Well-posedness of measurement error models for self-reported data
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*.
|Date of creation:||03 Dec 2009|
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- 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.
- Chen, Xiaohong & Reiss, Markus, 2011.
"On Rate Optimality For Ill-Posed Inverse Problems In Econometrics,"
Cambridge University Press, vol. 27(03), pages 497-521, June.
- Xiaohong Chen & Markus Reiss, 2007. "On Rate Optimality for Ill-posed Inverse Problems in Econometrics," Cowles Foundation Discussion Papers 1626, Cowles Foundation for Research in Economics, Yale University.
- Xiaohong Chen & Markus Reiss, 2007. "On rate optimality for ill-posed inverse problems in econometrics," CeMMAP working papers CWP20/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
- 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.
- Yingyao Hu & Geert Ridder, 2005.
"On Deconvolution as a First Stage Nonparametric Estimator,"
IEPR Working Papers
05.29, Institute of Economic Policy Research (IEPR).
- Yingyao Hu & Geert Ridder, 2010. "On Deconvolution as a First Stage Nonparametric Estimator," Econometric Reviews, Taylor & Francis Journals, vol. 29(4), pages 365-396.
- 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.
- Chen, Xiaohong & Hong, Han & Tarozzi, Alessandro, 2008. "Semiparametric Efficiency in GMM Models of Nonclassical Measurement Errors, Missing Data and Treatment Effects," Working Papers 42, Yale University, Department of Economics.
- 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.
- 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.
- 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.
- Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
- 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.
- Hesse, C. H., 1995. "Deconvolving a Density from Partially Contaminated Observations," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 246-260, November.
- 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.
- 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.
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