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Identification and estimation of nonlinear models using two samples with nonclassical measurement errors

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  • Raymond Carroll
  • Xiaohong Chen
  • Yingyao Hu
Abstract
This paper considers identification and estimation of a general nonlinear errors-in-variables (EIV) model using two samples. Both samples consist of a dependent variable, some error-free covariates, and an error-prone covariate, for which the measurement error has unknown distribution and could be arbitrarily correlated with the latent true values, and neither sample contains an accurate measurement of the corresponding true variable. We assume that the regression model of interest – the conditional distribution of the dependent variable given the latent true covariate and the error-free covariates – is the same in both samples, but the distributions of the latent true covariates vary with observed error-free discrete covariates. We first show that the general latent nonlinear model is nonparametrically identified using the two samples when both could have nonclassical errors, without either instrumental variables or independence between the two samples. When the two samples are independent and the nonlinear regression model is parameterised, we propose sieve quasi maximum likelihood estimation (Q-MLE) for the parameter of interest, and establish its root-n consistency and asymptotic normality under possible misspecification, and its semiparametric efficiency under correct specification, with easily estimated standard errors. A Monte Carlo simulation and a data application are presented to show the power of the approach.

Suggested Citation

  • Raymond Carroll & Xiaohong Chen & Yingyao Hu, 2010. "Identification and estimation of nonlinear models using two samples with nonclassical measurement errors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(4), pages 379-399.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:4:p:379-399
    DOI: 10.1080/10485250902874688
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    Cited by:

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    3. Hu, Yingyao, 2021. "Identification of Causal Models with Unobservables: A Self-Report Approach," Economics Working Paper Archive 64330, The Johns Hopkins University,Department of Economics.
    4. Shiu, Ji-Liang & Hu, Yingyao, 2013. "Identification and estimation of nonlinear dynamic panel data models with unobserved covariates," Journal of Econometrics, Elsevier, vol. 175(2), pages 116-131.
    5. Yingyao Hu & Yi Xin, 2019. "Identi?cation and estimation of dynamic structural models with unobserved choices," CeMMAP working papers CWP35/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Hu, Yingyao & Shiu, Ji-Liang, 2018. "Nonparametric Identification Using Instrumental Variables: Sufficient Conditions For Completeness," Econometric Theory, Cambridge University Press, vol. 34(3), pages 659-693, June.
    7. Louis Anthony (Tony) Cox, Jr., 2011. "An Exposure‐Response Threshold for Lung Diseases and Lung Cancer Caused by Crystalline Silica," Risk Analysis, John Wiley & Sons, vol. 31(10), pages 1543-1560, October.
    8. Susanne M. Schennach, 2013. "Regressions with Berkson errors in covariates - A nonparametric approach," Papers 1308.2836, arXiv.org.
    9. Lin, Zhongjian & Hu, Yingyao, 2024. "Binary choice with misclassification and social interactions, with an application to peer effects in attitude," Journal of Econometrics, Elsevier, vol. 238(1).
    10. Paul Schrimpf & Michio Suzuki & Hiroyuki Kasahara, 2015. "Identification and Estimation of Production Function with Unobserved Heterogeneity," 2015 Meeting Papers 924, Society for Economic Dynamics.
    11. Hu, Yingyao & Shum, Matthew, 2012. "Nonparametric identification of dynamic models with unobserved state variables," Journal of Econometrics, Elsevier, vol. 171(1), pages 32-44.
    12. Kasahara, Hiroyuki & Shimotsu, Katsumi, 2022. "Identification Of Regression Models With A Misclassified And Endogenous Binary Regressor," Econometric Theory, Cambridge University Press, vol. 38(6), pages 1117-1139, December.
    13. 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.
    14. Gagliardini, Patrick & Gouriéroux, Christian, 2019. "Identification by Laplace transforms in nonlinear time series and panel models with unobserved stochastic dynamic effects," Journal of Econometrics, Elsevier, vol. 208(2), pages 613-637.
    15. Diaz-Serrano, Luis & Nilsson, William, 2022. "The reliability of students’ earnings expectations," Labour Economics, Elsevier, vol. 76(C).
    16. Yingyao Hu, 2015. "Microeconomic models with latent variables: applications of measurement error models in empirical industrial organization and labor economics," CeMMAP working papers 03/15, Institute for Fiscal Studies.
    17. An, Yonghong & Hong, Shengjie & Zhang, Daiqiang, 2023. "A structural analysis of simple contracts," Journal of Econometrics, Elsevier, vol. 236(2).
    18. Hu, Yingyao, 2017. "The Econometrics of Unobservables -- Latent Variable and Measurement Error Models and Their Applications in Empirical Industrial Organization and Labor Economics [The Econometrics of Unobservables]," Economics Working Paper Archive 64578, The Johns Hopkins University,Department of Economics, revised 2021.
    19. 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.
    20. Yingyao Hu & Jiaxiong Yao, 2019. "Illuminating Economic Growth," IMF Working Papers 2019/077, International Monetary Fund.
    21. Hu, Yingyao & Yao, Jiaxiong, 2022. "Illuminating economic growth," Journal of Econometrics, Elsevier, vol. 228(2), pages 359-378.

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