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Identifiability of mean-reverting measurement error with instrumental variable

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  • Qing Li

Abstract

type="main"> In the context where one main regressor is measured with error and at least one instrumental variable is available for the correction of measurement error, this paper provides, to the best of our knowledge, a first point-identification result on the variance of measurement error, the variance of latent variable, and their covariance. We show that the parameters are identified if the regression model is not de facto linear. We illustrate the method in an application to identify mean-reverting measurement error, a typical issue in reported income where the measurement error of income is negatively correlated with the true income.

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  • Qing Li, 2014. "Identifiability of mean-reverting measurement error with instrumental variable," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(2), pages 118-129, May.
    • Handle: RePEc:bla:stanee:v:68:y:2014:i:2:p:118-129
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    1. John Strauss & Duncan Thomas, 1998. "Health, Nutrition, and Economic Development," Journal of Economic Literature, American Economic Association, vol. 36(2), pages 766-817, June.
    2. Meijer, Erik & Wansbeek, Tom, 2000. "Measurement error in a single regressor," Economics Letters, Elsevier, vol. 69(3), pages 277-284, December.
    3. Andersen, Torben G & Sorensen, Bent E, 1996. "GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 328-352, July.
    4. Amemiya, Yasuo, 1985. "Instrumental variable estimator for the nonlinear errors-in-variables model," Journal of Econometrics, Elsevier, vol. 28(3), pages 273-289, June.
    5. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, January.
    6. 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.
    7. Bound, John & Krueger, Alan B, 1991. "The Extent of Measurement Error in Longitudinal Earnings Data: Do Two Wrongs Make a Right?," Journal of Labor Economics, University of Chicago Press, vol. 9(1), pages 1-24, January.
    8. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    9. Lewbel, Arthur, 1996. "Demand Estimation with Expenditure Measurement Errors on the Left and Right Hand Side," The Review of Economics and Statistics, MIT Press, vol. 78(4), pages 718-725, November.
    10. Peter Gottschalk & Minh Huynh, 2010. "Are Earnings Inequality and Mobility Overstated? The Impact of Nonclassical Measurement Error," The Review of Economics and Statistics, MIT Press, vol. 92(2), pages 302-315, May.
    11. Erickson, Timothy, 1993. "Restricting Regression Slopes in the Errors-in-Variables Model by Bounding the Error Correlation," Econometrica, Econometric Society, vol. 61(4), pages 959-969, July.
    12. Hausman, J. A. & Newey, W. K. & Powell, J. L., 1995. "Nonlinear errors in variables Estimation of some Engel curves," Journal of Econometrics, Elsevier, vol. 65(1), pages 205-233, January.
    13. Hausman, Jerry A. & Newey, Whitney K. & Ichimura, Hidehiko & Powell, James L., 1991. "Identification and estimation of polynomial errors-in-variables models," Journal of Econometrics, Elsevier, vol. 50(3), pages 273-295, December.
    14. Bollinger, Christopher R, 1998. "Measurement Error in the Current Population Survey: A Nonparametric Look," Journal of Labor Economics, University of Chicago Press, vol. 16(3), pages 576-594, July.
    15. 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.
    16. Bonggeun Kim & Gary Solon, 2005. "Implications of Mean-Reverting Measurement Error for Longitudinal Studies of Wages and Employment," The Review of Economics and Statistics, MIT Press, vol. 87(1), pages 193-196, February.
    17. Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, January.
    18. Bound, John & Brown, Charles & Duncan, Greg J & Rodgers, Willard L, 1994. "Evidence on the Validity of Cross-Sectional and Longitudinal Labor Market Data," Journal of Labor Economics, University of Chicago Press, vol. 12(3), pages 345-368, July.
    19. repec:dgr:rugsom:00f14 is not listed on IDEAS
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    2. Qing Li & Alain A. Cohen & Linda P. Fried, 2017. "A novel health metric based on biomarkers," Cahiers de recherche 17-08, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.

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