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Title:Well-posedness of measurement error models for self-reported data PDF Logo
Authors:An, Yonghong
Hu, Yingyao
Issue Date:2009
Series/Report no.:Working papers // the Johns Hopkins University, Department of Economics 556
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*.
Subjects:Well-posed
conditionally well-posed
ill-posed
inverse problem
Fredholm integral equation
deconvolution
measurement error model
self-reported data
survey data
Document Type:Working Paper
Appears in Collections:Working Papers, Department of Economics, The Johns Hopkins University

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