IDEAS home Printed from https://ideas.repec.org/a/wly/emetrp/v92y2024i4p995-1031.html
   My bibliography  Save this article

Monotone Additive Statistics

Author

Listed:
  • Xiaosheng Mu
  • Luciano Pomatto
  • Philipp Strack
  • Omer Tamuz

Abstract

The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a number of applications to models of individual and group decision‐making. These include a representation of stationary monotone time preferences, extending the work of Fishburn and Rubinstein (1982) to time lotteries. This extension offers a new perspective on risk attitudes toward time, as well as on the aggregation of multiple discount factors. We also offer a novel class of non‐expected utility preferences over gambles which satisfy invariance to background risk as well as betweenness, but are versatile enough to capture mixed risk attitudes.

Suggested Citation

  • Xiaosheng Mu & Luciano Pomatto & Philipp Strack & Omer Tamuz, 2024. "Monotone Additive Statistics," Econometrica, Econometric Society, vol. 92(4), pages 995-1031, July.
    • Handle: RePEc:wly:emetrp:v:92:y:2024:i:4:p:995-1031
    DOI: 10.3982/ECTA19967
    as

    Download full text from publisher

    File URL: https://doi.org/10.3982/ECTA19967
    Download Restriction: no
    File URL: https://libkey.io/10.3982/ECTA19967?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
    ---><---

    References listed on IDEAS

    as
    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. Matthew O. Jackson & Leeat Yariv, 2014. "Present Bias and Collective Dynamic Choice in the Lab," American Economic Review, American Economic Association, vol. 104(12), pages 4184-4204, December.
    3. Simone Cerreia‐Vioglio & David Dillenberger & Pietro Ortoleva, 2015. "Cautious Expected Utility and the Certainty Effect," Econometrica, Econometric Society, vol. 83, pages 693-728, March.
    4. Stéphane Zuber, 2011. "Can Social Preferences be both Stationary and Paretian?," Annals of Economics and Statistics, GENES, issue 101-102, pages 347-360.
    5. Yoram Halevy, 2015. "Time Consistency: Stationarity and Time Invariance," Econometrica, Econometric Society, vol. 83, pages 335-352, January.
    6. Levon Barseghyan & Francesca Molinari & Ted O'Donoghue & Joshua C. Teitelbaum, 2018. "Estimating Risk Preferences in the Field," Journal of Economic Literature, American Economic Association, vol. 56(2), pages 501-564, June.
    7. Sebastian Ebert, 2021. "Prudent Discounting: Experimental Evidence On Higher Order Time Risk Preferences," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(4), pages 1489-1511, November.
    8. Cerreia-Vioglio, Simone & Dillenberger, David & Ortoleva, Pietro, 2020. "An explicit representation for disappointment aversion and other betweenness preferences," Theoretical Economics, Econometric Society, vol. 15(4), November.
    9. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56(4), pages 279-279.
    10. Zhou, Lin, 1997. "Harsanyi's Utilitarianism Theorems: General Societies," Journal of Economic Theory, Elsevier, vol. 72(1), pages 198-207, January.
    11. 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.
    12. Matthew Rabin & Georg Weizsacker, 2009. "Narrow Bracketing and Dominated Choices," American Economic Review, American Economic Association, vol. 99(4), pages 1508-1543, September.
    13. Luciano Pomatto & Philipp Strack & Omer Tamuz, 2020. "Stochastic Dominance under Independent Noise," Journal of Political Economy, University of Chicago Press, vol. 128(5), pages 1877-1900.
    14. Dekel, Eddie, 1986. "An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom," Journal of Economic Theory, Elsevier, vol. 40(2), pages 304-318, December.
    15. repec:adr:anecst:y:2011:i:101-102:p:17 is not listed on IDEAS
    16. Matthew O. Jackson & Leeat Yariv, 2015. "Collective Dynamic Choice: The Necessity of Time Inconsistency," American Economic Journal: Microeconomics, American Economic Association, vol. 7(4), pages 150-178, 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. Xiaosheng Mu & Luciano Pomatto & Philipp Strack & Omer Tamuz, 2021. "Monotone Additive Statistics," Working Papers 2021-36, Princeton University. Economics Department..
    2. Xiaosheng Mu & Luciano Pomatto & Philipp Strack & Omer Tamuz, 2021. "Monotone additive statistics," Papers 2102.00618, arXiv.org, revised Apr 2024.
    3. Feng, Tangren & Ke, Shaowei & McMillan, Andrew, 2022. "Utilitarianism and social discounting with countably many generations," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    4. Tangren Feng & Shaowei Ke, 2018. "Social Discounting and Intergenerational Pareto," Econometrica, Econometric Society, vol. 86(5), pages 1537-1567, September.
    5. Laurent Denant-Boemont & Enrico Diecidue & Olivier l’Haridon, 2017. "Patience and time consistency in collective decisions," Experimental Economics, Springer;Economic Science Association, vol. 20(1), pages 181-208, March.
    6. Luis A. Alcala, 2016. "On the time consistency of collective preferences," Papers 1607.02688, arXiv.org, revised Jul 2018.
    7. 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).
    8. Antony Millner & Geoffrey Heal, 2015. "Collective intertemporal choice: time consistency vs. time invariance," GRI Working Papers 220, Grantham Research Institute on Climate Change and the Environment.
    9. Mikhail Pakhnin, 2021. "Collective Choice with Heterogeneous Time Preferences," CESifo Working Paper Series 9141, CESifo.
    10. Anchugina, Nina & Ryan, Matthew & Slinko, Arkadii, 2019. "Mixing discount functions: Implications for collective time preferences," Mathematical Social Sciences, Elsevier, vol. 102(C), pages 1-14.
    11. Uri Gneezy & Yoram Halevy & Brian Hall & Theo Offerman & Jeroen van de Ven, 2024. "How Real is Hypothetical? A High-Stakes Test of the Allais Paradox," Working Papers tecipa-783, University of Toronto, Department of Economics.
    12. Craig S. Webb, 2024. "Dynamic preference foundations of expected exponentially-discounted utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(4), pages 921-940, June.
    13. Millner, Antony & Heal, Geoffrey, 2018. "Time consistency and time invariance in collective intertemporal choice," Journal of Economic Theory, Elsevier, vol. 176(C), pages 158-169.
    14. Glätzle-Rützler, Daniela & Lergetporer, Philipp & Sutter, Matthias, 2021. "Collective intertemporal decisions and heterogeneity in groups," Games and Economic Behavior, Elsevier, vol. 130(C), pages 131-147.
    15. Gonzalez, Francisco M. & Lazkano, Itziar & Smulders, Sjak A., 2018. "Intergenerational altruism with future bias," Journal of Economic Theory, Elsevier, vol. 178(C), pages 436-454.
    16. 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).
    17. Christopher P. Chambers & Federico Echenique & Alan D. Miller, 2023. "Decreasing Impatience," American Economic Journal: Microeconomics, American Economic Association, vol. 15(3), pages 527-551, August.
    18. Antony Millner, 2016. "Heterogeneous intergenerational altruism," GRI Working Papers 226, Grantham Research Institute on Climate Change and the Environment.
    19. 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.
    20. Jean Baccelli, 2018. "Risk attitudes in axiomatic decision theory: a conceptual perspective," Theory and Decision, Springer, vol. 84(1), pages 61-82, January.

    More about this item

    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:wly:emetrp:v:92:y:2024:i:4:p:995-1031. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.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.