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Estimating the membership function of the fuzzy willingness-to-pay/accept for health via Bayesian modelling

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  • Michal Jakubczyk

Abstract

Determining how to trade off individual criteria is often not obvious, especially when attributes of very different nature are juxtaposed, e.g. health and money. The difficulty stems both from the lack of adequate market experience and strong ethical component when valuing some goods, resulting in inherently imprecise preferences. Fuzzy sets can be used to model willingness-to-pay/accept (WTP/WTA), so as to quantify this imprecision and support the decision making process. The preferences need then to be estimated based on available data. In the paper I show how to estimate the membership function of fuzzy WTP/WTA, when decision makers’ preferences are collected via survey with Likert-based questions. I apply the proposed methodology to an exemplary data set on WTP/WTA for health. The mathematical model contains two elements: the parametric representation of the membership function and the mathematical model how it is translated into Likert options. The model parameters are estimated in a Bayesian approach using Markov-chain Monte Carlo. The results suggest a slight WTPWTA disparity and WTA being more fuzzy as WTP. The model is fragile to single respondents with lexicographic preferences, i.e. not willing to accept any trade-offs between health and money.

Suggested Citation

  • Michal Jakubczyk, 2016. "Estimating the membership function of the fuzzy willingness-to-pay/accept for health via Bayesian modelling," KAE Working Papers 2016-011, Warsaw School of Economics, Collegium of Economic Analysis.
    • Handle: RePEc:sgh:kaewps:2016011
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    File URL: http://kolegia.sgh.waw.pl/pl/KAE/Documents/WorkingPapersKAE/WPKAE_2016_011.pdf
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    References listed on IDEAS

    as
    1. Viscusi, W Kip & Aldy, Joseph E, 2003. "The Value of a Statistical Life: A Critical Review of Market Estimates throughout the World," Journal of Risk and Uncertainty, Springer, vol. 27(1), pages 5-76, August.
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    3. Bellavance, Franois & Dionne, Georges & Lebeau, Martin, 2009. "The value of a statistical life: A meta-analysis with a mixed effects regression model," Journal of Health Economics, Elsevier, vol. 28(2), pages 444-464, March.
    4. Hultkrantz, Lars & Svensson, Mikael, 2012. "The value of a statistical life in Sweden: A review of the empirical literature," Health Policy, Elsevier, vol. 108(2), pages 302-310.
    5. repec:reg:rpubli:282 is not listed on IDEAS
    6. Dubourg, W R & Jones-Lee, M W & Loomes, Graham, 1994. "Imprecise Preferences and the WTP-WTA Disparity," Journal of Risk and Uncertainty, Springer, vol. 9(2), pages 115-133, October.
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    More about this item

    Keywords

    willingness-to-pay/accept; fuzzy set; membership function; preference elicitation;
    All these keywords.

    JEL classification:

    • J17 - Labor and Demographic Economics - - Demographic Economics - - - Value of Life; Foregone Income
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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