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On the Estimation of Treatment Effects with Endogenous Misreporting

Author

Listed:
  • 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 for the Study of Labor (IZA).
  • Handle: RePEc:iza:izadps:dp11426
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    References listed on IDEAS

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    1. Yingying Dong & Arthur Lewbel & Thomas Tao Yang, 2012. "Comparing Features of Convenient Estimators for Binary Choice Models With Endogenous Regressors," Boston College Working Papers in Economics 789, Boston College Department of Economics, revised 15 May 2012.
    2. Melvin Stephens, Jr. & Takashi Unayama, 2015. "Estimating the Impacts of Program Benefits: Using Instrumental Variables with Underreported and Imputed Data," NBER Working Papers 21248, National Bureau of Economic Research, Inc.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Tripathi, Gautam, 1999. "A matrix extension of the Cauchy-Schwarz inequality," Economics Letters, Elsevier, vol. 63(1), pages 1-3, April.
    8. 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.
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    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. van Hasselt, Martijn & Bollinger, Christopher R., 2012. "Binary misclassification and identification in regression models," Economics Letters, Elsevier, vol. 115(1), pages 81-84.
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    17. 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), May.
    18. Aprajit Mahajan, 2006. "Identification and Estimation of Regression Models with Misclassification," Econometrica, Econometric Society, vol. 74(3), pages 631-665, May.
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    More about this item

    Keywords

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

    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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