Impatience holds if and only if risk aversion is \not too high" relative to the inverse elasticity of intertemporal substitution. This result has implications for many known models. For example, in the models of Epstein and Zin (1989) and Hansen and Sargent (1995), Stochastic Impatience is violated for all commonly used parameters. If Stochastic Impatience is taken normatively, this suggests a limit on the amount of separation between time and risk preference; otherwise, it provides a simple one-question test for it.

Suggested Citation

  • David Dillenberger & Daniel Gottlieb & Pietro Ortoleva, 2018. "Stochastic Impatience and the Separation of Time and Risk Preferences," PIER Working Paper Archive 18-020, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 08 Sep 2018.
    • Handle: RePEc:pen:papers:18-020
    as

    Download full text from publisher

    File URL: https://economics.sas.upenn.edu/system/files/working-papers/18-020%20PIER%20Paper%20Submission.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Alex Edmans & Xavier Gabaix, 2011. "Tractability in Incentive Contracting," The Review of Financial Studies, Society for Financial Studies, vol. 24(9), pages 2865-2894.
    2. Simone Cerreia‐Vioglio & David Dillenberger & Pietro Ortoleva, 2015. "Cautious Expected Utility and the Certainty Effect," Econometrica, Econometric Society, vol. 83, pages 693-728, March.
    3. Bansal, Ravi & Kiku, Dana & Yaron, Amir, 2016. "Risks for the long run: Estimation with time aggregation," Journal of Monetary Economics, Elsevier, vol. 82(C), pages 52-69.
    4. Paolo Ghirardato & Massimo Marinacci, 2001. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 864-890, November.
    5. Lars Peter Hansen & Thomas J Sargent, 2014. "Doubts or Variability?," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 7, pages 217-256, World Scientific Publishing Co. Pte. Ltd..
    6. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    7. Orazio P. Attanasio & Guglielmo Weber, 2010. "Consumption and Saving: Models of Intertemporal Allocation and Their Implications for Public Policy," Journal of Economic Literature, American Economic Association, vol. 48(3), pages 693-751, September.
    8. Campbell, John Y., 1999. "Asset prices, consumption, and the business cycle," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 19, pages 1231-1303, Elsevier.
    9. Larry G. Epstein & Emmanuel Farhi & Tomasz Strzalecki, 2014. "How Much Would You Pay to Resolve Long-Run Risk?," American Economic Review, American Economic Association, vol. 104(9), pages 2680-2697, September.
    10. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    11. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    12. Tomasz Strzalecki, 2013. "Temporal Resolution of Uncertainty and Recursive Models of Ambiguity Aversion," Econometrica, Econometric Society, vol. 81(3), pages 1039-1074, May.
    13. Larry G. Epstein & Martin Schneider, 2010. "Ambiguity and Asset Markets," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 315-346, December.
    14. David K. Backus & Bryan R. Routledge & Stanley E. Zin, 2005. "Exotic Preferences for Macroeconomists," NBER Chapters, in: NBER Macroeconomics Annual 2004, Volume 19, pages 319-414, National Bureau of Economic Research, Inc.
    15. Fulvio Ortu & Andrea Tamoni & Claudio Tebaldi, 2013. "Long-Run Risk and the Persistence of Consumption Shocks," The Review of Financial Studies, Society for Financial Studies, vol. 26(11), pages 2876-2915.
    16. Scott F. Richard, 1975. "Multivariate Risk Aversion, Utility Independence and Separable Utility Functions," Management Science, INFORMS, vol. 22(1), pages 12-21, September.
    17. TallariniJr., Thomas D., 2000. "Risk-sensitive real business cycles," Journal of Monetary Economics, Elsevier, vol. 45(3), pages 507-532, June.
    18. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-686, May.
    19. James Andreoni & Charles Sprenger, 2012. "Risk Preferences Are Not Time Preferences," American Economic Review, American Economic Association, vol. 102(7), pages 3357-3376, December.
    20. Antoine Bommier, 2007. "Risk Aversion, Intertemporal Elasticity of Substitution and Correlation Aversion," Economics Bulletin, AccessEcon, vol. 4(29), pages 1-8.
    21. Jonathan Gruber, 2013. "A Tax-Based Estimate of the Elasticity of Intertemporal Substitution," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 1-20.
    22. Jose Apesteguia & Miguel Ángel Ballester & Angelo Gutierrez, 2019. "Random models for the joint treatment of risk and time preferences," Economics Working Papers 1671, Department of Economics and Business, Universitat Pompeu Fabra.
