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Well-Posedness of Measurement Error Models for Self-Reported Data

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  • Yonghong An
  • Yingyao Hu

Abstract

It is widely admitted that the inverse problem of estimating the distribution of a latent variable X* from an observed sample of X, a contaminated measurement of X*, is ill-posed. This paper shows that a property of self-reporting errors, observed from validation studies, is that the probability of reporting the truth is nonzero conditional on the true values, and furthermore, this property implies that measurement error models for self-reporting data are in fact well-posed. We also illustrate that the classical measurement error models may in fact be conditionally well-posed given prior information on the distribution of the latent variable X*.

Suggested Citation

  • Yonghong An & Yingyao Hu, 2009. "Well-Posedness of Measurement Error Models for Self-Reported Data," Economics Working Paper Archive 556, The Johns Hopkins University,Department of Economics.
  • Handle: RePEc:jhu:papers:556
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    References listed on IDEAS

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    4. Yingyao Hu & Geert Ridder, 2010. "On Deconvolution as a First Stage Nonparametric Estimator," Econometric Reviews, Taylor & Francis Journals, vol. 29(4), pages 365-396.
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    6. Bound, John & Krueger, Alan B, 1991. "The Extent of Measurement Error in Longitudinal Earnings Data: Do Two Wrongs Make a Right?," Journal of Labor Economics, University of Chicago Press, vol. 9(1), pages 1-24, January.
    7. Li, Tong & Vuong, Quang, 1998. "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 139-165, May.
    8. Xiaohong Chen & Han Hong & Alessandro Tarozzi, 2008. "Semiparametric Efficiency in GMM Models of Nonclassical Measurement Errors, Missing Data and Treatment Effects," Cowles Foundation Discussion Papers 1644, Cowles Foundation for Research in Economics, Yale University.
    9. Hesse, C. H., 1995. "Deconvolving a Density from Partially Contaminated Observations," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 246-260, November.
    10. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, vol. 75(6), pages 1613-1669, November.
    11. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    12. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
    13. Xiaohong Chen & Han Hong & Elie Tamer, 2005. "Measurement Error Models with Auxiliary Data," Review of Economic Studies, Oxford University Press, vol. 72(2), pages 343-366.
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    Cited by:

    1. Andrews, Donald W.K., 2017. "Examples of L2-complete and boundedly-complete distributions," Journal of Econometrics, Elsevier, vol. 199(2), pages 213-220.
    2. Rohman, Ibrahim Kholilul & Bohlin, Erik, 2011. "Towards the alternative measurement: Discovering the relationships between technology adoption and quality of life in Indonesia," 22nd European Regional ITS Conference, Budapest 2011: Innovative ICT Applications - Emerging Regulatory, Economic and Policy Issues 52206, International Telecommunications Society (ITS).
    3. Kassas, Bachir & Palma, Marco A. & Anderson, David P., 2017. "Fine-Tuning Willingness-To-Pay Estimates in Second Price Auctions," 2017 Annual Meeting, July 30-August 1, Chicago, Illinois 258466, Agricultural and Applied Economics Association.
    4. Hu, Yingyao & Schennach, Susanne M. & Shiu, Ji-Liang, 2017. "Injectivity of a class of integral operators with compactly supported kernels," Journal of Econometrics, Elsevier, vol. 200(1), pages 48-58.
    5. Arthur Lewbel & Oliver Linton & Sorawoot Srisuma, 2010. "Nonparametric Euler Equation Identification and Estimation," Boston College Working Papers in Economics 757, Boston College Department of Economics, revised 23 Feb 2011.
    6. Kassas, Bachir & Palma, Marco A. & Anderson, David P., 2018. "Fine-tuning willingness-to-pay estimates in second price auctions for market goods," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 77(C), pages 50-61.
    7. Toru Kitagawa & Martin Nybom & Jan Stuhler, 2018. "Measurement error and rank correlations," CeMMAP working papers CWP28/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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