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Identification and Estimation of Regression Models with Misclassification

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  • Aprajit Mahajan

Abstract

This paper studies the problem of identification and estimation in nonparametric regression models with a misclassified binary regressor where the measurement error may be correlated with the regressors. We show that the regression function is nonparametrically identified in the presence of an additional random variable that is correlated with the unobserved true underlying variable but unrelated to the measurement error. Identification for semiparametric and parametric regression functions follows straightforwardly from the basic identification result. We propose a kernel estimator based on the identification strategy, derive its large sample properties, and discuss alternative estimation procedures. We also propose a test for misclassification in the model based on an exclusion restriction that is straightforward to implement. Copyright The Econometric Society 2006.

Suggested Citation

  • Aprajit Mahajan, 2006. "Identification and Estimation of Regression Models with Misclassification," Econometrica, Econometric Society, vol. 74(3), pages 631-665, May.
  • Handle: RePEc:ecm:emetrp:v:74:y:2006:i:3:p:631-665
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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2006.00677.x
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    References listed on IDEAS

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    1. Aigner, Dennis J., 1973. "Regression with a binary independent variable subject to errors of observation," Journal of Econometrics, Elsevier, vol. 1(1), pages 49-59, March.
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    9. Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, January.
    10. Bollinger, Christopher R., 1996. "Bounding mean regressions when a binary regressor is mismeasured," Journal of Econometrics, Elsevier, vol. 73(2), pages 387-399, August.
    11. Hausman, Jerry A. & Newey, Whitney K. & Ichimura, Hidehiko & Powell, James L., 1991. "Identification and estimation of polynomial errors-in-variables models," Journal of Econometrics, Elsevier, vol. 50(3), pages 273-295, December.
    12. Hausman, J. A. & Abrevaya, Jason & Scott-Morton, F. M., 1998. "Misclassification of the dependent variable in a discrete-response setting," Journal of Econometrics, Elsevier, vol. 87(2), pages 239-269, September.
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