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Instrument Assisted Regression for Errors in Variables Models with Binary Response

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  • Kun Xu
  • Yanyuan Ma
  • Liqun Wang

Abstract

type="main" xml:id="sjos12097-abs-0001"> We study errors-in-variables problems when the response is binary and instrumental variables are available. We construct consistent estimators through taking advantage of the prediction relation between the unobservable variables and the instruments. The asymptotic properties of the new estimator are established and illustrated through simulation studies. We also demonstrate that the method can be readily generalized to generalized linear models and beyond. The usefulness of the method is illustrated through a real data example.

Suggested Citation

  • Kun Xu & Yanyuan Ma & Liqun Wang, 2015. "Instrument Assisted Regression for Errors in Variables Models with Binary Response," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 104-117, March.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:1:p:104-117
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    File URL: http://hdl.handle.net/10.1111/sjos.12097
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    References listed on IDEAS

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    1. Amemiya, Yasuo, 1985. "Instrumental variable estimator for the nonlinear errors-in-variables model," Journal of Econometrics, Elsevier, vol. 28(3), pages 273-289, June.
    2. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, September.
    3. Taraneh Abarin & Liqun Wang, 2012. "Instrumental variable approach to covariate measurement error in generalized linear models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 475-493, June.
    4. Anastasios A. Tsiatis & Yanyuan Ma, 2004. "Locally efficient semiparametric estimators for functional measurement error models," Biometrika, Biometrika Trust, vol. 91(4), pages 835-848, December.
    5. Wang, Liqun & Hsiao, Cheng, 2011. "Method of moments estimation and identifiability of semiparametric nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 165(1), pages 30-44.
    6. Amemiya, Yasuo, 1990. "Two-stage instrumental variables estimators for the nonlinear errors-in-variables model," Journal of Econometrics, Elsevier, vol. 44(3), pages 311-332, June.
    7. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2009. "Choosing instrumental variables in conditional moment restriction models," Journal of Econometrics, Elsevier, vol. 152(1), pages 28-36, September.
    8. Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, January.
    9. Michael P. Murray, 2006. "Avoiding Invalid Instruments and Coping with Weak Instruments," Journal of Economic Perspectives, American Economic Association, vol. 20(4), pages 111-132, Fall.
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    Cited by:

    1. Qianqian Wang & Yanyuan Ma & Guangren Yang, 2020. "Locally efficient estimation in generalized partially linear model with measurement error in nonlinear function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 553-572, June.

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