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Identification and estimation of single‐index models with measurement error and endogeneity

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  • Yingyao Hu
  • Ji‐Liang Shiu
  • Tiemen Woutersen

Abstract

Economic variables are often measured with an error and may be endogenous. In this paper, we give new identification results for the ratio of partial effects in linear index models with measurement error and endogeneity. The identification restrictions include independence of covariates and error terms, and the derivative of some conditional mean functions being nonzero. We propose a local polynomial regression estimator to estimate the single‐index parameters. We apply these tools to estimate the labour‐supply elasticity and find that the labour‐supply elasticity for married men is positive, while the coefficients for married women are negative for the full sample and positive for the working sample.

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  • Yingyao Hu & Ji‐Liang Shiu & Tiemen Woutersen, 2015. "Identification and estimation of single‐index models with measurement error and endogeneity," Econometrics Journal, Royal Economic Society, vol. 18(3), pages 347-362, October.
    • Handle: RePEc:wly:emjrnl:v:18:y:2015:i:3:p:347-362
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    File URL: http://hdl.handle.net/10.1111/ectj.12053
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    3. Blundell, Richard & Macurdy, Thomas, 1999. "Labor supply: A review of alternative approaches," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 27, pages 1559-1695, Elsevier.
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    6. Michael P. Keane, 2011. "Labor Supply and Taxes: A Survey," Journal of Economic Literature, American Economic Association, vol. 49(4), pages 961-1075, December.
    7. Hu, Yingyao, 2008. "Identification and estimation of nonlinear models with misclassification error using instrumental variables: A general solution," Journal of Econometrics, Elsevier, vol. 144(1), pages 27-61, May.
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    Cited by:

    1. Nguimkeu, Pierre & Denteh, Augustine & Tchernis, Rusty, 2019. "On the estimation of treatment effects with endogenous misreporting," Journal of Econometrics, Elsevier, vol. 208(2), pages 487-506.
    2. Francis J. DiTraglia & Camilo Garcia-Jimeno, 2020. "Identifying the effect of a mis-classified, binary, endogenous regressor," Papers 2011.07272, arXiv.org.
    3. 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.
    4. Francis DiTraglia & Camilo Garcia-Jimeno, 2015. "On Mis-measured Binary Regressors: New Results And Some Comments on the Literature, Second Version," PIER Working Paper Archive 15-039, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 11 Nov 2015.
    5. Bollinger, Christopher R. & van Hasselt, Martijn, 2017. "Bayesian moment-based inference in a regression model with misclassification error," Journal of Econometrics, Elsevier, vol. 200(2), pages 282-294.
    6. Francis DiTraglia & Camilo Garcia-Jimeno, 2015. "On Mis-measured Binary Regressors: New Results And Some Comments on the Literature, Third Version," PIER Working Paper Archive 15-040, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 24 Nov 2015.
    7. DiTraglia, Francis J. & García-Jimeno, Camilo, 2019. "Identifying the effect of a mis-classified, binary, endogenous regressor," Journal of Econometrics, Elsevier, vol. 209(2), pages 376-390.
    8. Denni Tommasi & Arthur Lewbel & Rossella Calvi, 2017. "LATE with Mismeasured or Misspecified Treatment: An application to Women's Empowerment in India," Working Papers ECARES ECARES 2017-27, ULB -- Universite Libre de Bruxelles.
    9. Francis J. DiTraglia & Camilo García-Jimeno, 2017. "Mis-classified, Binary, Endogenous Regressors: Identification and Inference," NBER Working Papers 23814, National Bureau of Economic Research, Inc.

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