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Hierarchical Maximum Likelihood Parameter Estimation for Cumulative Prospect Theory: Improving the Reliability of Individual Risk Parameter Estimates

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  • Ryan O. Murphy

    (Department of Economics, University of Zürich, 8006 Zürich, Switzerland)

  • Robert H. W. ten Brincke

    (ETH Zürich, 8092 Zürich, Switzerland)

Abstract

An individual’s tolerance of risk can be quantified by using decision models with tuned parameters that maximally fit a set of risky choices the individual has made. A goal of this model fitting procedure is to identify parameters that correspond to stable underlying risk preferences. These preferences can be modeled as an individual difference, indicating a particular decision maker’s tastes and willingness to accept risk. Using hierarchical statistical methods, we show significant improvements in the reliability of individual risk preference parameter estimates over other common methods for cumulative prospect theory. This hierarchical procedure uses population-level information (in addition to an individual’s choices) to break “ties” (or near ties) in the fit quality for sets of possible risk preference parameters. By breaking these statistical ties in a sensible way, researchers can avoid overfitting choice data and thus more resiliently measure individual differences in people’s risk preferences.

Suggested Citation

  • Ryan O. Murphy & Robert H. W. ten Brincke, 2018. "Hierarchical Maximum Likelihood Parameter Estimation for Cumulative Prospect Theory: Improving the Reliability of Individual Risk Parameter Estimates," Management Science, INFORMS, vol. 64(1), pages 308-328, January.
  • Handle: RePEc:inm:ormnsc:v:64:y:2018:i:1:p:308-328
    DOI: 10.1287/mnsc.2016.2591
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    4. Kpegli, Yao Thibaut & Corgnet, Brice & Zylbersztejn, Adam, 2023. "All at once! A comprehensive and tractable semi-parametric method to elicit prospect theory components," Journal of Mathematical Economics, Elsevier, vol. 104(C).
    5. Liu, Hui-hui & Song, Yao-yao & Liu, Xiao-xiao & Yang, Guo-liang, 2020. "Aggregating the DEA prospect cross-efficiency with an application to state key laboratories in China," Socio-Economic Planning Sciences, Elsevier, vol. 71(C).
    6. Emmanuel Kemel & Antoine Nebout & Bruno Ventelou, 2021. "To test or not to test? Risk attitudes and prescribing by French GPs," Working Papers hal-03330153, HAL.
    7. Alam, Jessica & Georgalos, Konstantinos & Rolls, Harrison, 2022. "Risk preferences, gender effects and Bayesian econometrics," Journal of Economic Behavior & Organization, Elsevier, vol. 202(C), pages 168-183.
    8. Balcombe, Kelvin & Fraser, Iain, 2024. "A Note on an Alternative Approach to Experimental Design of Lottery Prospects," MPRA Paper 119743, University Library of Munich, Germany.
    9. Villacis, Alexis H., 2023. "Inconsistent choices over prospect theory lottery games: Evidence from field experiments," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 103(C).
    10. Wakker, Peter P., 2023. "A criticism of Bernheim & Sprenger's (2020) tests of rank dependence," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 107(C).
    11. Xiaoxue Sherry Gao & Glenn W. Harrison & Rusty Tchernis, 2020. "Behavioral Welfare Economics and Risk Preferences: A Bayesian Approach," NBER Working Papers 27685, National Bureau of Economic Research, Inc.
    12. Victor H. Gonzalez-Jimenez, 2019. "Contracting Probability Distortions," Vienna Economics Papers vie1901, University of Vienna, Department of Economics.
    13. Víctor González-Jiménez, 2021. "Incentive contracts when agents distort probabilities," Vienna Economics Papers 2101, University of Vienna, Department of Economics.
    14. Louis Eeckhoudt & Anna Maria Fiori & Emanuela Rosazza Gianin, 2018. "Risk Aversion, Loss Aversion, and the Demand for Insurance," Risks, MDPI, vol. 6(2), pages 1-19, May.
    15. Fidanoski, Filip & Johnson, Timothy, 2023. "A z-Tree implementation of the Dynamic Experiments for Estimating Preferences [DEEP] method," Journal of Behavioral and Experimental Finance, Elsevier, vol. 38(C).
    16. Qian Wu & Monique Vanerum & Anouk Agten & Andrés Christiansen & Frank Vandenabeele & Jean-Michel Rigo & Rianne Janssen, 2021. "Certainty-Based Marking on Multiple-Choice Items: Psychometrics Meets Decision Theory," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 518-543, June.
    17. Shi, Hai-Liu & Chen, Sheng-Qun & Chen, Lei & Wang, Ying-Ming, 2021. "A neutral cross-efficiency evaluation method based on interval reference points in consideration of bounded rational behavior," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1098-1110.
    18. Ferro, Giuseppe M. & Kovalenko, Tatyana & Sornette, Didier, 2021. "Quantum decision theory augments rank-dependent expected utility and Cumulative Prospect Theory," Journal of Economic Psychology, Elsevier, vol. 86(C).

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