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Nonparametric identification and semiparametric estimation of classical measurement error models without side information

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  • Susanne Schennach

    (Institute for Fiscal Studies and Brown University)

  • Yingyao Hu

    (Institute for Fiscal Studies and Johns Hopkins University)

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 mode is identifiable from data on the regressor and the dependent variable alone, unless the model takes a very specific parametric form. The parametric family includes (but is not limited to) the linear specification with normally distributed variables as a well-known special cast. 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 data sets where it was previously considered impossible (due to the lack of additional information regarding the measurement error). We suggest an estimator based on non/semi-parametric 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 behaviour and market value, the latter being notoriously mismeasured.

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Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP40/12.

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Date of creation: Dec 2012
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Handle: RePEc:ifs:cemmap:40/12

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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, 01.
  2. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, 01.
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Cited by:
  1. Susanne M. Schennach, 2014. "Entropic Latent Variable Integration via Simulation," Econometrica, Econometric Society, vol. 82(1), pages 345-385, 01.
  2. Lance Lochner & Youngki Shin, 2014. "Understanding Earnings Dynamics: Identifying and Estimating the Changing Roles of Unobserved Ability, Permanent and Transitory Shocks," University of Western Ontario, CIBC Centre for Human Capital and Productivity Working Papers 20142, University of Western Ontario, CIBC Centre for Human Capital and Productivity.
  3. Susanne Schennach, 2012. "Measurement error in nonlinear models- a review," CeMMAP working papers CWP41/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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