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First-Order and Second-Order Ambiguity Aversion

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  • Matthias Lang

    (Max Planck Institute for Research on Collective Goods, Bonn)

Abstract

Different models of uncertainty aversion imply strikingly different economic behavior. The key to understanding these differences lies in the dichotomy between first-order and second-order ambiguity aversion which I define here. My definition and its characterization are independent of specific representations of decisions under uncertainty. I show that with second-order ambiguity aversion a positive exposure to ambiguity is optimal if and only if there is a subjective belief such that the act’s expected outcome is positive. With first-order ambiguity aversion, zero exposure to ambiguity can be optimal. Examples in finance, insurance and contracting demonstrate the economic relevance of this dichotomy.

Suggested Citation

  • Matthias Lang, 2015. "First-Order and Second-Order Ambiguity Aversion," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2015_13, Max Planck Institute for Research on Collective Goods.
    • Handle: RePEc:mpg:wpaper:2015_13
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    1. Johanna Etner & Meglena Jeleva & Jean‐Marc Tallon, 2012. "Decision Theory Under Ambiguity," Journal of Economic Surveys, Wiley Blackwell, vol. 26(2), pages 234-270, April.
    2. Mohammed Abdellaoui & Frank Vossmann & Martin Weber, 2005. "Choice-Based Elicitation and Decomposition of Decision Weights for Gains and Losses Under Uncertainty," Management Science, INFORMS, vol. 51(9), pages 1384-1399, September.
    3. Irma Machielse & Danielle Timmermans & Peter Wakker, 2007. "The effects of statistical information on risk ambiguity attitudes, and on rational insurance decisions," Natural Field Experiments 00338, The Field Experiments Website.
    4. Larry G. Epstein & Martin Schneider, 2010. "Ambiguity and Asset Markets," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 315-346, December.
    5. Fabio Maccheroni & Massimo Marinacci & Doriana Ruffino, 2013. "Alpha as Ambiguity: Robust Mean‐Variance Portfolio Analysis," Econometrica, Econometric Society, vol. 81(3), pages 1075-1113, May.
    6. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    7. ,, 2013. "Endogenous indeterminacy and volatility of asset prices under ambiguity," Theoretical Economics, Econometric Society, vol. 8(3), September.
    8. Mohammed Abdellaoui & Peter Klibanoff & Lætitia Placido, 2015. "Experiments on Compound Risk in Relation to Simple Risk and to Ambiguity," Management Science, INFORMS, vol. 61(6), pages 1306-1322, June.
    9. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    10. Sujoy Mukerji & Jean-Marc Tallon, 2001. "Ambiguity Aversion and Incompleteness of Financial Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(4), pages 883-904.
    11. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M. & Montrucchio, L., 2011. "Uncertainty averse preferences," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1275-1330, July.
    12. George Wu & Richard Gonzalez, 1999. "Nonlinear Decision Weights in Choice Under Uncertainty," Management Science, INFORMS, vol. 45(1), pages 74-85, January.
    13. Rinaldi, Francesca, 2009. "Endogenous incompleteness of financial markets: The role of ambiguity and ambiguity aversion," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 880-901, December.
    14. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M. & Rustichini, A., 2015. "The structure of variational preferences," Journal of Mathematical Economics, Elsevier, vol. 57(C), pages 12-19.
    15. Lars Tyge Nielsen, 1999. "Differentiable von Neumann-Morgenstern utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(2), pages 285-296.
    16. Kellner, Christian, 2015. "Tournaments as a response to ambiguity aversion in incentive contracts," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 627-655.
    17. Christian Gollier, 2011. "Portfolio Choices and Asset Prices: The Comparative Statics of Ambiguity Aversion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(4), pages 1329-1344.
    18. Chateauneuf, Alain & Faro, José Heleno, 2009. "Ambiguity through confidence functions," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 535-558, September.
    19. Robert F. Nau, 2006. "Uncertainty Aversion with Second-Order Utilities and Probabilities," Management Science, INFORMS, vol. 52(1), pages 136-145, January.
    20. Chew, Soo Hong & Sagi, Jacob S., 2008. "Small worlds: Modeling attitudes toward sources of uncertainty," Journal of Economic Theory, Elsevier, vol. 139(1), pages 1-24, March.
    21. Johanna Etner & Meglena Jeleva & Jean‐Marc Tallon, 2012. "Decision Theory Under Ambiguity," Journal of Economic Surveys, Wiley Blackwell, vol. 26(2), pages 234-270, April.
    22. Segal, Uzi & Spivak, Avia, 1990. "First order versus second order risk aversion," Journal of Economic Theory, Elsevier, vol. 51(1), pages 111-125, June.
    23. Mukerji, Sujoy & Tallon, Jean-Marc, 2004. "Ambiguity aversion and the absence of wage indexation," Journal of Monetary Economics, Elsevier, vol. 51(3), pages 653-670, April.
    24. Yaari, Menahem E., 1969. "Some remarks on measures of risk aversion and on their uses," Journal of Economic Theory, Elsevier, vol. 1(3), pages 315-329, October.
    25. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    26. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    27. Gijs van de Kuilen & Peter P. Wakker, 2011. "The Midweight Method to Measure Attitudes Toward Risk and Ambiguity," Management Science, INFORMS, vol. 57(3), pages 582-598, March.
    28. Steven R. Williams & Roy Radner, 1988. "Efficiency in Partnership When The Joint Output is Uncertain," Discussion Papers 760, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    29. Massimo Marinacci & Doriana Ruffino & Fabio Maccheroni, 2011. "Does Uncertainty Vanish in the Small? The Smooth Ambiguity Case," 2011 Meeting Papers 619, Society for Economic Dynamics.
    30. Kyoungwon Seo, 2009. "Ambiguity and Second-Order Belief," Econometrica, Econometric Society, vol. 77(5), pages 1575-1605, September.
    31. Ergin, Haluk & Gul, Faruk, 2009. "A theory of subjective compound lotteries," Journal of Economic Theory, Elsevier, vol. 144(3), pages 899-929, May.
    32. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    33. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2012. "Probabilistic sophistication, second order stochastic dominance and uncertainty aversion," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 271-283.
    34. Paolo Ghirardato & Marciano Siniscalchi, 2012. "Ambiguity in the Small and in the Large," Econometrica, Econometric Society, vol. 80(6), pages 2827-2847, November.
    35. MOSSIN, Jan, 1968. "Aspects of rational insurance purchasing," LIDAM Reprints CORE 23, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    36. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    37. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
    38. Uzi Segal & Avia Spivak, 1996. "First-order risk aversion and non-differentiability (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 179-183.
    39. Dow, James & Werlang, Sergio Ribeiro da Costa, 1992. "Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio," Econometrica, Econometric Society, vol. 60(1), pages 197-204, January.
    40. Kip Smith & John Dickhaut & Kevin McCabe & José V. Pardo, 2002. "Neuronal Substrates for Choice Under Ambiguity, Risk, Gains, and Losses," Management Science, INFORMS, vol. 48(6), pages 711-718, June.
    41. David Ahn & Syngjoo Choi & Douglas Gale & Shachar Kariv, 2014. "Estimating ambiguity aversion in a portfolio choice experiment," Quantitative Economics, Econometric Society, vol. 5, pages 195-223, July.
    42. Peter P. Wakker & Daniëlle R. M. Timmermans & Irma Machielse, 2007. "The Effects of Statistical Information on Risk and Ambiguity Attitudes, and on Rational Insurance Decisions," Management Science, INFORMS, vol. 53(11), pages 1770-1784, November.
    43. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    44. Craig R. Fox & Amos Tversky, 1998. "A Belief-Based Account of Decision Under Uncertainty," Management Science, INFORMS, vol. 44(7), pages 879-895, July.
    45. Michael Kilka & Martin Weber, 2001. "What Determines the Shape of the Probability Weighting Function Under Uncertainty?," Management Science, INFORMS, vol. 47(12), pages 1712-1726, December.
    46. Ayala Arad & Gabrielle Gayer, 2012. "Imprecise Data Sets as a Source of Ambiguity: A Model and Experimental Evidence," Management Science, INFORMS, vol. 58(1), pages 188-202, January.
    47. Ning Du & David V. Budescu, 2005. "The Effects of Imprecise Probabilities and Outcomes in Evaluating Investment Options," Management Science, INFORMS, vol. 51(12), pages 1791-1803, December.
    48. Mukerji, Sujoy, 1998. "Ambiguity Aversion and Incompleteness of Contractual Form," American Economic Review, American Economic Association, vol. 88(5), pages 1207-1231, December.
    49. repec:hal:pseose:halshs-00643580 is not listed on IDEAS
    50. Luca Rigotti & Chris Shannon & Tomasz Strzalecki, 2008. "Subjective Beliefs and ex ante Trade," Econometrica, Econometric Society, vol. 76(5), pages 1167-1190, September.
    51. Rigotti, Luca & Shannon, Chris, 2012. "Sharing risk and ambiguity," Journal of Economic Theory, Elsevier, vol. 147(5), pages 2028-2039.
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    Cited by:

