IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v208y2019i2p487-506.html
   My bibliography  Save this article

On the estimation of treatment effects with endogenous misreporting

Author

Listed:
  • Nguimkeu, Pierre
  • Denteh, Augustine
  • Tchernis, Rusty

Abstract

Participation in social programs is often misreported in survey data, complicating the estimation of treatment effects. We propose a model to estimate treatment effects under endogenous participation and endogenous misreporting. We present an expression for the asymptotic bias of both OLS and IV estimators and discuss the conditions under which sign reversal may occur. We provide a method for eliminating this bias when researchers have access to information regarding participation and misreporting. We establish the consistency and asymptotic normality of our proposed estimator and assess its small sample performance through Monte Carlo simulations. An empirical example illustrates the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:econom:v:208:y:2019:i:2:p:487-506
    DOI: 10.1016/j.jeconom.2018.10.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407618301994
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2018.10.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Brent Kreider, 2010. "Regression Coefficient Identification Decay in The Presence of Infrequent Classification Errors," The Review of Economics and Statistics, MIT Press, vol. 92(4), pages 1017-1023, November.
    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. Arthur Lewbel & Yingying Dong & Thomas Tao Yang, 2012. "Comparing features of convenient estimators for binary choice models with endogenous regressors," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 45(3), pages 809-829, August.
    4. Christopher Baum & Yingying Dong & Arthur Lewbel & Tao Yang, 2012. "Binary choice models with endogenous regressors," SAN12 Stata Conference 9, Stata Users Group.
    5. Melvin Stephens & Takashi Unayama, 2019. "Estimating the Impacts of Program Benefits: Using Instrumental Variables with Underreported and Imputed Data," The Review of Economics and Statistics, MIT Press, vol. 101(3), pages 468-475, July.
    6. 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.
    7. 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.
    8. Steven Haider & Gary Solon, 2006. "Life-Cycle Variation in the Association between Current and Lifetime Earnings," American Economic Review, American Economic Association, vol. 96(4), pages 1308-1320, September.
    9. Elton Mykerezi & Bradford Mills, 2010. "The Impact of Food Stamp Program Participation on Household Food Insecurity," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 92(5), pages 1379-1391.
    10. Tripathi, Gautam, 1999. "A matrix extension of the Cauchy-Schwarz inequality," Economics Letters, Elsevier, vol. 63(1), pages 1-3, April.
    11. Néstor Gandelman & Alejandro Rasteletti, 2017. "Credit Constraints, Sector Informality and Firm Investments: Evidence from a Panel of Uruguayan Firms," Journal of Applied Economics, Taylor & Francis Journals, vol. 20(2), pages 351-372, November.
    12. 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.
    13. 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.
    14. 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.
    15. Takuya Ura, 2018. "Heterogeneous treatment effects with mismeasured endogenous treatment," Quantitative Economics, Econometric Society, vol. 9(3), pages 1335-1370, November.
    16. Arthur Lewbel, 2007. "Estimation of Average Treatment Effects with Misclassification," Econometrica, Econometric Society, vol. 75(2), pages 537-551, March.
    17. Meyer, Bruce D. & Goerge, Robert M., 2011. "Errors in Survey Reporting and Imputation and Their Effects on Estimates of Food Stamp Program Participation," Contractor and Cooperator Reports 312394, United States Department of Agriculture, Economic Research Service.
    18. 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.
    19. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    20. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    21. Bollinger, Christopher R., 1996. "Bounding mean regressions when a binary regressor is mismeasured," Journal of Econometrics, Elsevier, vol. 73(2), pages 387-399, August.
    22. 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.
    23. Feinstein, Jonathan S, 1990. "Detection Controlled Estimation," Journal of Law and Economics, University of Chicago Press, vol. 33(1), pages 233-276, April.
    24. Bruce D. Meyer & Wallace K. C. Mok & James X. Sullivan, 2009. "The Under-Reporting of Transfers in Household Surveys: Its Nature and Consequences," NBER Working Papers 15181, National Bureau of Economic Research, Inc.
    25. 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.
    26. 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.
    27. 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.
    28. Hu, Yingyao & Shiu, Ji-Liang & Woutersen, Tiemen, 2016. "Identification in nonseparable models with measurement errors and endogeneity," Economics Letters, Elsevier, vol. 144(C), pages 33-36.
    29. van Hasselt, Martijn & Bollinger, Christopher R., 2012. "Binary misclassification and identification in regression models," Economics Letters, Elsevier, vol. 115(1), pages 81-84.
    30. Arthur Lewbel & Yingying Dong & Thomas Tao Yang, 2012. "Viewpoint: Comparing features of convenient estimators for binary choice models with endogenous regressors," Canadian Journal of Economics, Canadian Economics Association, vol. 45(3), pages 809-829, August.
