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Nonparametric Identification and Estimation with Non-Classical Errors-in-Variables (2403.11309v1)
Published 17 Mar 2024 in econ.EM
Abstract: This paper considers nonparametric identification and estimation of the regression function when a covariate is mismeasured. The measurement error need not be classical. Employing the small measurement error approximation, we establish nonparametric identification under weak and easy-to-interpret conditions on the instrumental variable. The paper also provides nonparametric estimators of the regression function and derives their rates of convergence.
- Bound, J., C. Brown, and N. Mathiowetz (2001): “Measurement Error in Survey Data,” in Handbook of Econometrics, Elsevier, 3705–3843.
- Carroll, R. J. and L. A. Stefanski (1990): “Approximate quasi-likelihood estimation in models with surrogate predictors,” Journal of the American Statistical Association, 85, 652–663.
- Chesher, A. (1991): “The effect of measurement error,” Biometrika, 78, 451–462.
- ——— (2000): “Measurement Error Bias Reduction,” Working paper.
- Chesher, A. and C. Schluter (2002): “Welfare measurement and measurement error,” The Review of Economic Studies, 69, 357–378.
- Evdokimov, K. S. and A. Zeleneev (2018): “Issues of Nonstandard Inference in Measurement Error Models,” Working Paper, Princeton University.
- ——— (2022): “Simple Estimation of Semiparametric Models with Measurement Errors,” CeMMAP Working Paper.
- Hausman, J. A., H. Ichimura, W. K. Newey, and J. L. Powell (1991): “Identification and estimation of polynomial errors-in-variables models,” Journal of Econometrics, 50, 273–295.
- Hausman, J. A., W. K. Newey, and J. L. Powell (1995): “Nonlinear errors in variables Estimation of some Engel curves,” Journal of Econometrics, 65, 205–233.
- Hu, Y. (2008): “Identification and estimation of nonlinear models with misclassification error using instrumental variables: A general solution,” Journal of Econometrics, 144, 27–61.
- Hu, Y. and S. M. Schennach (2008): “Instrumental Variable Treatment of Nonclassical Measurement Error Models,” Econometrica, 76, 195–216.
- Li, T. and Q. Vuong (1998): “Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators,” Journal of Multivariate Analysis, 65, 139–165.
- Newey, W. K. (2001): “Flexible Simulated Moment Estimation of Nonlinear Errors-in-Variables Models,” The Review of Economics and Statistics, 83, 616–627.
- Schennach, S. (2022): “Measurement Systems,” Journal of Economic Literature, 60, 1223–1263.
- Schennach, S. M. (2004): “Estimation of Nonlinear Models with Measurement Error,” Econometrica, 72, 33–75.
- ——— (2007): “Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models,” Econometrica, 75, 201–239.
- Stone, C. J. (1980): “Optimal Rates of Convergence for Nonparametric Estimators,” Annals of Statistics, 8, 1348–1360.
- Wilhelm, D. (2019): “Testing for the presence of measurement error,” CeMMAP working papers CWP48/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Wolter, K. M. and W. A. Fuller (1982): “Estimation of Nonlinear Errors-in-Variables Models,” The Annals of Statistics, 10, 539–548.