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    2. Jingyi Xue, 2020. "Preferences with changing ambiguity aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(1), pages 1-60, February.
    3. Christoph Bühren & Fabian Meier & Marco Pleßner, 2023. "Ambiguity aversion: bibliometric analysis and literature review of the last 60 years," Management Review Quarterly, Springer, vol. 73(2), pages 495-525, June.
    4. Kräkel, Matthias, 2016. "Peer effects and incentives," Games and Economic Behavior, Elsevier, vol. 97(C), pages 120-127.
    5. Kellner, Christian & Le Quement, Mark T., 2018. "Endogenous ambiguity in cheap talk," Journal of Economic Theory, Elsevier, vol. 173(C), pages 1-17.
    6. Soheil Ghili & Peter Klibanoff, 2021. "If It Is Surely Better, Do It More? Implications for Preferences Under Ambiguity," Management Science, INFORMS, vol. 67(12), pages 7619-7636, December.
    7. Galanis, Spyros, 2018. "Financial complexity and trade," Games and Economic Behavior, Elsevier, vol. 112(C), pages 219-230.
    8. Andrew J. Keith & Darryl K. Ahner, 2021. "A survey of decision making and optimization under uncertainty," Annals of Operations Research, Springer, vol. 300(2), pages 319-353, May.
    9. Luigi Alberto Franzoni, 2022. "Efficient liability law when parties genuinely disagree," Working Papers wp1176, Dipartimento Scienze Economiche, Universita' di Bologna.
    10. Thomas Knispel & Roger J. A. Laeven & Gregor Svindland, 2021. "Asymptotic Analysis of Risk Premia Induced by Law-Invariant Risk Measures," Papers 2107.01730, arXiv.org.
    11. Bao, Xing & Diabat, Ali & Zheng, Zhongliang, 2020. "An ambiguous manager's disruption decisions with insufficient data in recovery phase," International Journal of Production Economics, Elsevier, vol. 221(C).
    12. Christian Kellner, 2017. "The principal-agent problem with smooth ambiguity," Review of Economic Design, Springer;Society for Economic Design, vol. 21(2), pages 83-119, June.

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    More about this item

    Keywords

    Uncertainty Aversion; Ambiguity; Smooth Ambiguity Aversion; Sub-jective Beliefs; Kinked preferences;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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