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On the Estimation of Treatment Effects with Endogenous Misreporting

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  • Nguimkeu, Pierre

    (Georgia State University)

  • Denteh, Augustine

    (Georgia State University)

  • Tchernis, Rusty

    (Georgia State University)

Abstract

Participation in social programs is often misreported in survey data, complicating the estimation of the effects of those programs. In this paper, we propose a model to estimate treatment effects under endogenous participation and endogenous misreporting. We show that failure to account for endogenous misreporting can result in the estimate of the treatment effect having an opposite sign from the true effect. 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 related to both participation and misreporting. We establish the consistency and asymptotic normality of our estimator and assess its small sample performance through Monte Carlo simulations. An empirical example is given to illustrate the proposed method.

Suggested Citation

  • Nguimkeu, Pierre & Denteh, Augustine & Tchernis, Rusty, 2018. "On the Estimation of Treatment Effects with Endogenous Misreporting," IZA Discussion Papers 11426, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp11426
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    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. 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. 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.
    8. Arthur Lewbel, 2007. "Estimation of Average Treatment Effects with Misclassification," Econometrica, Econometric Society, vol. 75(2), pages 537-551, March.
    9. 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.
    10. 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.
    11. Bollinger, Christopher R., 1996. "Bounding mean regressions when a binary regressor is mismeasured," Journal of Econometrics, Elsevier, vol. 73(2), pages 387-399, August.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Néstor Gandelman & Alejandro Rasteletti, 2017. "Credit constraints, sector informality and firm investments: Evidence from a panel of Uruguayan firms," Journal of Applied Economics, Universidad del CEMA, vol. 20, pages 351-372, November.
    19. 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.
    20. 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.
    21. 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).
    22. Poirier, Dale J., 1980. "Partial observability in bivariate probit models," Journal of Econometrics, Elsevier, vol. 12(2), pages 209-217, February.
    23. Tripathi, Gautam, 1999. "A matrix extension of the Cauchy-Schwarz inequality," Economics Letters, Elsevier, vol. 63(1), pages 1-3, April.
    24. 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.
    25. 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.
    26. Takuya Ura, 2018. "Heterogeneous treatment effects with mismeasured endogenous treatment," Quantitative Economics, Econometric Society, vol. 9(3), pages 1335-1370, November.
    27. 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.
    28. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    29. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    30. Feinstein, Jonathan S, 1990. "Detection Controlled Estimation," Journal of Law and Economics, University of Chicago Press, vol. 33(1), pages 233-276, April.
    31. 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.
    32. 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.
    33. van Hasselt, Martijn & Bollinger, Christopher R., 2012. "Binary misclassification and identification in regression models," Economics Letters, Elsevier, vol. 115(1), pages 81-84.
    34. 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.
    35. 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.
    36. 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.
    37. 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).
    38. Brachet, Tanguy, 2008. "Maternal Smoking, Misclassification, and Infant Health," MPRA Paper 21466, University Library of Munich, Germany.
    39. Aprajit Mahajan, 2006. "Identification and Estimation of Regression Models with Misclassification," Econometrica, Econometric Society, vol. 74(3), pages 631-665, May.
    40. 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..
    41. 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.
    42. Ichimura, H., 1991. "Semiparametric Least Squares (sls) and Weighted SLS Estimation of Single- Index Models," Papers 264, Minnesota - Center for Economic Research.
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    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.

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    More about this item

    Keywords

    partial observability; binary regressor; treatment effect; misclassification; endogeneity; 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

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