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A note on the closed-form identification of regression models with a mismeasured binary regressor

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  • Chen, Xiaohong
  • Hu, Yingyao
  • Lewbel, Arthur

Abstract

This note considers the identification of a nonparametric regression model with an unobserved 0-1 dichotomous regressor. The sample consists of a dependent variable and a 0-1 dichotomous proxy of the unobserved regressor. We obtain nonparametric identification of every element in the model as a closed-form function of the observed moments or densities. Our identification strategy does not require any additional sample information, such as instrumental variables or a secondary sample. The closed-form solution may be used to construct estimators of the unknowns.

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Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 78 (2008)
Issue (Month): 12 (September)
Pages: 1473-1479

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Handle: RePEc:eee:stapro:v:78:y:2008:i:12:p:1473-1479

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  1. Bollinger, Christopher R., 1996. "Bounding mean regressions when a binary regressor is mismeasured," Journal of Econometrics, Elsevier, vol. 73(2), pages 387-399, August.
  2. Erickson, Timothy & Whited, Toni M., 2002. "Two-Step Gmm Estimation Of The Errors-In-Variables Model Using High-Order Moments," Econometric Theory, Cambridge University Press, vol. 18(03), pages 776-799, June.
  3. Aprajit Mahajan, 2006. "Identification and Estimation of Regression Models with Misclassification," Econometrica, Econometric Society, vol. 74(3), pages 631-665, 05.
  4. 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.
  5. Xiaohong Chen & Yingyao Hu & Arthur Lewbel, 2007. "Nonparametric identification and estimation of nonclassical errors-in-variables models without additional information," CeMMAP working papers CWP18/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. Arthur Lewbel, 2004. "Estimation of Average Treatment Effects With Misclassification," Econometric Society 2004 North American Winter Meetings 210, Econometric Society.
  7. Klepper, Steven, 1988. "Bounding the effects of measurement error in regressions involving dichotomous variables," Journal of Econometrics, Elsevier, vol. 37(3), pages 343-359, March.
  8. Arthur Lewbel, 1997. "Constructing Instruments for Regressions with Measurement Error when no Additional Data are Available, with an Application to Patents and R&D," Econometrica, Econometric Society, vol. 65(5), pages 1201-1214, September.
  9. Huwang, Longcheen & Gene Hwang, J. T., 2002. "Prediction and confidence intervals for nonlinear measurement error models without identifiability information," Statistics & Probability Letters, Elsevier, vol. 58(4), pages 355-362, July.
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Cited by:
  1. van Hasselt, Martijn & Bollinger, Christopher R., 2012. "Binary misclassification and identification in regression models," Economics Letters, Elsevier, vol. 115(1), pages 81-84.
  2. Fu, Lianyan & Gao, Wei & Shi, Ning-Zhong, 2011. "Estimation of relative average treatment effects with misclassification," Economics Letters, Elsevier, vol. 111(1), pages 95-98, April.

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