    31. Kane, Thomas J & Rouse, Cecilia Elena, 1995. "Labor-Market Returns to Two- and Four-Year College," American Economic Review, American Economic Association, vol. 85(3), pages 600-614, June.
    32. John Bound, 1991. "Self-Reported Versus Objective Measures of Health in Retirement Models," Journal of Human Resources, University of Wisconsin Press, vol. 26(1), pages 106-138.
    33. Erich Battistin & Barbara Sianesi, 2011. "Misclassified Treatment Status and Treatment Effects: An Application to Returns to Education in the United Kingdom," The Review of Economics and Statistics, MIT Press, vol. 93(2), pages 495-509, May.
    34. 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.
    35. 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).
    36. Brachet, Tanguy, 2008. "Maternal Smoking, Misclassification, and Infant Health," MPRA Paper 21466, University Library of Munich, Germany.
    37. Aprajit Mahajan, 2006. "Identification and Estimation of Regression Models with Misclassification," Econometrica, Econometric Society, vol. 74(3), pages 631-665, May.
    38. 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..
    39. 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.
    40. 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).
    41. Poirier, Dale J., 1980. "Partial observability in bivariate probit models," Journal of Econometrics, Elsevier, vol. 12(2), pages 209-217, February.
    42. Ichimura, H., 1991. "Semiparametric Least Squares (sls) and Weighted SLS Estimation of Single- Index Models," Papers 264, Minnesota - Center for Economic Research.
    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. Francis J. DiTraglia & Camilo Garcia-Jimeno, 2020. "Identifying the effect of a mis-classified, binary, endogenous regressor," Papers 2011.07272, arXiv.org.
    2. 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.
    3. Mittag, Nikolas, 2016. "Correcting for Misreporting of Government Benefits," IZA Discussion Papers 10266, Institute of Labor Economics (IZA).
    4. Acerenza, Santiago & Ban, Kyunghoon & Kedagni, Desire, 2021. "Marginal Treatment Effects with Misclassified Treatment," ISU General Staff Papers 202106180700001132, Iowa State University, Department of Economics.
    5. Tommasi, Denni & Zhang, Lina, 2024. "Bounding program benefits when participation is misreported," Journal of Econometrics, Elsevier, vol. 238(1).
    6. Akanksha Negi & Digvijay Singh Negi, 2022. "Difference-in-Differences with a Misclassified Treatment," Papers 2208.02412, arXiv.org.
    7. 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.
    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. Helen H. Jensen & Brent Kreider & Oleksandr Zhylyevskyy, 2019. "Investigating Treatment Effects of Participating Jointly in SNAP and WIC when the Treatment Is Validated Only for SNAP," Southern Economic Journal, John Wiley & Sons, vol. 86(1), pages 124-155, July.
    10. 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.
    11. Augustine Denteh & D'esir'e K'edagni, 2022. "Misclassification in Difference-in-differences Models," Papers 2207.11890, arXiv.org, revised Jul 2022.
    12. Sung Jae Jun & Sokbae Lee, 2023. "Identifying the Effect of Persuasion," Journal of Political Economy, University of Chicago Press, vol. 131(8), pages 2032-2058.
    13. 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.
    14. Tammy Leonard & David Andrews & Sandi L. Pruitt, 2022. "Impact of changes in the frequency of food pantry utilization on client food security and well‐being," Applied Economic Perspectives and Policy, John Wiley & Sons, vol. 44(2), pages 1049-1067, June.
    15. 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.
    16. Jones, Jordan & Courtemanche, Charles & Denteh, Augustine & Marton, James & Tchernis, Rusty, 2021. "Do State Snap Policies Influence Program Participation among Seniors?," IZA Discussion Papers 14564, Institute of Labor Economics (IZA).
    17. Flores-Lagunes, Alfonso & Jales, Hugo B. & Liu, Judith & Wilson, Norbert L., 2023. "Moving Policies Toward Racial and Ethnic Equality: The Case of the Supplemental Nutrition Assistance Program," GLO Discussion Paper Series 1272, Global Labor Organization (GLO).
    18. Martijn van Hasselt & Christopher R. Bollinger & Jeremy W. Bray, 2022. "A Bayesian approach to account for misclassification in prevalence and trend estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(2), pages 351-367, March.
    19. Seoyun Hong & Chang Sik Kim & Hyunchul Kim, 2022. "Measuring the Effects of Bid-Rigging on Prices with Binary Misclassification," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 61(3), pages 319-339, November.
    20. Pablo A. Celhay & Bruce D. Meyer & Nikolas Mittag, 2022. "What Leads to Measurement Errors? Evidence from Reports of Program Participation in Three Surveys," NBER Working Papers 29652, National Bureau of Economic Research, Inc.
    21. Jordan W. Jones & Charles Courtemanche & Augustine Denteh & James Marton & Rusty Tchernis, 2022. "Do state Supplemental Nutrition Assistance Program policies influence program participation among seniors?," Applied Economic Perspectives and Policy, John Wiley & Sons, vol. 44(2), pages 591-608, June.
    22. 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).
    23. Jones, Jordan W. & Marton, James & Courtemanche, Charles & Tchernis, Rusty & Denteh, Augustine, 2021. "Policy Determinants of Senior SNAP Participation," 2021 Annual Meeting, August 1-3, Austin, Texas 313925, Agricultural and Applied Economics Association.
    24. Wossen, Tesfamicheal & Alene, Arega & Abdoulaye, Tahirou & Feleke, Shiferaw & Manyong, Victor, 2019. "Agricultural technology adoption and household welfare: Measurement and evidence," Food Policy, Elsevier, vol. 87(C), pages 1-1.

