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Identification of Expected Outcomes in a Data Error Mixing Model With Multiplicative Mean Independence

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  • Brent Kreider
  • John V. Pepper

Abstract

We consider the problem of identifying a mean outcome in corrupt sampling where the observed outcome is drawn from a mixture of the distribution of interest and another distribution. Relaxing the contaminated sampling assumption that the outcome is statistically independent of the mixing process, we assess the identifying power of an assumption that the conditional means of the distributions differ by a factor of proportionality. For binary outcomes, we consider the special case that all draws from the alternative distribution are erroneous. We illustrate how these models can inform researchers about illicit drug use in the presence of reporting errors.

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  • Brent Kreider & John V. Pepper, 2011. "Identification of Expected Outcomes in a Data Error Mixing Model With Multiplicative Mean Independence," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 49-60, January.
    • Handle: RePEc:taf:jnlbes:v:29:y:2011:i:1:p:49-60
    DOI: 10.1198/jbes.2009.07223
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    3. Kreider, Brent & Pepper, John V., 2007. "Disability and Employment: Reevaluating the Evidence in Light of Reporting Errors," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 432-441, June.
    4. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    5. 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.
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    8. Horowitz, Joel L & Manski, Charles F, 1995. "Identification and Robustness with Contaminated and Corrupted Data," Econometrica, Econometric Society, vol. 63(2), pages 281-302, March.
    9. Brent Kreider & John Pepper, 2008. "Inferring disability status from corrupt data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(3), pages 329-349.
    10. Barron, John M & Berger, Mark C & Black, Dan A, 1997. "Employer Search, Training, and Vacancy Duration," Economic Inquiry, Western Economic Association International, vol. 35(1), pages 167-192, January.
    11. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, July.
    12. Brent Kreider, 1999. "Latent Work Disability and Reporting Bias," Journal of Human Resources, University of Wisconsin Press, vol. 34(4), pages 734-769.
    13. Bollinger, Christopher R., 1996. "Bounding mean regressions when a binary regressor is mismeasured," Journal of Econometrics, Elsevier, vol. 73(2), pages 387-399, August.
    14. Bound, John, 1991. "The Health and Earnings of Rejected Disability Insurance Applicants: Reply," American Economic Review, American Economic Association, vol. 81(5), pages 1427-1434, December.
    15. Molinari, Francesca, 2008. "Partial identification of probability distributions with misclassified data," Journal of Econometrics, Elsevier, vol. 144(1), pages 81-117, May.
    16. Barry T. Hirsch & Edward J. Schumacher, 2004. "Match Bias in Wage Gap Estimates Due to Earnings Imputation," Journal of Labor Economics, University of Chicago Press, vol. 22(3), pages 689-722, July.
    17. V. Joseph Hotz & Charles H. Mullin & Seth G. Sanders, 1997. "Bounding Causal Effects Using Data from a Contaminated Natural Experiment: Analysing the Effects of Teenage Childbearing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(4), pages 575-603.
    18. 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.
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    1. 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.
    2. Kaspar W thrich, 2013. "Set Identification of Generalized Linear Predictors in the Presence of Non-Classical Measurement Errors," Diskussionsschriften dp1304, Universitaet Bern, Departement Volkswirtschaft.
    3. Gundersen, Craig & Kreider, Brent & Pepper, John, 2012. "The impact of the National School Lunch Program on child health: A nonparametric bounds analysis," Journal of Econometrics, Elsevier, vol. 166(1), pages 79-91.
    4. Orville Mondal & Rui Wang, 2024. "Partial Identification of Binary Choice Models with Misreported Outcomes," Papers 2401.17137, arXiv.org.
    5. Brent Kreider & John V. Pepper & Manan Roy, 2016. "Identifying the Effects of WIC on Food Insecurity Among Infants and Children," Southern Economic Journal, John Wiley & Sons, vol. 82(4), pages 1106-1122, April.
    6. Meyer, Bruce D. & Mittag, Nikolas, 2017. "Misclassification in binary choice models," Journal of Econometrics, Elsevier, vol. 200(2), pages 295-311.

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