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Semiparametric Estimation of Willingness to Pay Distributions

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  • An, Mark Yuying

Abstract

The most popular survey method used in contingent valuations asks "open-ended" dichotomous choice questions. This method generates grouped or interval-censored data on respondents' willingness to pay. This paper specifies the willingness to pay distribution using the proportional hazard specification in duration analysis. This semiparametric distribution, on the one hand, controls for the effects of observed personal characteristics, and on the other, allows the shape of the distribution to be unspecified. To estimate the willingness to pay distribution from grouped data, we propose both a maximum likelihood estimation method and a minimum Chi-square method. The latter procedure applies to "many observations per cell" cases where the observable covariates are either categorical or amendable to sensible grouping. Specification tests for the proportionality assumption are proposed. The statistical inference procedures are illustrated using the data set from the San Joaquin Valley contingent valuation survey.

Suggested Citation

  • An, Mark Yuying, 1996. "Semiparametric Estimation of Willingness to Pay Distributions," Working Papers 96-20, Duke University, Department of Economics.
  • Handle: RePEc:duk:dukeec:96-20
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    References listed on IDEAS

    as
    1. Mark Yuying An & Roberto Ayala, 1996. "Nonparametric Estimation of a Survivor Function with Across- Interval-Censored Data," Econometrics 9611003, EconWPA.
    2. Sueyoshi, Glenn T, 1995. "A Class of Binary Response Models for Grouped Duration Data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(4), pages 411-431, Oct.-Dec..
    3. Carson, Richard T. & Hanemann, W. Michael & Kopp, Raymond J. & Krosnick, Jon A. & Mitchell, Robert C. & Presser, Stanley & Ruud, Paul A. & Smith, V. Kerry, 1996. "Was the NOAA Panel Correct about Contingent Valuation?," Working Papers 96-21, Duke University, Department of Economics.
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    6. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
    7. An, Mark Y. & Roberto Ayala, 1995. "A Mixture Model of Willingness to Pay Distributions," Working Papers 95-21, Duke University, Department of Economics.
    8. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    9. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    10. An, Mark Y., 1995. "Econometric Analysis of Sequential Discrete Choice Models," Working Papers 95-55, Duke University, Department of Economics.
    11. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August.
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    Cited by:

    1. An, Mark Yuying, 1996. "Statistical Inference of a Bivariate Proportional Hazard Model with Grouped Data," Working Papers 96-06, Duke University, Department of Economics.
    2. Mark Yuying An & Roberto Ayala, 1996. "Nonparametric Estimation of a Survivor Function with Across- Interval-Censored Data," Econometrics 9611003, EconWPA.
    3. Rebecca L. McDonald & Susan M. Chilton & Michael W. Jones-Lee & Hugh R. T. Metcalf, 2016. "Dread and latency impacts on a VSL for cancer risk reductions," Journal of Risk and Uncertainty, Springer, vol. 52(2), pages 137-161, April.
    4. Hammitt, James & Haninger, Kevin, 2010. "Diminishing Willingness to Pay per Quality-Adjusted Life Year: Valuing Acute Foodborne Illness," LERNA Working Papers 11.01.335, LERNA, University of Toulouse.
    5. James K. Hammitt, 2017. "Valuing Non-Fatal Health Risks: Monetary and Health-Utility Measures," Revue économique, Presses de Sciences-Po, vol. 68(3), pages 335-356.
    6. Henrik Andersson & Mikael Svensson, 2014. "Scale sensitivity and question order in the contingent valuation method," Journal of Environmental Planning and Management, Taylor & Francis Journals, vol. 57(11), pages 1746-1761, November.
    7. repec:kap:jrisku:v:55:y:2017:i:2:d:10.1007_s11166-017-9267-x is not listed on IDEAS
    8. Henrik Andersson & James K. Hammitt & Kristian Sundström, 2015. "Willingness to Pay and QALYs: What Can We Learn about Valuing Foodborne Risk?," Journal of Agricultural Economics, Wiley Blackwell, vol. 66(3), pages 727-752, September.
    9. Antoine Bommier & Bertrand Villeneuve, 2012. "Risk Aversion and the Value of Risk to Life," Post-Print hal-01685924, HAL.
    10. Stefan Felder & Andreas Werblow, 2009. "The Marginal Cost of Saving a Life in Health Care: Age, Gender and Regional Differences in Switzerland," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 145(II), pages 137-153, June.
    11. Henrik Andersson & Nicolas Treich, 2011. "The Value of a Statistical Life," Chapters,in: A Handbook of Transport Economics, chapter 17 Edward Elgar Publishing.
    12. Adler, Matthew & Hammitt, James & Treich, Nicolas, 2012. "The Social Value of Mortality Risk Reduction: VSL vs. the Social Welfare Function Approach," LERNA Working Papers 12.08.365, LERNA, University of Toulouse.
    13. Andersson, Henrik, 2013. "Consistency in preferences for road safety: An analysis of precautionary and stated behavior," Research in Transportation Economics, Elsevier, vol. 43(1), pages 41-49.
    14. Lisa A. Robinson & James K. Hammitt, 2013. "Behavioral economics and the conduct of benefit–cost analysis: towards principles and standards," Chapters,in: Principles and Standards for Benefit–Cost Analysis, chapter 10, pages 317-363 Edward Elgar Publishing.
    15. Arnaud Z. Dragicevic, 2017. "Option Fund Market Dynamics for Threshold Public Goods," Dynamic Games and Applications, Springer, vol. 7(1), pages 21-33, March.
    16. Christoph M. Rheinberger & Nicolas Treich, 2017. "Attitudes Toward Catastrophe," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 67(3), pages 609-636, July.
    17. Courbage, Christophe & Rey, Béatrice & Treich, Nicolas, 2013. "Prevention and precaution," TSE Working Papers 13-445, Toulouse School of Economics (TSE).
    18. Christoph M. Rheinberger & Felix Schläpfer & Michael Lobsiger, 2017. "A Novel Approach to Estimating the Demand Value of Road Safety," Working Papers 2017.15, Fondazione Eni Enrico Mattei.
    19. Anna Alberini, 2017. "Measuring the economic value of the effects of chemicals on ecological systems and human health," OECD Environment Working Papers 116, OECD Publishing.
    20. Maliheh Mansouri & Julie Rowney, 2014. "The Dilemma of Accountability for Professionals: A Challenge for Mainstream Management Theories," Journal of Business Ethics, Springer, vol. 123(1), pages 45-56, August.
    21. David Crainich & Louis Eeckhoudt, 2017. "Average willingness to pay for disease prevention with personalized health information," Journal of Risk and Uncertainty, Springer, vol. 55(1), pages 29-39, August.
    22. Zapata, Samuel D. & Carpio, Carlos E., 2014. "Distribution-free Methods for Estimation of Willingness to Pay Models Using Discrete Response Valuation Data," 2014 Annual Meeting, July 27-29, 2014, Minneapolis, Minnesota 170453, Agricultural and Applied Economics Association.

    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • Q20 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - General

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