IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2011.07272.html
   My bibliography  Save this paper

Identifying the effect of a mis-classified, binary, endogenous regressor

Author

Listed:
  • Francis J. DiTraglia

    (Department of Economics University of Oxford)

  • Camilo Garcia-Jimeno

    (Federal Reserve Bank of Chicago)

Abstract

This paper studies identification of the effect of a mis-classified, binary, endogenous regressor when a discrete-valued instrumental variable is available. We begin by showing that the only existing point identification result for this model is incorrect. We go on to derive the sharp identified set under mean independence assumptions for the instrument and measurement error. The resulting bounds are novel and informative, but fail to point identify the effect of interest. This motivates us to consider alternative and slightly stronger assumptions: we show that adding second and third moment independence assumptions suffices to identify the model.

Suggested Citation

  • Francis J. DiTraglia & Camilo Garcia-Jimeno, 2020. "Identifying the effect of a mis-classified, binary, endogenous regressor," Papers 2011.07272, arXiv.org.
  • Handle: RePEc:arx:papers:2011.07272
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2011.07272
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Shuaizhang Feng & Yingyao Hu, 2013. "Misclassification Errors and the Underestimation of the US Unemployment Rate," American Economic Review, American Economic Association, vol. 103(2), pages 1054-1070, April.
    2. 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.
    3. 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.
    4. van Hasselt, Martijn & Bollinger, Christopher R., 2012. "Binary misclassification and identification in regression models," Economics Letters, Elsevier, vol. 115(1), pages 81-84.
    5. repec:fth:prinin:419 is not listed on IDEAS
    6. Song, Suyong, 2015. "Semiparametric estimation of models with conditional moment restrictions in the presence of nonclassical measurement errors," Journal of Econometrics, Elsevier, vol. 185(1), pages 95-109.
    7. Chen, Xiaohong & Hu, Yingyao & Lewbel, Arthur, 2008. "Nonparametric identification of regression models containing a misclassified dichotomous regressor without instruments," Economics Letters, Elsevier, vol. 100(3), pages 381-384, September.
    8. Thomas J. Kane & Cecilia E. Rouse & Douglas Staiger, 1999. "Estimating Returns to Schooling When Schooling is Misreported," Working Papers 798, Princeton University, Department of Economics, Industrial Relations Section..
    9. Yingyao Hu & Arthur Lewbel, 2012. "Returns to Lying? Identifying the Effects of Misreporting When the Truth Is Unobserved," Frontiers of Economics in China-Selected Publications from Chinese Universities, Higher Education Press, vol. 7(2), pages 163-192, June.
    10. Molinari, Francesca, 2008. "Partial identification of probability distributions with misclassified data," Journal of Econometrics, Elsevier, vol. 144(1), pages 81-117, May.
    11. Angrist, Joshua D, 1990. "Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records: Errata," American Economic Review, American Economic Association, vol. 80(5), pages 1284-1286, December.
    12. Lewbel, Arthur, 2007. "A local generalized method of moments estimator," Economics Letters, Elsevier, vol. 94(1), pages 124-128, January.
    13. Bound, John & Brown, Charles & Mathiowetz, Nancy, 2001. "Measurement error in survey data," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 59, pages 3705-3843, Elsevier.
    14. Chen, Xiaohong & Hu, Yingyao & Lewbel, Arthur, 2008. "A note on the closed-form identification of regression models with a mismeasured binary regressor," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1473-1479, September.
    15. Battistin, Erich & De Nadai, Michele & Sianesi, Barbara, 2014. "Misreported schooling, multiple measures and returns to educational qualifications," Journal of Econometrics, Elsevier, vol. 181(2), pages 136-150.
    16. Angrist, Joshua D, 1990. "Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records," American Economic Review, American Economic Association, vol. 80(3), pages 313-336, June.
    17. Brent Kreider & John V. Pepper & Craig Gundersen & Dean Jolliffe, 2012. "Identifying the Effects of SNAP (Food Stamps) on Child Health Outcomes When Participation Is Endogenous and Misreported," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 958-975, September.
    18. 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.
    19. Arthur Lewbel, 2007. "Estimation of Average Treatment Effects with Misclassification," Econometrica, Econometric Society, vol. 75(2), pages 537-551, March.
