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Estimating features of a distribution from binomial data

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  • Arthur Lewbel
  • Oliver Linton
  • D. L. McFadden

Abstract

A statistical problem that arises in several fields is that of estimating the features of an unknown distribution, which may be conditioned on covariates, using a sample of binomial observations on whether draws from this distribution exceed threshold levels set by experimental design. Applications include bioassay and destructive duration analysis. The empirical application we consider is referendum contingent valuation in resource economics, where one is interested in features of the distribution of values (willingness to pay) placed by consumers on a public good such as endangered species. Sample consumers are asked whether they favor a referendum that would provide the good at a cost specified by experimental design. This paper provides estimators for moments and quantiles of the unknown distribution in this problem under both nonparametric and semiparametric specifications.

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File URL: http://eprints.lse.ac.uk/4418/
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Bibliographic Info

Paper provided by London School of Economics and Political Science, LSE Library in its series LSE Research Online Documents on Economics with number 4418.

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Length: 58 pages
Date of creation: Sep 2006
Date of revision:
Handle: RePEc:ehl:lserod:4418

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Related research

Keywords: Willingness to Pay; Contingent Valuation; Discrete Choice; Bi-nomial response; Bioassay; Destructive Duration Testing; Semiparametric; Nonparametric; Latent Variable Models;

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References

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  1. Arthur Lewbel, 1999. "Semiparametric Qualitative Response Model Estimation with Unknown Heteroskedasticity or Instrumental Variables," Boston College Working Papers in Economics 454, Boston College Department of Economics.
  2. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, Econometric Society, vol. 57(5), pages 1027-57, September.
  3. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of semiparametric models when the criterion function is not smooth," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 2167, London School of Economics and Political Science, LSE Library.
  4. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, Econometric Society, vol. 61(2), pages 387-421, March.
  5. Green, Donald & Jacowitz, Karen E. & Kahneman, Daniel & McFadden, Daniel, 1998. "Referendum contingent valuation, anchoring, and willingness to pay for public goods," Resource and Energy Economics, Elsevier, Elsevier, vol. 20(2), pages 85-116, June.
  6. HÄRDLE, Wolfgang, 1992. "Applied nonparametric methods," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1992003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, Econometric Society, vol. 62(6), pages 1349-82, November.
  8. Creel, M. & Loomis, J., 1995. "Semi-Nonparametric Distribution-Free Dichotomous Choice Contingent Valuation," UFAE and IAE Working Papers, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) 273.94, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  9. John Crooker & Joseph Herriges, 2004. "Parametric and Semi-Nonparametric Estimation of Willingness-to-Pay in the Dichotomous Choice Contingent Valuation Framework," Environmental & Resource Economics, European Association of Environmental and Resource Economists, European Association of Environmental and Resource Economists, vol. 27(4), pages 451-480, April.
  10. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, Econometric Society, vol. 70(2), pages 519-546, March.
  11. Mark Yuying An, 2000. "A Semiparametric Distribution for Willingness to Pay and Statistical Inference with Dichotomous Choice Contingent Valuation Data," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, Agricultural and Applied Economics Association, vol. 82(3), pages 487-500.
  12. Delgado, Miguel A & Mora, Juan, 1995. "Nonparametric and Semiparametric Estimation with Discrete Regressors," Econometrica, Econometric Society, Econometric Society, vol. 63(6), pages 1477-84, November.
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  14. Masry, Elias, 1996. "Multivariate regression estimation local polynomial fitting for time series," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 65(1), pages 81-101, December.
  15. Chen, Heng Z. & Randall, Alan, 1997. "Semi-nonparametric estimation of binary response models with an application to natural resource valuation," Journal of Econometrics, Elsevier, Elsevier, vol. 76(1-2), pages 323-340.
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  18. repec:cup:etheor:v:13:y:1997:i:1:p:32-51 is not listed on IDEAS
  19. Gozalo, Pedro & Linton, Oliver, 2000. "Local nonlinear least squares: Using parametric information in nonparametric regression," Journal of Econometrics, Elsevier, Elsevier, vol. 99(1), pages 63-106, November.
  20. Bryan W. Brown & Whitney K. Newey, 1998. "Efficient Semiparametric Estimation of Expectations," Econometrica, Econometric Society, Econometric Society, vol. 66(2), pages 453-464, March.
  21. Lewbel, Arthur, 1997. "Semiparametric Estimation of Location and Other Discrete Choice Moments," Econometric Theory, Cambridge University Press, vol. 13(01), pages 32-51, February.
  22. Horowitz, Joel L., 2001. "The Bootstrap," Handbook of Econometrics, Elsevier, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 52, pages 3159-3228 Elsevier.
  23. Sherman, Robert P, 1993. "The Limiting Distribution of the Maximum Rank Correlation Estimator," Econometrica, Econometric Society, Econometric Society, vol. 61(1), pages 123-37, January.
  24. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, Elsevier, vol. 119(1), pages 99-130, March.
  25. Oliver LINTON, . "Applied nonparametric methods," Statistic und Oekonometrie 9312, Humboldt Universitaet Berlin.
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