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

Arbeitspapier

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*.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Working Paper ; No. 556

Classification and Topics

• Classification: Wirtschaft
• Subject: Well-posed ; conditionally well-posed ; ill-posed ; inverse problem ; Fredholm integral equation ; deconvolution ; measurement error model ; self-reported data ; survey data ; Schätztheorie ; Befragung ; Statistischer Fehler ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): An, Yonghong ; Hu, Yingyao
• Event: Veröffentlichung
• (who): The Johns Hopkins University, Department of Economics
• (where): Baltimore, MD
• (when): 2009

Further information

• Handle: http://hdl.handle.net/10419/49889
• Last update: 10.03.2025, 11:42 AM CET