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Distribution-free estimation with interval-censored contingent valuation data: troubles with Turnbull?

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  • Brett Day

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    Contingent valuation (CV) surveys frequently employ elicitation procedures that return interval-censored data on respondents’ willingness to pay (WTP). Almost without exception, CV practitioners have applied Turnbull’s self-consistent algorithm to such data in order to obtain nonparametric maximum likelihood (NPML) estimates of the WTP distribution. This paper documents two failings of Turnbull’s algorithm; (1) that it may not converge to NPML estimates and (2) that it may be very slow to converge. With regards to (1) we propose starting and stopping criteria for the algorithm that guarantee convergence to the NPML estimates. With regards to (2) we present a variety of alternative estimators and demonstrate, through Monte Carlo simulations, their performance advantages over Turnbull’s algorithm. Copyright Springer Science+Business Media, Inc. 2007

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    File URL: http://hdl.handle.net/10.1007/s10640-006-9061-8
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    Article provided by Springer & European Association of Environmental and Resource Economists in its journal Environmental and Resource Economics.

    Volume (Year): 37 (2007)
    Issue (Month): 4 (August)
    Pages: 777-795

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    Handle: RePEc:kap:enreec:v:37:y:2007:i:4:p:777-795
    DOI: 10.1007/s10640-006-9061-8
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    1. Haab, Timothy C. & McConnell, Kenneth E., 1997. "Referendum Models and Negative Willingness to Pay: Alternative Solutions," Journal of Environmental Economics and Management, Elsevier, vol. 32(2), pages 251-270, February.
    2. Mark Yuying An & Roberto Ayala, 1996. "Nonparametric Estimation of a Survivor Function with Across- Interval-Censored Data," Econometrics 9611003, EconWPA.
    3. Paulo Nunes & Jeroen van den Bergh, 2004. "Can People Value Protection against Invasive Marine Species? Evidence from a Joint TC–CV Survey in the Netherlands," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 28(4), pages 517-532, August.
    4. Mattias Boman & Göran Bostedt & Bengt Kriström, 1999. "Obtaining Welfare Bounds in Discrete-Response Valuation Studies: A Non-Parametric Approach," Land Economics, University of Wisconsin Press, vol. 75(2), pages 284-294.
    5. Creel, Michael & Loomis, John, 1997. "Semi-nonparametric Distribution-Free Dichotomous Choice Contingent Valuation," Journal of Environmental Economics and Management, Elsevier, vol. 32(3), pages 341-358, March.
    6. Joseph C. Cooper & Michael Hanemann & Giovanni Signorello, 2002. "One-and-One-Half-Bound Dichotomous Choice Contingent Valuation," The Review of Economics and Statistics, MIT Press, vol. 84(4), pages 742-750, November.
    7. Kerr, Geoffrey N., 2000. "Dichotomous choice contingent valuation probability distributions," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 44(2), June.
    8. Richard C. Ready & Dayuan Hu, 1995. "Statistical Approaches to the Fat Tail Problem for Dichotomous Choice Contingent Valuation," Land Economics, University of Wisconsin Press, vol. 71(4), pages 491-499.
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