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

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  • Kreider, Brent
  • Pepper, John V.

Abstract

We consider the problem of identifying a mean outcome in corrupt sampling where the observed outcome is a mixture of the distribution of interest and some other distribution. We make two contributions to this literature. First, the statistical independence assumption maintained under contaminated sampling is relaxed to the weaker assumption that the outcome is mean independent of the mixing process. We then generalize this restriction to allow the two conditional means to differ by a known or bounded factor of proportionality. Second, in the special case of a binary outcome, we consider the possibility that draws from the alternative distribution are known to be erroneous, as might be the case in a mixture model of response error. We illustrate how these assumptions can be used to inform researchers about the population's use of illicit drugs in the presence of nonrandom reporting errors. In this application, we find that a response error model with multiplicative mean independence is easy to motivate and can have substantial identifying power.

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Bibliographic Info

Article provided by American Statistical Association in its journal Journal of Business and Economic Statistics.

Volume (Year): 29 (2011)
Issue (Month): 1 ()
Pages: 49-60

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Handle: RePEc:bes:jnlbes:v:29:i:1:y:2011:p:49-60

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  1. 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.
  2. 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.
  3. Bound, John, 1991. "The Health and Earnings of Rejected Disability Insurance Applicants: Reply," American Economic Review, American Economic Association, vol. 81(5), pages 1427-34, December.
  4. Molinari, Francesca, 2008. "Partial identification of probability distributions with misclassified data," Journal of Econometrics, Elsevier, vol. 144(1), pages 81-117, May.
  5. Mark C. Berger & Dan A. Black & Frank A. Scott, 1998. "How Well Do We Measure Employer-Provided Health Insurance Coverage?," Contemporary Economic Policy, Western Economic Association International, vol. 16(3), pages 356-367, 07.
  6. John Pepper & Brent Kreider, 2001. "Inferring Disability Status from Corrupt Data," Virginia Economics Online Papers 354, University of Virginia, Department of Economics.
  7. 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.
  8. Bollinger, Christopher R., 1996. "Bounding mean regressions when a binary regressor is mismeasured," Journal of Econometrics, Elsevier, vol. 73(2), pages 387-399, August.
  9. Bound, John & Burkhauser, Richard V., 1999. "Economic analysis of transfer programs targeted on people with disabilities," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 51, pages 3417-3528 Elsevier.
  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 167-92, January.
  11. Kreider, Brent, 1999. "Latent Work Disability and Reporting Bias," Staff General Research Papers 5185, Iowa State University, Department of Economics.
  12. E. Tamer & V. Chernozhukov & H. Hong, 2004. "Parameter Set Inference in a Class of Econometric Models," Econometric Society 2004 North American Winter Meetings 382, Econometric Society.
  13. 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.
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Cited by:
  1. Gundersen, Craig & Kreider, Brent & Pepper, John V., 2011. "The Impact of the National School Lunch Program on Child Health: A Nonparametric Bounds Analysis," Staff General Research Papers 32720, Iowa State University, Department of Economics.

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