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Nonparametric Identification and Semiparametric Estimation of Classical Measurement Error Models Without Side Information

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  • S. M. Schennach
  • Yingyao Hu
Abstract
Virtually all methods aimed at correcting for covariate measurement error in regressions rely on some form of additional information (e.g., validation data, known error distributions, repeated measurements, or instruments). In contrast, we establish that the fully nonparametric classical errors-in-variables model is identifiable from data on the regressor and the dependent variable alone, unless the model takes a very specific parametric form. This parametric family includes (but is not limited to) the linear specification with normally distributed variables as a well-known special case. This result relies on standard primitive regularity conditions taking the form of smoothness constraints and nonvanishing characteristic functions' assumptions. Our approach can handle both monotone and nonmonotone specifications, provided the latter oscillate a finite number of times. Given that the very specific unidentified parametric functional form is arguably the exception rather than the rule, this identification result should have a wide applicability. It leads to a new perspective on handling measurement error in nonlinear and nonparametric models, opening the way to a novel and practical approach to correct for measurement error in datasets where it was previously considered impossible (due to the lack of additional information regarding the measurement error). We suggest an estimator based on non/semiparametric maximum likelihood, derive its asymptotic properties, and illustrate the effectiveness of the method with a simulation study and an application to the relationship between firm investment behavior and market value, the latter being notoriously mismeasured. Supplementary materials for this article are available online.

Suggested Citation

  • S. M. Schennach & Yingyao Hu, 2013. "Nonparametric Identification and Semiparametric Estimation of Classical Measurement Error Models Without Side Information," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 177-186, March.
    • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:501:p:177-186
    DOI: 10.1080/01621459.2012.751872
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    References listed on IDEAS

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    1. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, January.
    2. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    3. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
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