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Identification of additive and polynomial models of mismeasured regressors without instruments

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  • Ben-Moshe, Dan
  • D’Haultfœuille, Xavier
  • Lewbel, Arthur

Abstract

We show nonparametric point identification of a measurement error model with covariates that can be interpreted as invalid instruments. Our main contribution is to replace standard exclusion restrictions with the weaker assumption of additivity in the covariates. Measurement errors are ubiquitous and additive models are popular, so our results combining the two should have widespread potential application. We also identify a model that replaces the nonparametric function of the mismeasured regressor with a polynomial in that regressor and other covariates. This allows for rich interactions between the variables, at the expense of introducing a parametric restriction. Our identification proofs are constructive, and so can be used to form estimators. We establish root-n asymptotic normality for one of our estimators.

Suggested Citation

  • Ben-Moshe, Dan & D’Haultfœuille, Xavier & Lewbel, Arthur, 2017. "Identification of additive and polynomial models of mismeasured regressors without instruments," Journal of Econometrics, Elsevier, vol. 200(2), pages 207-222.
    • Handle: RePEc:eee:econom:v:200:y:2017:i:2:p:207-222
    DOI: 10.1016/j.jeconom.2017.06.006
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    References listed on IDEAS

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    Cited by:

    1. Christoph Breunig, 2018. "Varying Random Coefficient Models," Papers 1804.03110, arXiv.org, revised Aug 2020.
    2. Huang, Liquan & Khalil, Umair & Yıldız, Neşe, 2019. "Identification and estimation of a triangular model with multiple endogenous variables and insufficiently many instrumental variables," Journal of Econometrics, Elsevier, vol. 208(2), pages 346-366.
    3. Souza, André Portela & Zylberstajn, Eduardo, 2019. "Estimating the returns to education using a parametric control function approach: evidences for a developing country," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 39(2).
    4. Takahide Yanagi, 2019. "Inference on local average treatment effects for misclassified treatment," Econometric Reviews, Taylor & Francis Journals, vol. 38(8), pages 938-960, September.
    5. Breunig, Christoph, 2021. "Varying random coefficient models," Journal of Econometrics, Elsevier, vol. 221(2), pages 381-408.
    6. Christoph Breunig & Stephan Martin, 2020. "Nonclassical Measurement Error in the Outcome Variable," Papers 2009.12665, arXiv.org, revised May 2021.
    7. Souza, André Portela & Zylberstajn, Eduardo, 2020. "Estimating the returns to education using a parametric control function approach: evidences for a developing country," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 39(2), March.

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    More about this item

    Keywords

    Nonparametric; Semiparametric; Measurement error; Additive regression; Polynomial regression; Identification;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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