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Estimating Features of a Distribution from Binomial Data

  • Arthur Lewbel

    ()

    (Boston College)

  • Daniel McFadden

    ()

    (University of California-Berkeley)

  • Oliver Linton

    ()

    (London School of Economics)

We propose estimators of features of the distribution of an unobserved random variable W. What is observed is a sample of Y; V; X where a binary Y equals one when W exceeds a threshold V determined by experimental design, and X are covariates. Potential applications include bioassay and destructive duration analysis. Our empirical application is referendum contingent valuation in resource economics, where one is interested in features of the distribution of values W (willingness to pay) placed by consumers on a public good such as endangered species. Sample consumers with characteristics X are asked whether they favor (with Y = 1 if yes and zero otherwise) a referendum that would provide the good at a cost V specified by experimental design. This paper provides estimators for quantiles and conditional on X moments of W under both nonparametric and semiparametric specifications.

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Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 442.

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Date of creation: 15 May 1997
Date of revision: 01 Jul 2010
Handle: RePEc:boc:bocoec:442
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  1. repec:cup:etheor:v:13:y:1997:i:1:p:32-51 is not listed on IDEAS
  2. Klein, R.W. & Spady, R.H., 1991. "An Efficient Semiparametric Estimator for Binary Response Models," Papers 70, Bell Communications - Economic Research Group.
  3. 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.
  4. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November.
  5. Donald Green & Karen Jacowitz & Daniel Kahneman & Daniel McFadden, 1995. "Referendum Contingent Valuation, Anchoring, and Willingness to Pay for Public Goods," Working Papers _010, University of California at Berkeley, Econometrics Laboratory Software Archive.
  6. 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, vol. 27(4), pages 451-480, April.
  7. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
  8. Lewbel, Arthur, 2000. "Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables," Journal of Econometrics, Elsevier, vol. 97(1), pages 145-177, July.
  9. Delgado, Miguel A & Mora, Juan, 1995. "Nonparametric and Semiparametric Estimation with Discrete Regressors," Econometrica, Econometric Society, vol. 63(6), pages 1477-84, November.
  10. 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, vol. 82(3), pages 487-500.
  11. Xiaohong Chen & Oliver Linton & Ingred Van Keilegom, 2002. "Estimation of semiparametric models when the criterion function is not smooth," CeMMAP working papers CWP02/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  12. Lewbel, Arthur, 1997. "Semiparametric Estimation of Location and Other Discrete Choice Moments," Econometric Theory, Cambridge University Press, vol. 13(01), pages 32-51, February.
  13. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339 Elsevier.
  14. Bryan W. Brown & Whitney K. Newey, 1998. "Efficient Semiparametric Estimation of Expectations," Econometrica, Econometric Society, vol. 66(2), pages 453-464, March.
  15. Masry, Elias, 1996. "Multivariate regression estimation local polynomial fitting for time series," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 81-101, December.
  16. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
  17. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
  18. Chen, Heng Z. & Randall, Alan, 1997. "Semi-nonparametric estimation of binary response models with an application to natural resource valuation," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 323-340.
  19. Newey, W.K., 1989. "The Asymptotic Variance Of Semiparametric Estimotors," Papers 346, Princeton, Department of Economics - Econometric Research Program.
  20. Horowitz, Joel L., 2001. "The Bootstrap," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 52, pages 3159-3228 Elsevier.
  21. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  22. Sherman, Robert P, 1993. "The Limiting Distribution of the Maximum Rank Correlation Estimator," Econometrica, Econometric Society, vol. 61(1), pages 123-37, January.
  23. Gozalo, Pedro & Linton, Oliver, 2000. "Local nonlinear least squares: Using parametric information in nonparametric regression," Journal of Econometrics, Elsevier, vol. 99(1), pages 63-106, November.
  24. Coppejans, Mark, 2003. "Effective nonparametric estimation in the case of severely discretized data," Journal of Econometrics, Elsevier, vol. 117(2), pages 331-367, December.
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