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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*.

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Paper provided by The Johns Hopkins University,Department of Economics in its series Economics Working Paper Archive with number 556.

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Date of creation: Oct 2009
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Handle: RePEc:jhu:papers:556

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  1. 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.
  2. Bollinger, Christopher R, 1998. "Measurement Error in the Current Population Survey: A Nonparametric Look," Journal of Labor Economics, University of Chicago Press, vol. 16(3), pages 576-94, July.
  3. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
  4. Chen, Xiaohong & Reiss, Markus, 2011. "On Rate Optimality For Ill-Posed Inverse Problems In Econometrics," Econometric Theory, Cambridge University Press, vol. 27(03), pages 497-521, June.
  5. Hesse, C. H., 1995. "Deconvolving a Density from Partially Contaminated Observations," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 246-260, November.
  6. John Bound & Alan B. Krueger, 1989. "The Extent of Measurement Error In Longitudinal Earnings Data: Do Two Wrongs Make A Right?," NBER Working Papers 2885, National Bureau of Economic Research, Inc.
  7. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
  8. 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.
  9. Bound, John & Brown, Charles & Mathiowetz, Nancy, 2001. "Measurement error in survey data," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 59, pages 3705-3843 Elsevier.
  10. Yingyao Hu & Geert Ridder, 2010. "On Deconvolution as a First Stage Nonparametric Estimator," Econometric Reviews, Taylor & Francis Journals, vol. 29(4), pages 365-396.
  11. 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.
  12. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2003. "Nonparametric IV estimation of shape-invariant Engel curves," CeMMAP working papers CWP15/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  13. 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.
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Cited by:
  1. 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).

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