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Estimation in Binary Choice Models with Measurement Errors

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Abstract

In this paper we develop a simple maximum likelihood estimator for probit models where the regressors have measurement error. We first assume precise information about the reliability ratios (or, equivalently, the proxy correlations) of the regressors. We then show how reasonable bounds for the parameter estimates can be obtained when only imprecise information is available. The analysis is also extended to situations where the measurement error has non-zero mean and is correlated with the true values of the regressors. An extensive simulation study shows that the estimator works very well, even in quite small samples. Finally the method is applied to data explaining sick leave in Sweden.

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  • Edgerton, David & Jochumzen, Peter, 2003. "Estimation in Binary Choice Models with Measurement Errors," Working Papers 2003:4, Lund University, Department of Economics, revised 07 Jul 2003.
  • Handle: RePEc:hhs:lunewp:2003_004 Note: Gauss program available
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    References listed on IDEAS

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    1. Amemiya, Yasuo, 1985. "Instrumental variable estimator for the nonlinear errors-in-variables model," Journal of Econometrics, Elsevier, vol. 28(3), pages 273-289, June.
    2. 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.
    3. Hsiao, Cheng & Wang, Q Kevin, 2000. "Estimation of Structural Nonlinear Errors-in-Variables Models by Simulated Least-Squares Method," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(2), pages 523-542, May.
    4. Kao, Chihwa & Schnell, John F., 1987. "Errors in variables in panel data with a binary dependent variable," Economics Letters, Elsevier, vol. 24(1), pages 45-49.
    5. Klepper, Steven & Leamer, Edward E, 1984. "Consistent Sets of Estimates for Regressions with Errors in All Variables," Econometrica, Econometric Society, vol. 52(1), pages 163-183, January.
    6. Murphy, Kevin M & Topel, Robert H, 2002. "Estimation and Inference in Two-Step Econometric Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 88-97, January.
    7. Whitney K. Newey, 2001. "Flexible Simulated Moment Estimation Of Nonlinear Errors-In-Variables Models," The Review of Economics and Statistics, MIT Press, vol. 83(4), pages 616-627, November.
    8. Kao, Chihwa & Schnell, John F., 1987. "Errors in variables in a random-effects probit model for panel data," Economics Letters, Elsevier, vol. 24(4), pages 339-342.
    9. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
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    Cited by:

    1. Ruhm, Christopher J. & Jones, Alison Snow & McGeary, Kerry Anne & Kerr, William C. & Terza, Joseph V. & Greenfield, Thomas K. & Pandian, Ravi S., 2012. "What U.S. data should be used to measure the price elasticity of demand for alcohol?," Journal of Health Economics, Elsevier, vol. 31(6), pages 851-862.
    2. Hvide, Hans K. & Panos, Georgios A., 2014. "Risk tolerance and entrepreneurship," Journal of Financial Economics, Elsevier, vol. 111(1), pages 200-223.
    3. Akib Khan & Atonu Rabbani, 2015. "Assessing The Spatial Accessibility Of Microfinance In Northern Bangladesh: A Gis Analysis," Journal of Regional Science, Wiley Blackwell, vol. 55(5), pages 842-870, November.
    4. Dhawan, Rajeev & Jochumzen, Peter, 1999. "Stochastic Frontier Production Function With Errors-In-Variables," Working Papers 1999:007, Lund University, Department of Economics.

    More about this item

    Keywords

    Measurement error; errors-in-variables; probit; binary choice; bounds;

    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C29 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Other

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