    23. Selden, Larry, 1978. "A New Representation of Preferences over "Certain A Uncertain" Consumption Pairs: The "Ordinal Certainty Equivalent" Hypothesis," Econometrica, Econometric Society, vol. 46(5), pages 1045-1060, September.
    24. Emi Nakamura & Dmitriy Sergeyev & Jón Steinsson, 2017. "Growth-Rate and Uncertainty Shocks in Consumption: Cross-Country Evidence," American Economic Journal: Macroeconomics, American Economic Association, vol. 9(1), pages 1-39, January.
    25. Dean, Mark & Ortoleva, Pietro, 2017. "Allais, Ellsberg, and preferences for hedging," Theoretical Economics, Econometric Society, vol. 12(1), January.
    26. Patrick DeJarnette & David Dillenberger & Daniel Gottlieb & Pietro Ortoleva, 2020. "Time Lotteries and Stochastic Impatience," Econometrica, Econometric Society, vol. 88(2), pages 619-656, March.
    27. Peter P. Wakker & Sylvia J. T. Jansen & Anne M. Stiggelbout, 2004. "Anchor Levels as a New Tool for the Theory and Measurement of Multiattribute Utility," Decision Analysis, INFORMS, vol. 1(4), pages 217-234, December.
    28. Kihlstrom, Richard E. & Mirman, Leonard J., 1974. "Risk aversion with many commodities," Journal of Economic Theory, Elsevier, vol. 8(3), pages 361-388, July.
    29. Emi Nakamura & Jón Steinsson & Robert Barro & José Ursúa, 2013. "Crises and Recoveries in an Empirical Model of Consumption Disasters," American Economic Journal: Macroeconomics, American Economic Association, vol. 5(3), pages 35-74, July.
    30. Segal, Uzi & Spivak, Avia, 1990. "First order versus second order risk aversion," Journal of Economic Theory, Elsevier, vol. 51(1), pages 111-125, June.
    31. Robert J. Barro, 2009. "Rare Disasters, Asset Prices, and Welfare Costs," American Economic Review, American Economic Association, vol. 99(1), pages 243-264, March.
    32. Larry G. Epstein, 1999. "A Definition of Uncertainty Aversion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(3), pages 579-608.
    33. Antoine Bommier & Asen Kochov & François Le Grand, 2017. "On Monotone Recursive Preferences," Econometrica, Econometric Society, vol. 85, pages 1433-1466, September.
    34. Chew, Soo Hong & Epstein, Larry G., 1990. "Nonexpected utility preferences in a temporal framework with an application to consumption-savings behaviour," Journal of Economic Theory, Elsevier, vol. 50(1), pages 54-81, February.
    35. Ric Colacito & Max Croce & Steven Ho & Philip Howard, 2018. "BKK the EZ Way: International Long-Run Growth News and Capital Flows," American Economic Review, American Economic Association, vol. 108(11), pages 3416-3449, November.
    36. Daniel Garrett & Alessandro Pavan, 2014. "Dynamic Managerial Compensation: On the Optimality of Seniority-based Schemes," Discussion Papers 1579, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    37. repec:bla:jfinan:v:59:y:2004:i:4:p:1481-1509 is not listed on IDEAS
    38. 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.
    39. Hansen, Lars Peter & Heaton, John & Lee, Junghoon & Roussanov, Nikolai, 2007. "Intertemporal Substitution and Risk Aversion," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 61, Elsevier.
    40. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
    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. Lorenzo Maria Stanca, 2023. "Recursive Preferences, Correlation Aversion, and the Temporal Resolution of Uncertainty," Papers 2304.04599, arXiv.org, revised Jul 2023.
    2. Svetlana Pashchenko & Ponpoje Porapakkarm, 2022. "Value of life and annuity demand," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(2), pages 371-396, June.
    3. Patrick DeJarnette & David Dillenberger & Daniel Gottlieb & Pietro Ortoleva, 2020. "Time Lotteries and Stochastic Impatience," Econometrica, Econometric Society, vol. 88(2), pages 619-656, March.
    4. Stanca Lorenzo, 2023. "Recursive preferences, correlation aversion, and the temporal resolution of uncertainty," Working papers 080, Department of Economics, Social Studies, Applied Mathematics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino.
    5. Minghao Pan, 2022. "Risk and Intertemporal Preferences over Time Lotteries," Papers 2209.01790, arXiv.org.
    6. Al-Najjar, Nabil I. & Pomatto, Luciano, 2020. "Aggregate risk and the Pareto principle," Journal of Economic Theory, Elsevier, vol. 189(C).
    7. Lorenzo Stanca, 2023. "Recursive Preferences, Correlation Aversion, and the Temporal Resolution of Uncertainty," Carlo Alberto Notebooks 693 JEL Classification: C, Collegio Carlo Alberto.
    8. Mu Zhang, 2021. "A Theory of Choice Bracketing under Risk," Papers 2102.07286, arXiv.org, revised Aug 2021.

