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Point identification in the presence of measurement error in discrete variables: application - wages and disability


  • Eirini-Christina Saloniki


  • Amanda Gosling



This paper addresses the problem of point identification in the presence of measurement error in discrete variables; in particular, it considers the case of having two "noisy" indicators of the same latent variable and without any prior information about the true value of the variable of interest. Based on the concept of the fourfold table and creating a nonlinear system of simultaneous equations from the observed proportions and predicted wages, we examine the need for different assumptions in order to obtain unique solutions for the system. We show that by imposing a simple restriction(s) for the joint misclassification probabilities, it is possible to measure the extent of the misclassification error in that specific variable. The proposed methodology is then used to identify whether people misreport their disability status using data from the British Household Panel Survey. Our results show that the probability of underreporting is greater than the probability of overreporting disability.

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  • Eirini-Christina Saloniki & Amanda Gosling, 2012. "Point identification in the presence of measurement error in discrete variables: application - wages and disability," Studies in Economics 1214, School of Economics, University of Kent.
  • Handle: RePEc:ukc:ukcedp:1214

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    References listed on IDEAS

    1. 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.
    2. Jones, Melanie K. & Latreille, Paul L. & Sloane, Peter J., 2007. "Disability and Work: A Review of the British Evidence," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 25, pages 473-498, Abril.
    3. 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.
    4. David Madden, 2004. "Labour market discrimination on the basis of health: an application to UK data," Applied Economics, Taylor & Francis Journals, vol. 36(5), pages 421-442.
    5. Kreider, Brent, 2006. "Partially Identifying the Prevalence of Health Insurance Given Contaminated Sampling Response Error," Staff General Research Papers Archive 12588, Iowa State University, Department of Economics.
    6. Melanie K. Jones & Peter J. Sloane, 2010. "Disability and Skill Mismatch," The Economic Record, The Economic Society of Australia, vol. 86(s1), pages 101-114, September.
    7. 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.
    8. Marjorie L. Baldwin & Edward J. Schumacher, "undated". "Job Mobility among Workers with Disabilities," Working Papers 9805, East Carolina University, Department of Economics.
    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. 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.
    11. Robert B. Wallace & A. Regula Herzog, 1995. "Overview of the Health Measures in the Health and Retirement Study," Journal of Human Resources, University of Wisconsin Press, vol. 30, pages s84-s107.
    12. Christopher R. Bollinger, 2003. "Measurement Error in Human Capital and the Black-White Wage Gap," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 578-585, August.
    13. Melanie K. Jones, 2009. "The Employment Effect of the Disability Discrimination Act: Evidence from the Health Survey for England," LABOUR, CEIS, vol. 23(2), pages 349-369, June.
    14. Phelps, Edmund S, 1972. "The Statistical Theory of Racism and Sexism," American Economic Review, American Economic Association, vol. 62(4), pages 659-661, September.
    15. Melanie K. Jones & Paul L. Latreille & Peter J. Sloane, 2006. "Disability, gender, and the British labour market," Oxford Economic Papers, Oxford University Press, vol. 58(3), pages 407-449, July.
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    More about this item


    measurement error; discrete; misclassification probabilities; identification; disability;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • J14 - Labor and Demographic Economics - - Demographic Economics - - - Economics of the Elderly; Economics of the Handicapped; Non-Labor Market Discrimination
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials

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