Well-posedness of measurement error models for self-reported data
AbstractThis paper considers the widely admitted ill-posed inverse problem for measurement error models: estimating the distribution of a latent variable X∗ from an observed sample of X, a contaminated measurement of X∗. We show that the inverse problem is well-posed for self-reporting data under the assumption that the probability of truthful reporting is nonzero, which is supported by empirical evidences. Comparing with ill-posedness, well-posedness generally can be translated into faster rates of convergence for the nonparametric estimators of the latent distribution. Therefore, our optimistic result on well-posedness is of importance in economic applications, and it suggests that researchers should not ignore the point mass at zero in the measurement error distribution when they model measurement errors with self-reported data. We also analyze the implications of our results on the estimation of classical measurement error models. Then by both a Monte Carlo study and an empirical application, we show that failing to account for the nonzero probability of truthful reporting can lead to significant bias on estimation of the latent distribution.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 168 (2012)
Issue (Month): 2 ()
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Web page: http://www.elsevier.com/locate/jeconom
Well-posed; Ill-posed; Inverse problem; Fredholm integral equation; Deconvolution; Rate of convergence; Measurement error model; Self-reported data; Survey data;
Other versions of this item:
- 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.
- 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.
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
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