    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. Patrick DeJarnette & David Dillenberger & Daniel Gottlieb & Pietro Ortoleva, 2020. "Time Lotteries and Stochastic Impatience," Econometrica, Econometric Society, vol. 88(2), pages 619-656, March.
    2. Mu Zhang, 2021. "A Theory of Choice Bracketing under Risk," Papers 2102.07286, arXiv.org, revised Aug 2021.
    3. Lorenzo Maria Stanca, 2023. "Recursive Preferences, Correlation Aversion, and the Temporal Resolution of Uncertainty," Papers 2304.04599, arXiv.org, revised Jul 2023.
    4. Lorenzo Stanca, 2023. "Recursive Preferences, Correlation Aversion, and the Temporal Resolution of Uncertainty," Carlo Alberto Notebooks 693 JEL Classification: C, Collegio Carlo Alberto.
    5. Stanca Lorenzo, 2023. "Recursive preferences, correlation aversion, and the temporal resolution of uncertainty," Working papers 080, Department of Economics, Social Studies, Applied Mathematics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino.
    6. Patrick DeJarnette & David Dillenberger & Daniel Gottlieb & Pietro Ortoleva, 2014. "Time Lotteries, Second Version," PIER Working Paper Archive 15-026v2, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 12 Jan 2018.
    7. Patrick DeJarnette & David Dillenberger & Daniel Gottlieb & Pietro Ortoleva, 2015. "Time Lotteries," PIER Working Paper Archive 15-026, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 31 Jul 2015.
    8. Meyer-Gohde, Alexander, 2019. "Generalized entropy and model uncertainty," Journal of Economic Theory, Elsevier, vol. 183(C), pages 312-343.
    9. Nengjiu Ju & Jianjun Miao, 2012. "Ambiguity, Learning, and Asset Returns," Econometrica, Econometric Society, vol. 80(2), pages 559-591, March.
    10. Thomas J. Sargent & John Stachurski, 2024. "Dynamic Programming: Finite States," Papers 2401.10473, arXiv.org.
    11. Claudio Campanale & Rui Castro & Gian Luca Clementi, 2010. "Asset Pricing in a Production Economy with Chew-Dekel Preferences," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 13(2), pages 379-402, April.
    12. Meissner, Thomas & Pfeiffer, Philipp, 2022. "Measuring preferences over the temporal resolution of consumption uncertainty," Journal of Economic Theory, Elsevier, vol. 200(C).
    13. Jinrui Pan & Craig S. Webb & Horst Zank, 2019. "Delayed probabilistic risk attitude: a parametric approach," Theory and Decision, Springer, vol. 87(2), pages 201-232, September.
    14. Dillenberger, David & Gottlieb, Daniel & Ortoleva, Pietro, 0. "Stochastic impatience and the separation of time and risk preferences," Theoretical Economics, Econometric Society.
    15. Luca De Gennaro Aquino & Sascha Desmettre & Yevhen Havrylenko & Mogens Steffensen, 2024. "Equilibrium control theory for Kihlstrom-Mirman preferences in continuous time," Papers 2407.16525, arXiv.org, revised Oct 2024.
    16. Bommier, Antoine & Lanz, Bruno & Zuber, Stéphane, 2015. "Models-as-usual for unusual risks? On the value of catastrophic climate change," Journal of Environmental Economics and Management, Elsevier, vol. 74(C), pages 1-22.
    17. Larry G. Epstein & Emmanuel Farhi & Tomasz Strzalecki, 2014. "How Much Would You Pay to Resolve Long-Run Risk?," American Economic Review, American Economic Association, vol. 104(9), pages 2680-2697, September.
    18. Mohammed Abdellaoui & Enrico Diecidue & Emmanuel Kemel & Ayse Onculer, 2022. "Temporal Risk: Utility vs. Probability Weighting," Management Science, INFORMS, vol. 68(7), pages 5162-5186, July.
    19. Stephen L. Cheung, 2020. "Eliciting utility curvature in time preference," Experimental Economics, Springer;Economic Science Association, vol. 23(2), pages 493-525, June.
    20. Zvi Safra & Uzi Segal, 2005. "Are Universal Preferences Possible? Calibration Results for Non-Expected Utility Theories," Boston College Working Papers in Economics 633, Boston College Department of Economics.

    More about this item

    Keywords

    Stochastic Impatience; Epstein and Zin preferences; Separation of Risk and Time preferences; Risk Sensitive Preferences; Non-Expected Utility;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • E7 - Macroeconomics and Monetary Economics - - Macro-Based Behavioral Economics

    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:pen:papers:18-020. 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: Administrator (email available below). General contact details of provider: https://edirc.repec.org/data/deupaus.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.