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Estimating features of a distribution from binomial data

Author

Listed:
  • Arthur Lewbel

    () (Institute for Fiscal Studies and Boston College)

  • Oliver Linton

    () (Institute for Fiscal Studies and University of Cambridge)

  • Daniel McFadden

    () (Institute for Fiscal Studies and University of California, Berkeley)

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. One application is destructive duration analysis, where the process is censored at an observation test time. Another is referendum contingent valuation in resource economics, where one is interested in features of the distribution of values placed by consumers on a public good such as endangered species. Sample consumers are asked whether they would vote for a referendum that would provide the good at a cost specied by experimental design. This paper provides estimators for moments and quantiles of the unknown distribution in this problem.

Suggested Citation

  • Arthur Lewbel & Oliver Linton & Daniel McFadden, 2001. "Estimating features of a distribution from binomial data," CeMMAP working papers CWP07/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:07/01
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    File URL: http://cemmap.ifs.org.uk/wps/cwp0107.pdf
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    References listed on IDEAS

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    1. repec:cup:etheor:v:13:y:1997:i:1:p:32-51 is not listed on IDEAS
    2. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
    3. 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.
    4. 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, vol. 20(2), pages 85-116, June.
    5. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
    6. 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.
    7. Bryan W. Brown & Whitney K. Newey, 1998. "Efficient Semiparametric Estimation of Expectations," Econometrica, Econometric Society, vol. 66(2), pages 453-464, March.
    8. 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.
    9. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    10. 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.
    11. Delgado, Miguel A & Mora, Juan, 1995. "Nonparametric and Semiparametric Estimation with Discrete Regressors," Econometrica, Econometric Society, vol. 63(6), pages 1477-1484, November.
    12. 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.
    13. 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.
    14. 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.
    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. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    17. John Crooker & Joseph Herriges, 2004. "Parametric and Semi-Nonparametric Estimation of Willingness-to-Pay in the Dichotomous Choice Contingent Valuation Framework," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 27(4), pages 451-480, April.
    18. Lewbel, Arthur, 1997. "Semiparametric Estimation of Location and Other Discrete Choice Moments," Econometric Theory, Cambridge University Press, vol. 13(01), pages 32-51, February.
    19. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    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. 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.
    22. 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.
    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.
    25. Sherman, Robert P, 1993. "The Limiting Distribution of the Maximum Rank Correlation Estimator," Econometrica, Econometric Society, vol. 61(1), pages 123-137, January.
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    Citations

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    Cited by:

    1. Christian Bontemps & Thierry Magnac & Eric Maurin, 2012. "Set Identified Linear Models," Econometrica, Econometric Society, vol. 80(3), pages 1129-1155, May.
    2. Lewbel, Arthur & Tang, Xun, 2015. "Identification and estimation of games with incomplete information using excluded regressors," Journal of Econometrics, Elsevier, vol. 189(1), pages 229-244.
    3. Yingying Dong & Arthur Lewbel, 2015. "A Simple Estimator for Binary Choice Models with Endogenous Regressors," Econometric Reviews, Taylor & Francis Journals, vol. 34(1-2), pages 82-105, February.
    4. Lewbel, Arthur, 2007. "Endogenous selection or treatment model estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 777-806, December.
    5. Kim, Sooil, 2006. "Bias and Efficiency of Uniform Bid Design in Contingent Valuation," 2006 Annual meeting, July 23-26, Long Beach, CA 21335, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    6. Fosgerau, Mogens, 2006. "Investigating the distribution of the value of travel time savings," Transportation Research Part B: Methodological, Elsevier, vol. 40(8), pages 688-707, September.
    7. Mogens Fosgerau, 2005. "Specification Of A Model To Measure - The Value Of Travel Time Savings From Binomial Data," ERSA conference papers ersa05p77, European Regional Science Association.
    8. Arthur Lewbel & Oliver Linton, 2003. "Nonparametric estimation of homothetic and homothetically separable functions," CeMMAP working papers CWP14/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Magnac, Thierry & Maurin, Eric, 2007. "Identification and information in monotone binary models," Journal of Econometrics, Elsevier, vol. 139(1), pages 76-104, July.
    10. Chu, Ba & Jacho-Chávez, David T., 2012. "k-NEAREST NEIGHBOR ESTIMATION OF INVERSE-DENSITY-WEIGHTED EXPECTATIONS WITH DEPENDENT DATA," Econometric Theory, Cambridge University Press, vol. 28(04), pages 769-803, August.
    11. Bo E. Honore & Arthur Lewbel, 2002. "Semiparametric Binary Choice Panel Data Models Without Strictly Exogeneous Regressors," Econometrica, Econometric Society, vol. 70(5), pages 2053-2063, September.
    12. Fosgerau, Mogens & Hjort, Katrine & Vincent Lyk-Jensen, Stéphanie, 2007. "An approach to the estimation of the distribution of marginal valuations from discrete choice data," MPRA Paper 3907, University Library of Munich, Germany.
    13. repec:eee:enepol:v:111:y:2017:i:c:p:362-370 is not listed on IDEAS
    14. 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.
    15. Arthur Lewbel, 2005. "Simple Endogenous Binary Choice and Selection Panel Model Estimators," Boston College Working Papers in Economics 613, Boston College Department of Economics, revised 04 Sep 2006.
    16. Arthur Lewbel, 2006. "Modeling Heterogeneity," Boston College Working Papers in Economics 650, Boston College Department of Economics.
    17. Arthur Lewbel, 2012. "An Overview of the Special Regressor Method," Boston College Working Papers in Economics 810, Boston College Department of Economics.
    18. Mogens Fosgerau, 2014. "Nonparametric approaches to describing heterogeneity," Chapters,in: Handbook of Choice Modelling, chapter 11, pages 257-267 Edward Elgar Publishing.
    19. Arthur Lewbel & Susanne M. Schennach, 2003. "A Simple Ordered Data Estimator For Inverse Density Weighted Functions," Boston College Working Papers in Economics 557, Boston College Department of Economics, revised 01 May 2005.
    20. Arthur Lewbel & Oliver Linton, 2007. "Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions," Econometrica, Econometric Society, vol. 75(4), pages 1209-1227, July.
    21. Arthur Lewbel, 2002. "Ordered Response Threshold Estimation," Boston College Working Papers in Economics 535, Boston College Department of Economics, revised 29 Oct 2003.
    22. Arthur Lewbel & Xun Tang, 2010. "Identification and Estimation of Games with Incomplete Information Using Excluded Regressors, Second Version," PIER Working Paper Archive 12-018, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 20 Mar 2012.
    23. Yingying Dong & Arthur Lewbel, 2012. "Simple Estimators for Binary Choice Models with Endogenous Regressors," Working Papers 111204, University of California-Irvine, Department of Economics.
    24. Matzkin, Rosa L., 2012. "Identification in nonparametric limited dependent variable models with simultaneity and unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 166(1), pages 106-115.
    25. repec:eee:eneeco:v:69:y:2018:i:c:p:225-236 is not listed on IDEAS

    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
    • C42 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Survey Methods
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

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