[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v38y2022i6p1117-1139_4.html
   My bibliography  Save this article

Identification Of Regression Models With A Misclassified And Endogenous Binary Regressor

Author

Listed:
  • Kasahara, Hiroyuki
  • Shimotsu, Katsumi
Abstract
We study identification in nonparametric regression models with a misclassified and endogenous binary regressor when an instrument is correlated with misclassification error. We show that the regression function is nonparametrically identified if one binary instrument variable and one binary covariate satisfy the following conditions. The instrumental variable corrects endogeneity; the instrumental variable must be correlated with the unobserved true underlying binary variable, must be uncorrelated with the error term in the outcome equation, but is allowed to be correlated with the misclassification error. The covariate corrects misclassification; this variable can be one of the regressors in the outcome equation, must be correlated with the unobserved true underlying binary variable, and must be uncorrelated with the misclassification error. We also propose a mixture-based framework for modeling unobserved heterogeneous treatment effects with a misclassified and endogenous binary regressor and show that treatment effects can be identified if the true treatment effect is related to an observed regressor and another observable variable.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:etheor:v:38:y:2022:i:6:p:1117-1139_4
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0266466621000451/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. James J. Heckman & Sergio Urzua & Edward Vytlacil, 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 389-432, August.
    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. Irene Botosaru & Federico H. Gutierrez, 2018. "Difference‐in‐differences when the treatment status is observed in only one period," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(1), pages 73-90, January.
    4. Bruce Meyer & Robert Goerge, 2011. "Errors in Survey Reporting and Imputation and Their Effects on Estimates of Food Stamp Program Participation," Working Papers 11-14, Center for Economic Studies, U.S. Census Bureau.
    5. 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.
    6. Lorenzo Almada & Ian McCarthy & Rusty Tchernis, 2016. "What Can We Learn about the Effects of Food Stamps on Obesity in the Presence of Misreporting?," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 98(4), pages 997-1017.
    7. 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..
    8. 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.
    9. 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.
    10. 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.
    11. Meyerhoefer, Chad D. & Pylypchuk, Vuriy, 2008. "AJAE Appendix: Does Participation in the Food Stamp Program Increase the Prevalence of Obesity and Health Care Spending?," American Journal of Agricultural Economics APPENDICES, Agricultural and Applied Economics Association, vol. 90(2), pages 1-6.
    12. Takahide Yanagi, 2019. "Inference on local average treatment effects for misclassified treatment," Econometric Reviews, Taylor & Francis Journals, vol. 38(8), pages 938-960, September.
    13. Takuya Ura, 2018. "Heterogeneous treatment effects with mismeasured endogenous treatment," Quantitative Economics, Econometric Society, vol. 9(3), pages 1335-1370, November.
    14. 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).
    15. David Card, 1993. "Using Geographic Variation in College Proximity to Estimate the Return to Schooling," Working Papers 696, Princeton University, Department of Economics, Industrial Relations Section..
    16. Krueger, Alan & Rouse, Cecilia, 1998. "The Effect of Workplace Education on Earnings, Turnover, and Job Performance," Journal of Labor Economics, University of Chicago Press, vol. 16(1), pages 61-94, January.
    17. Aprajit Mahajan, 2006. "Identification and Estimation of Regression Models with Misclassification," Econometrica, Econometric Society, vol. 74(3), pages 631-665, May.
    18. 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..
    19. Raymond Carroll & Xiaohong Chen & Yingyao Hu, 2010. "Identification and estimation of nonlinear models using two samples with nonclassical measurement errors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(4), pages 379-399.
    20. Black, Dan & Sanders, Seth & Taylor, Lowell, 2003. "Measurement of Higher Education in the Census and Current Population Survey," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 545-554, January.
    21. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    22. 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.
    23. repec:fth:prinin:317 is not listed on IDEAS
    24. Hiroyuki Kasahara & Katsumi Shimotsu, 2009. "Nonparametric Identification of Finite Mixture Models of Dynamic Discrete Choices," Econometrica, Econometric Society, vol. 77(1), pages 135-175, January.
    25. David Card, 1993. "Using Geographic Variation in College Proximity to Estimate the Return to Schooling," NBER Working Papers 4483, National Bureau of Economic Research, Inc.
    26. Fan, Yanqin & Park, Sang Soo, 2010. "Sharp Bounds On The Distribution Of Treatment Effects And Their Statistical Inference," Econometric Theory, Cambridge University Press, vol. 26(3), pages 931-951, June.
    27. Meyer, Bruce D. & Mittag, Nikolas & Goerge, Robert M., 2018. "Errors in Survey Reporting and Imputation and Their Effects on Estimates of Food Stamp Program Participation," IZA Discussion Papers 11776, Institute of Labor Economics (IZA).
    28. Poirier, Dale J., 1980. "Partial observability in bivariate probit models," Journal of Econometrics, Elsevier, vol. 12(2), pages 209-217, February.
    29. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Augustine Denteh & D'esir'e K'edagni, 2022. "Misclassification in Difference-in-differences Models," Papers 2207.11890, arXiv.org, revised Jul 2022.

    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. Tommasi, Denni & Zhang, Lina, 2024. "Bounding program benefits when participation is misreported," Journal of Econometrics, Elsevier, vol. 238(1).
    2. 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.
    3. Takahide Yanagi, 2019. "Inference on local average treatment effects for misclassified treatment," Econometric Reviews, Taylor & Francis Journals, vol. 38(8), pages 938-960, September.
    4. Akanksha Negi & Digvijay Singh Negi, 2022. "Difference-in-Differences with a Misclassified Treatment," Papers 2208.02412, arXiv.org.
    5. 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.
    6. 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.
    7. 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.
    8. Francis J. DiTraglia & Camilo Garcia-Jimeno, 2020. "Identifying the effect of a mis-classified, binary, endogenous regressor," Papers 2011.07272, arXiv.org.
    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. 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.
    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. 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).
    13. Lorenzo Almada & Ian McCarthy & Rusty Tchernis, 2016. "What Can We Learn about the Effects of Food Stamps on Obesity in the Presence of Misreporting?," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 98(4), pages 997-1017.
    14. 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.
    15. Charles Courtemanche & Augustine Denteh & Rusty Tchernis, 2019. "Estimating the Associations between SNAP and Food Insecurity, Obesity, and Food Purchases with Imperfect Administrative Measures of Participation," Southern Economic Journal, John Wiley & Sons, vol. 86(1), pages 202-228, July.
    16. 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.
    17. Vitor Possebom, 2021. "Crime and Mismeasured Punishment: Marginal Treatment Effect with Misclassification," Papers 2106.00536, arXiv.org, revised Jul 2023.
    18. Augustine Denteh & D'esir'e K'edagni, 2022. "Misclassification in Difference-in-differences Models," Papers 2207.11890, arXiv.org, revised Jul 2022.
    19. Orville Mondal & Rui Wang, 2024. "Partial Identification of Binary Choice Models with Misreported Outcomes," Papers 2401.17137, arXiv.org.
    20. Kyung Min Kang & Robert A. Moffitt, 2019. "The Effect of SNAP and School Food Programs on Food Security, Diet Quality, and Food Spending: Sensitivity to Program Reporting Error," Southern Economic Journal, John Wiley & Sons, vol. 86(1), pages 156-201, July.

    More about this item

    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:cup:etheor:v:38:y:2022:i:6:p:1117-1139_4. 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: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/ect .

    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.