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Measuring Loss Aversion under Ambiguity: A Method to Make Prospect Theory Completely Observable

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Abstract

We propose a simple, parameter-free method that, for the first time, makes it possible to completely observe Tversky and Kahneman’s (1992) prospect theory. While methods exist to measure event weighting and the utility for gains and losses separately, there was no method to measure loss aversion under ambiguity. Our method allows this and thereby it can measure prospect theory’s entire utility function. Consequently, we can properly identify properties of utility and perform new tests of prospect theory. We implemented our method in an experiment and obtained support for prospect theory. Utility was concave for gains and convex for losses and there was substantial loss aversion. Both utility and loss aversion were the same for risk and ambiguity, as assumed by prospect theory, and sign-comonotonic trade-off consistency, the central condition of prospect theory, held.

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Notes

  1. This extension requires finding events with decision weight ½, which can be complex.

  2. Throughout this paper we use the term prospect theory for the 1992 version of the theory and the term original prospect theory (OPT) for the 1979 version. Because we only consider two-outcome prospects, OPT is the special case of prospect theory for decision under risk in which probability weighting for gains and losses are the same.

  3. For example, Choquet expected utility (Schmeidler 1989), maxmin expected utility (Gilboa and Schmeidler 1989), α-maxmin expected utility (Ghirardato et al. 2004), and contraction expected utility (Gajdos et al. 2008).

  4. For example, original prospect theory (Kahneman and Tversky 1979), rank-dependent expected utility (Quiggin 1981; Quiggin 1982), prospective reference theory (Viscusi 1989), and disappointment aversion theory (Gul 1991).

  5. Booij and van de Kuilen (2009) investigated the robustness of their findings by using probability weights estimated in other studies.

  6. Again, we may select an event \( E^{{\prime\prime} } \) different from the events employed in the other two stages.

  7. Köbberling and Wakker (2003) define sign-comonotonic trade-off consistency formally. In a nutshell, the condition holds because changing ℓ from -€300 into €0 does not change the rank-ordering and the sign (no loss is turned into a gain or vice versa) of each prospect’s payoffs. Then utility differences should not be affected according to prospect theory.

  8. Three subjects (two for risk and one for ambiguity) violated monotonicity so that \( {x}_6^{-} \) was not the largest loss. For these subjects we transformed losses \( {x}_j^{-} \) to \( {x}_j^{-}/\left\{\underset{i=1,\dots, 6}{ \min }{x}_i^{-}\right\} \).

  9. These computations required that \( -{x}_j^{+} \) was contained in [\( {x}_6^{-},0) \) and \( -{x}_j^{-} \) in (\( 0,{x}_6^{+}]. \)

  10. We use the (standard) nomenclature of Landis and Koch (1977) to describe the strength of associations.

  11. For a given j, \( {x}_j^{+} \) and \( {x}_j^{-} \) have the same absolute value of utility by construction, \( U\left({x}_j^{+}\right)=-U\left({x}_j^{-}\right), \) and, thus, \( {x}_j^{+}>-{x}_j^{-} \) implies that \( U\left({x}_j^{+}\right)<-U\left(-{x}_j^{+}\right) \), consistent with Kahneman and Tversky’s definition of loss aversion (U(x) <   – U(– x) for all x > 0).

  12. Bleichrodt et al. (2010) also concluded that error propagation was negligible in their measurements using the trade-off method.

  13. We assumed that the error terms followed an AR(1) process ϵ t  + ρϵ t - 1 = u t  with u t normally distributed with expectation 0 and variance σ 2 and estimated this using generalized least squares.

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Acknowledgments

We gratefully acknowledge helpful comments from Aurélien Baillon, Ferdinand Vieider, Peter P. Wakker, Horst Zank, and an anonymous reviewer and financial support from the Erasmus Research Institute of Management, the Netherlands Organisation for Scientific Research (NWO), the Tinbergen Institute, Rennes Metropole district (AIS_2013), and the Economic and Social Research Council via the Network for Integrated Behavioral Sciences (award n. ES/K002201/1).

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Authors and Affiliations

  1. HEC-Paris GREGHEC-CNRS, 1 Rue de la Libération, F78351, Jouy-en-Josas, France

    Mohammed Abdellaoui

  2. Erasmus School of Economics, Rotterdam, Netherlands

    Han Bleichrodt

  3. Crem-Université de Rennes 1 & GREGHEC, Rennes, France

    Olivier L’Haridon

  4. Nottingham School of Economics, University of Nottingham, Nottingham, UK

    Dennie van Dolder

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  1. Mohammed Abdellaoui
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  2. Han Bleichrodt
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  3. Olivier L’Haridon
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  4. Dennie van Dolder
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Correspondence to Mohammed Abdellaoui.

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Abdellaoui, M., Bleichrodt, H., L’Haridon, O. et al. Measuring Loss Aversion under Ambiguity: A Method to Make Prospect Theory Completely Observable. J Risk Uncertain 52, 1–20 (2016). https://doi.org/10.1007/s11166-016-9234-y

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