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Regressions with Berkson errors in covariates - A nonparametric approach

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  • Susanne M. Schennach

Abstract

This paper establishes that so-called instrumental variables enable the identification and the estimation of a fully nonparametric regression model with Berkson-type measurement error in the regressors. An estimator is proposed and proven to be consistent. Its practical performance and feasibility are investigated via Monte Carlo simulations as well as through an epidemiological application investigating the effect of particulate air pollution on respiratory health. These examples illustrate that Berkson errors can clearly not be neglected in nonlinear regression models and that the proposed method represents an effective remedy.

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  • Susanne M. Schennach, 2013. "Regressions with Berkson errors in covariates - A nonparametric approach," Papers 1308.2836, arXiv.org.
    • Handle: RePEc:arx:papers:1308.2836
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    Cited by:

    1. Katharina Proksch & Nicolai Bissantz & Hajo Holzmann, 2022. "Simultaneous inference for Berkson errors-in-variables regression under fixed design," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 773-800, August.
    2. Pierre Dubois & Rachel Griffith & Martin O'Connell, 2020. "How Well Targeted Are Soda Taxes?," American Economic Review, American Economic Association, vol. 110(11), pages 3661-3704, November.
    3. 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.
    4. D’Haultfœuille, Xavier & Février, Philippe, 2015. "Identification of mixture models using support variations," Journal of Econometrics, Elsevier, vol. 189(1), pages 70-82.
    5. Richard Blundell & Joel Horowitz & Matthias Parey, 2022. "Estimation of a Heterogeneous Demand Function with Berkson Errors," The Review of Economics and Statistics, MIT Press, vol. 104(5), pages 877-889, December.
    6. Hu, Yingyao, 2017. "The econometrics of unobservables: Applications of measurement error models in empirical industrial organization and labor economics," Journal of Econometrics, Elsevier, vol. 200(2), pages 154-168.
    7. Pei Geng & Hira L. Koul, 2019. "Minimum distance model checking in Berkson measurement error models with validation data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 879-899, September.
    8. Cornelis J. Potgieter & Rubin Wei & Victor Kipnis & Laurence S. Freedman & Raymond J. Carroll, 2016. "Moment reconstruction and moment‐adjusted imputation when exposure is generated by a complex, nonlinear random effects modeling process," Biometrics, The International Biometric Society, vol. 72(4), pages 1369-1377, December.
    9. Sriya Iyer & Chander Velu & Melvyn Weeks, 2014. "Divine Competition: Religious Organisations and Service Provision in India," Cambridge Working Papers in Economics 1409, Faculty of Economics, University of Cambridge.
    10. Chuanlong Xie & Lixing Zhu, 2018. "A minimum projected-distance test for parametric single-index Berkson models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 700-715, September.
    11. Richard Blundell & Joel L. Horowitz & Matthias Parey, 2018. "Estimation of a nonseparable heterogenous demand function with shape restrictions and Berkson errors," CeMMAP working papers CWP67/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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