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

Author

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  • Susanne M. 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.

Suggested Citation

  • Susanne M. Schennach & Yingyao Hu, 2012. "Nonparametric identification and semiparametric estimation of classical measurement error models without side information," CeMMAP working papers CWP40/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:40/12
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    File URL: http://www.cemmap.ac.uk/wps/cwp401212.pdf
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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.
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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, January.
    2. Stefan Hoderlein & Bettina Siflinger & Joachim Winter, 2015. "Identification of structural models in the presence of measurement error due to rounding in survey responses," Boston College Working Papers in Economics 869, Boston College Department of Economics.
    3. Erickson, Timothy & Jiang, Colin Huan & Whited, Toni M., 2014. "Minimum distance estimation of the errors-in-variables model using linear cumulant equations," Journal of Econometrics, Elsevier, vol. 183(2), pages 211-221.
    4. repec:eee:econom:v:200:y:2017:i:2:p:154-168 is not listed on IDEAS
    5. Chesher, Andrew, 2017. "Understanding the effect of measurement error on quantile regressions," Journal of Econometrics, Elsevier, vol. 200(2), pages 223-237.
    6. Lance Lochner & Youngki Shin, 2014. "Understanding Earnings Dynamics: Identifying and Estimating the Changing Roles of Unobserved Ability, Permanent and Transitory Shocks," NBER Working Papers 20068, National Bureau of Economic Research, Inc.
    7. repec:eee:econom:v:200:y:2017:i:2:p:194-206 is not listed on IDEAS
    8. repec:eee:econom:v:200:y:2017:i:2:p:207-222 is not listed on IDEAS
    9. Bustamante, M. Cecilia, 2016. "How Do Frictions Affect Corporate Investment? A Structural Approach," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 51(06), pages 1863-1895, December.
    10. Gospodinov, Nikolay & Komunjer, Ivana & Ng, Serena, 2014. "Minimum Distance Estimation of Dynamic Models with Errors-In-Variables," FRB Atlanta Working Paper 2014-11, Federal Reserve Bank of Atlanta.
    11. Susanne M. Schennach, 2012. "Measurement error in nonlinear models - a review," CeMMAP working papers CWP41/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. repec:eee:econom:v:200:y:2017:i:2:p:181-193 is not listed on IDEAS
    13. Yingyao Hu, 2015. "Microeconomic models with latent variables: applications of measurement error models in empirical industrial organization and labor economics," CeMMAP working papers CWP03/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    14. repec:cup:etheor:v:34:y:2018:i:01:p:134-165_00 is not listed on IDEAS
    15. repec:eee:econom:v:200:y:2017:i:2:p:238-250 is not listed on IDEAS
    16. Daniel Wilhelm, 2015. "Identification and estimation of nonparametric panel data regressions with measurement error," CeMMAP working papers CWP34/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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