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On Mis-measured Binary Regressors: New Results And Some Comments on the Literature

Author

Listed:
  • Francis DiTraglia

    (Department of Economics, University of Pennsylvania)

  • Camilo Garcia-Jimeno

    (Department of Economics, University of Pennsylvania)

Abstract

This paper studies the use of a discrete instrumental variable to identify the causal effect of a endogenous, mis-measured, binary treatment in a homogeneous effects model with additively separable errors. We begin by showing that the only existing identification result for this case, which appears in Mahajan (2006), is incorrect. As such, identification in this model remains an open question. We provide a convenient notational framework to address this question and use it to derive a number of results. First, we prove that the treatment effect is unidentified based on conditional first-moment information, regardless of the number of values that the instrument may take. Second, we derive a novel partial identification result based on conditional second moments that can be used to test for the presence of mis-classification and to construct bounds for the treatment effect. In certain special cases, we can in fact obtain point identification of the treatment effect based on second moment information alone. When this is not possible, we show that adding conditional third moment information point identifies the treatment effect and completely characterizes the measurement error process.

Suggested Citation

  • Francis DiTraglia & Camilo Garcia-Jimeno, 2015. "On Mis-measured Binary Regressors: New Results And Some Comments on the Literature," PIER Working Paper Archive 15-037, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 02 Nov 2015.
    • Handle: RePEc:pen:papers:15-037
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    References listed on IDEAS

    as
    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.
    2. repec:fth:prinin:419 is not listed on IDEAS
    3. Frazis, Harley & Loewenstein, Mark A., 2003. "Estimating linear regressions with mismeasured, possibly endogenous, binary explanatory variables," Journal of Econometrics, Elsevier, vol. 117(1), pages 151-178, November.
    4. Arthur Lewbel, 2007. "Estimation of Average Treatment Effects with Misclassification," Econometrica, Econometric Society, vol. 75(2), pages 537-551, March.
    5. Thomas J. Kane & Cecilia Elena Rouse & Douglas Staiger, 1999. "Estimating Returns to Schooling When Schooling is Misreported," NBER Working Papers 7235, National Bureau of Economic Research, Inc.
    6. Bollinger, Christopher R., 1996. "Bounding mean regressions when a binary regressor is mismeasured," Journal of Econometrics, Elsevier, vol. 73(2), pages 387-399, August.
    7. AIGNER, Dennis J., 1973. "Regression with a binary independent variable subject to errors of observation," LIDAM Reprints CORE 130, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Aprajit Mahajan, 2006. "Identification and Estimation of Regression Models with Misclassification," Econometrica, Econometric Society, vol. 74(3), pages 631-665, May.
    9. Thomas J. Kane & Cecilia Rouse & Douglas Staiger, 1999. "Estimating Returns to Schooling When Schooling is Misreported," Working Papers 798, Princeton University, Department of Economics, Industrial Relations Section..
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    Citations

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    Cited by:

    1. Kédagni, Désiré, 2023. "Identifying treatment effects in the presence of confounded types," Journal of Econometrics, Elsevier, vol. 234(2), pages 479-511.

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    More about this item

    Keywords

    Instrumental variables; Measurement error; Endogeneity; Binary regressor; Partial Identification;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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