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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, University Library of Munich, Germany.
    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 & Conaway, Michael & Martin, Kerry, 1996. "Was the NOAA Panel Correct about Contingent Valuation?," Discussion Papers 10503, Resources for the Future.
    4. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    5. Daniel McFadden, 1994. "Contingent Valuation and Social Choice," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 76(4), pages 689-708.
    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.
    12. Ichimura, H., 1991. "Semiparametric Least Squares (sls) and Weighted SLS Estimation of Single- Index Models," Papers 264, Minnesota - Center for Economic Research.
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    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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