    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. Francis J. DiTraglia & Camilo Garcia-Jimeno, 2020. "Identifying the effect of a mis-classified, binary, endogenous regressor," Papers 2011.07272, arXiv.org.
    3. 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.
    4. 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.
    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. 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.
    7. 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.
    8. 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.
    9. Akanksha Negi & Digvijay Singh Negi, 2022. "Difference-in-Differences with a Misclassified Treatment," Papers 2208.02412, arXiv.org.
    10. Takahide Yanagi, 2019. "Inference on local average treatment effects for misclassified treatment," Econometric Reviews, Taylor & Francis Journals, vol. 38(8), pages 938-960, September.
    11. 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.
    12. 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.
    13. Acerenza, Santiago & Ban, Kyunghoon & Kedagni, Desire, 2021. "Marginal Treatment Effects with Misclassified Treatment," ISU General Staff Papers 202106180700001132, Iowa State University, Department of Economics.
    14. Martijn van Hasselt & Christopher R. Bollinger & Jeremy W. Bray, 2022. "A Bayesian approach to account for misclassification in prevalence and trend estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(2), pages 351-367, March.
    15. 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).
    16. Augustine Denteh & D'esir'e K'edagni, 2022. "Misclassification in Difference-in-differences Models," Papers 2207.11890, arXiv.org, revised Jul 2022.
    17. Francis J. DiTraglia & Camilo Garcia-Jimeno, 2020. "A Framework for Eliciting, Incorporating, and Disciplining Identification Beliefs in Linear Models," Papers 2011.07276, arXiv.org.
    18. 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.
    19. Orville Mondal & Rui Wang, 2024. "Partial Identification of Binary Choice Models with Misreported Outcomes," Papers 2401.17137, arXiv.org.
    20. Adele Bergin, 2015. "Employer Changes and Wage Changes: Estimation with Measurement Error in a Binary Variable," LABOUR, CEIS, vol. 29(2), pages 194-223, June.

    More about this item

    Keywords

    Treatment effect; Misclassification; Endogeneity; Binary regressor; Partial observability; Bias;
    All these keywords.

    JEL classification:

    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

    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:eee:econom:v:208:y:2019:i:2:p:487-506. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.