    20. 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.
    21. 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.
    22. Toru Kitagawa, 2015. "A Test for Instrument Validity," Econometrica, Econometric Society, vol. 83(5), pages 2043-2063, September.
    23. Takuya Ura, 2018. "Heterogeneous treatment effects with mismeasured endogenous treatment," Quantitative Economics, Econometric Society, vol. 9(3), pages 1335-1370, November.
    24. 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).
    25. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    26. Aprajit Mahajan, 2006. "Identification and Estimation of Regression Models with Misclassification," Econometrica, Econometric Society, vol. 74(3), pages 631-665, May.
    27. Shiu, Ji-Liang, 2016. "Identification and estimation of endogenous selection models in the presence of misclassification errors," Economic Modelling, Elsevier, vol. 52(PB), pages 507-518.
    28. 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..
    29. 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.
    30. Guido W. Imbens & Donald B. Rubin, 1997. "Estimating Outcome Distributions for Compliers in Instrumental Variables Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(4), pages 555-574.
    31. Bollinger, Christopher R., 1996. "Bounding mean regressions when a binary regressor is mismeasured," Journal of Econometrics, Elsevier, vol. 73(2), pages 387-399, August.
    32. Donald W. K. Andrews & Gustavo Soares, 2010. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Econometrica, Econometric Society, vol. 78(1), pages 119-157, January.
    33. 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.
    34. Xiaohong Chen & Han Hong & Elie Tamer, 2005. "Measurement Error Models with Auxiliary Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(2), pages 343-366.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    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. 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.
    6. Takahide Yanagi, 2019. "Inference on local average treatment effects for misclassified treatment," Econometric Reviews, Taylor & Francis Journals, vol. 38(8), pages 938-960, September.
    7. Akanksha Negi & Digvijay Singh Negi, 2022. "Difference-in-Differences with a Misclassified Treatment," Papers 2208.02412, arXiv.org.
    8. Steven J. Haider & Melvin Stephens Jr., 2020. "Correcting for Misclassified Binary Regressors Using Instrumental Variables," NBER Working Papers 27797, National Bureau of Economic Research, Inc.
    9. Acerenza, Santiago & Ban, Kyunghoon & Kedagni, Desire, 2021. "Marginal Treatment Effects with Misclassified Treatment," ISU General Staff Papers 202106180700001132, Iowa State University, Department of Economics.
    10. Tommasi, Denni & Zhang, Lina, 2024. "Bounding program benefits when participation is misreported," Journal of Econometrics, Elsevier, vol. 238(1).
    11. Battistin, Erich & De Nadai, Michele & Sianesi, Barbara, 2014. "Misreported schooling, multiple measures and returns to educational qualifications," Journal of Econometrics, Elsevier, vol. 181(2), pages 136-150.
    12. Hu, Yingyao, 2017. "The Econometrics of Unobservables -- Latent Variable and Measurement Error Models and Their Applications in Empirical Industrial Organization and Labor Economics [The Econometrics of Unobservables]," Economics Working Paper Archive 64578, The Johns Hopkins University,Department of Economics, revised 2021.
    13. Wossen, Tesfamicheal & Abay, Kibrom A. & Abdoulaye, Tahirou, 2022. "Misperceiving and misreporting input quality: Implications for input use and productivity," Journal of Development Economics, Elsevier, vol. 157(C).
    14. 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.
    15. 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.
    16. 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.
    17. Battistin, Erich & De Nadai, Michele & Vuri, Daniela, 2017. "Counting rotten apples: Student achievement and score manipulation in Italian elementary Schools," Journal of Econometrics, Elsevier, vol. 200(2), pages 344-362.
    18. Francis J. DiTraglia & Camilo Garcia-Jimeno, 2020. "A Framework for Eliciting, Incorporating, and Disciplining Identification Beliefs in Linear Models," Papers 2011.07276, arXiv.org.
    19. Orville Mondal & Rui Wang, 2024. "Partial Identification of Binary Choice Models with Misreported Outcomes," Papers 2401.17137, arXiv.org.
    20. Erich Battistin & Barbara Sianesi, 2006. "Misreported schooling and returns to education: evidence from the UK," CeMMAP working papers CWP07/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2011.07272. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.