Institute for Economic and Social Research


Journal of Econometrics


Identification of Nonparametric Monotonic Regression Models with Continuous Nonclassical Measurement Errors

Journal of Econometrics, forthcoming

Yingyao Hu, Susanne Schennach, Ji-Liang Shiu


This paper provides sufficient conditions for identification of a nonparametric regression model with an unobserved continuous regressor subject to nonclassical measurement error. The measurement error may be directly correlated with the latent regressor in the model. Our identification strategy does not require the availability of additional data information, such as a secondary measurement, an instrumental variable, or an auxiliary sample. Our main assumptions for nonparametric identification include monotonicity of the regression function, independence of the regression error, and completeness of the measurement error distribution. We also propose a sieve maximum likelihood estimator and investigate its finite sample property through Monte Carlo simulations.

Keywords: Nonclassical measurement error; Nonparametric identification; Spectral decomposition; Nonparametric regression;  Sieve maximum likelihood estimation.


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