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Well-posedness of measurement error models for self-reported data

Author

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  • Yonghong An

    (Institute for Fiscal Studies)

  • Yingyao Hu

    (Institute for Fiscal Studies and Johns Hopkins University)

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 measurement error models for self-reporting data are well-posed, assuming the probability of reporting truthfully is nonzero, which is an observed property in validation studies. This optimistic result suggests that one should not ignore the point mass at zero in the error distribution when modeling measurement errors in self-reported data. 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*. By both a Monte Carlo study and an empirical application, we show that failing to account for the property can lead to significant bias on estimation of distribution of X*.

Suggested Citation

  • Yonghong An & Yingyao Hu, 2009. "Well-posedness of measurement error models for self-reported data," CeMMAP working papers CWP35/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:35/09
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    File URL: https://cemmap.ifs.org.uk/wps/cwp3509.pdf
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    Cited by:

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    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. Enache, Andreea & Florens, Jean-Pierre, 2020. "Quantile Analysis of "Hazard-Rate" Game Models," TSE Working Papers 20-1117, Toulouse School of Economics (TSE).
    4. 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.
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    7. Hu, Yingyao & Shiu, Ji-Liang, 2018. "Nonparametric Identification Using Instrumental Variables: Sufficient Conditions For Completeness," Econometric Theory, Cambridge University Press, vol. 34(3), pages 659-693, June.
    8. 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.
    9. Jerry Hausman & Haoyang Liu & Ye Luo & Christopher Palmer, 2021. "Errors in the Dependent Variable of Quantile Regression Models," Econometrica, Econometric Society, vol. 89(2), pages 849-873, March.
    10. Escanciano, Juan Carlos & Hoderlein, Stefan & Lewbel, Arthur & Linton, Oliver & Srisuma, Sorawoot, 2021. "Nonparametric Euler Equation Identification And Estimation," Econometric Theory, Cambridge University Press, vol. 37(5), pages 851-891, October.
    11. Andrews, Donald W.K., 2017. "Examples of L2-complete and boundedly-complete distributions," Journal of Econometrics, Elsevier, vol. 199(2), pages 213-220.
    12. 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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