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Misclassification In Binary Choice Models

Author

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  • Bruce Meyer
  • Nikolas Mittag

Abstract

We derive the asymptotic bias from misclassification of the dependent variable in binary choice models. Measurement error is necessarily non-classical in this case, which leads to bias in linear and non-linear models even if only the dependent variable is mismeasured. A Monte Carlo study and an application to food stamp receipt show that the bias formulas are useful to analyze the sensitivity of substantive conclusions, to interpret biased coefficients and imply features of the estimates that are robust to misclassification. Using administrative records linked to survey data as validation data, we examine estimators that are consistent under misclassification. They can improve estimates if their assumptions hold, but can aggravate the problem if the assumptions are invalid. The estimators differ in their robustness to such violations, which can be improved by incorporating additional information. We propose tests for the presence and nature of misclassification that can help to choose an estimator.

Suggested Citation

  • Bruce Meyer & Nikolas Mittag, 2013. "Misclassification In Binary Choice Models," Working Papers 13-27, Center for Economic Studies, U.S. Census Bureau.
  • Handle: RePEc:cen:wpaper:13-27
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    File URL: https://www2.census.gov/ces/wp/2013/CES-WP-13-27.pdf
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    References listed on IDEAS

    as
    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. Ruud, Paul A., 1986. "Consistent estimation of limited dependent variable models despite misspecification of distribution," Journal of Econometrics, Elsevier, vol. 32(1), pages 157-187, June.
    3. Bollinger, Christopher R & David, Martin H, 2001. "Estimation with Response Error and Nonresponse: Food-Stamp Participation in the SIPP," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 129-141, April.
    4. Guido W. Imbens & Tony Lancaster, 1994. "Combining Micro and Macro Data in Microeconometric Models," Review of Economic Studies, Oxford University Press, vol. 61(4), pages 655-680.
    5. Steven D. Levitt, 1998. "Juvenile Crime and Punishment," Journal of Political Economy, University of Chicago Press, vol. 106(6), pages 1156-1185, December.
    6. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
    7. Lancaster, Tony & Imbens, Guido, 1996. "Case-control studies with contaminated controls," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 145-160.
    8. Bruce D. Meyer & Wallace K. C. Mok & James X. Sullivan, 2009. "The Under-Reporting of Transfers in Household Surveys: Its Nature and Consequences," Working Papers 0903, Harris School of Public Policy Studies, University of Chicago.
    9. 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.
    10. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    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. Zvi Eckstein & Kenneth I. Wolpin, 1999. "Why Youths Drop Out of High School: The Impact of Preferences, Opportunities, and Abilities," Econometrica, Econometric Society, vol. 67(6), pages 1295-1340, November.
    13. Hausman, J.A. & Morton, F.M.S., 1994. "Misclassification of Dependent Variable in a Discrete Response Setting," Working papers 94-19, Massachusetts Institute of Technology (MIT), Department of Economics.
    14. 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.
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    More about this item

    Keywords

    measurement error; binary choice models; program take-up; food stamps.;

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • I38 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Government Programs; Provision and Effects of Welfare Programs

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