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Extreme Points of First-Order Stochastic Dominance Intervals: Theory and Applications

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Abstract

We characterize the extreme points of first-order stochastic dominance (FOSD) intervals and show how these intervals are at the heart of many topics in economics. Using knowledge of these extreme points, we characterize the distributions of posterior quantiles under a given prior, leading to an analogue of a classical result regarding the distribution of posterior means. We apply this analogue to various economic subjects, including the psychology of judgement, political economy, and Bayesian persuasion. In addition, FOSD intervals provide a common structure to security design. We use the extreme points to unify and generalize seminal results in that literature when either adverse selection or moral hazard pertains.

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  • Kai Hao Yang & Alexander K. Zentefis, 2023. "Extreme Points of First-Order Stochastic Dominance Intervals: Theory and Applications," Cowles Foundation Discussion Papers 2355, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2355
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    1. Whitmore, G A, 1970. "Third-Degree Stochastic Dominance," American Economic Review, American Economic Association, vol. 60(3), pages 457-459, June.
    2. Anne-Katrin Roesler & Balázs Szentes, 2017. "Buyer-Optimal Learning and Monopoly Pricing," American Economic Review, American Economic Association, vol. 107(7), pages 2072-2080, July.
    3. John Bradbury & W. Crain, 2005. "Legislative district configurations and fiscal policy in American States," Public Choice, Springer, vol. 125(3), pages 385-407, December.
    4. Stephen Coate & Brian Knight, 2007. "Socially Optimal Districting: A Theoretical and Empirical Exploration," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(4), pages 1409-1471.
    5. Timothy Besley & Ian Preston, 2007. "Electoral Bias and Policy Choice: Theory and Evidence," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(4), pages 1473-1510.
    6. Innes, Robert D., 1990. "Limited liability and incentive contracting with ex-ante action choices," Journal of Economic Theory, Elsevier, vol. 52(1), pages 45-67, October.
    7. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 335-346.
    8. Samuelson, William F, 1984. "Bargaining under Asymmetric Information," Econometrica, Econometric Society, vol. 52(4), pages 995-1005, July.
    9. Belayet Hossain & Panagiotis Tsigaris, 2015. "Are grade expectations rational? A classroom experiment," Education Economics, Taylor & Francis Journals, vol. 23(2), pages 199-212, April.
    10. Vijay S. Bawa, 1982. "Research Bibliography---Stochastic Dominance: A Research Bibliography," Management Science, INFORMS, vol. 28(6), pages 698-712, June.
    11. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65(2), pages 135-135.
    12. Hart, Oliver, 1995. "Firms, Contracts, and Financial Structure," OUP Catalogue, Oxford University Press, number 9780198288817.
    13. Klaus M. Schmidt, 1997. "Managerial Incentives and Product Market Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(2), pages 191-213.
    14. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    15. Gerhard Winkler, 1988. "Extreme Points of Moment Sets," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 581-587, November.
    16. Simon Loertscher & Ellen V. Muir, 2022. "Monopoly Pricing, Optimal Randomization, and Resale," Journal of Political Economy, University of Chicago Press, vol. 130(3), pages 566-635.
    17. Eduardo Borensztein & Paolo Mauro, 2004. "The case for GDP-indexed bonds [‘World income components: measuring and exploiting risk-sharing opportunities’]," Economic Policy, CEPR, CESifo, Sciences Po;CES;MSH, vol. 19(38), pages 166-216.
    18. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn.
    19. Colin F. Camerer, 1997. "Progress in Behavioral Game Theory," Journal of Economic Perspectives, American Economic Association, vol. 11(4), pages 167-188, Fall.
    20. Matthew Gentzkow & Emir Kamenica, 2016. "A Rothschild-Stiglitz Approach to Bayesian Persuasion," American Economic Review, American Economic Association, vol. 106(5), pages 597-601, May.
    21. Emir Kamenica, 2019. "Bayesian Persuasion and Information Design," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 249-272, August.
    22. repec:bla:jfinan:v:58:y:2003:i:5:p:2059-2086 is not listed on IDEAS
    23. Piotr Dworczak & Giorgio Martini, 2019. "The Simple Economics of Optimal Persuasion," Journal of Political Economy, University of Chicago Press, vol. 127(5), pages 1993-2048.
    24. Paul W. Grimes, 2002. "The Overconfident Principles of Economics Student: An Examination of a Metacognitive Skill," The Journal of Economic Education, Taylor & Francis Journals, vol. 33(1), pages 15-30, January.
    25. Peter DeMarzo & Darrell Duffie, 1999. "A Liquidity-Based Model of Security Design," Econometrica, Econometric Society, vol. 67(1), pages 65-100, January.
    26. Cho, Seok-ju & Duggan, John, 2009. "Bargaining foundations of the median voter theorem," Journal of Economic Theory, Elsevier, vol. 144(2), pages 851-868, March.
    27. SHOR, BORIS & McCARTY, NOLAN, 2011. "The Ideological Mapping of American Legislatures," American Political Science Review, Cambridge University Press, vol. 105(3), pages 530-551, August.
    28. Roland G. Fryer Jr. & Richard Holden, 2011. "Measuring the Compactness of Political Districting Plans," Journal of Law and Economics, University of Chicago Press, vol. 54(3), pages 493-535.
    29. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    30. McCarty, Nolan & Poole, Keith T. & Rosenthal, Howard, 2001. "The Hunt for Party Discipline in Congress," American Political Science Review, Cambridge University Press, vol. 95(3), pages 673-687, September.
    31. Nachman, David C & Noe, Thomas H, 1994. "Optimal Design of Securities under Asymmetric Information," The Review of Financial Studies, Society for Financial Studies, vol. 7(1), pages 1-44.
    32. Bruno Biais & Thomas Mariotti, 2005. "Strategic Liquidity Supply and Security Design," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 615-649.
    33. Erik Hoelzl & Aldo Rustichini, 2005. "Overconfident: Do You Put Your Money On It?," Economic Journal, Royal Economic Society, vol. 115(503), pages 305-318, April.
    34. Catherine Casamatta, 2003. "Financing and Advising: Optimal Financial Contracts with Venture Capitalists," Journal of Finance, American Finance Association, vol. 58(5), pages 2059-2085, October.
    35. John N. Friedman & Richard Holden, 2020. "Optimal Gerrymandering in a competitive environment," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 347-367, October.
    36. Moore, Don A., 2007. "Not so above average after all: When people believe they are worse than average and its implications for theories of bias in social comparison," Organizational Behavior and Human Decision Processes, Elsevier, vol. 102(1), pages 42-58, January.
    37. John N. Friedman & Richard T. Holden, 2008. "Optimal Gerrymandering: Sometimes Pack, but Never Crack," American Economic Review, American Economic Association, vol. 98(1), pages 113-144, March.
    38. Vasiliki Skreta, 2006. "Sequentially Optimal Mechanisms -super-1," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(4), pages 1085-1111.
    39. Jeffrey R. Lax & Justin H. Phillips, 2009. "How Should We Estimate Public Opinion in The States?," American Journal of Political Science, John Wiley & Sons, vol. 53(1), pages 107-121, January.
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    Cited by:

    1. Anton Kolotilin & Alexander Wolitzky, 2020. "The Economics of Partisan Gerrymandering," Discussion Papers 2020-12, School of Economics, The University of New South Wales.
    2. Anton Kolotilin & Roberto Corrao & Alexander Wolitzky, 2022. "Persuasion with Non-Linear Preferences," Papers 2206.09164, arXiv.org, revised Aug 2022.

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