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Simple estimation of semiparametric models with measurement errors

Author

Listed:
  • Kirill Evdokimov
  • Andrei Zeleneev

Abstract

We develop a practical way of addressing the Errors-In-Variables (EIV) problem in the Generalized Method of Moments (GMM) framework. We focus on the settings in which the variability of the EIV is a fraction of that of the mismeasured variables, which is typical for empirical applications. For any initial set of moment conditions our approach provides a “corrected” set of moment conditions that are robust to the EIV. We show that the GMM estimator based on these moments is √n-consistent, with the standard tests and confidence intervals providing valid inference. This is true even when the EIV are so large that naive estimators (that ignore the EIV problem) are heavily biased with their confidence intervals having 0% coverage. Our approach involves no nonparametric estimation, which is especially important for applications with many covariates, and settings with multivariate or non-classical EIV. In particular, the approach makes it easy to use instrumental variables to address EIV in nonlinear models.

Suggested Citation

  • Kirill Evdokimov & Andrei Zeleneev, 2024. "Simple estimation of semiparametric models with measurement errors," CeMMAP working papers 05/24, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:05/24
    DOI: 10.47004/wp.cem.2024.0524
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    References listed on IDEAS

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    1. S. M. Schennach & Yingyao Hu, 2013. "Nonparametric Identification and Semiparametric Estimation of Classical Measurement Error Models Without Side Information," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 177-186, March.
    2. James Heckman & Edward Vytlacil, 1998. "Instrumental Variables Methods for the Correlated Random Coefficient Model: Estimating the Average Rate of Return to Schooling When the Return is Correlated with Schooling," Journal of Human Resources, University of Wisconsin Press, vol. 33(4), pages 974-987.
    3. Hong, Han & Tamer, Elie, 2003. "A simple estimator for nonlinear error in variable models," Journal of Econometrics, Elsevier, vol. 117(1), pages 1-19, November.
    4. Hahn, Jinyong & Hausman, Jerry & Kim, Jeonghwan, 2021. "A small sigma approach to certain problems in errors-in-variables models," Economics Letters, Elsevier, vol. 208(C).
    5. Donald W. K. Andrews & Patrik Guggenberger, 2015. "Identification- and Singularity-Robust Inference for Moment Condition," Cowles Foundation Discussion Papers 1978, Cowles Foundation for Research in Economics, Yale University.
    6. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, September.
    7. Stéphane Bonhomme & Martin Weidner, 2022. "Minimizing sensitivity to model misspecification," Quantitative Economics, Econometric Society, vol. 13(3), pages 907-954, July.
    8. Guggenberger, Patrik & Smith, Richard J., 2005. "Generalized Empirical Likelihood Estimators And Tests Under Partial, Weak, And Strong Identification," Econometric Theory, Cambridge University Press, vol. 21(4), pages 667-709, August.
    9. Arthur Lewbel, 1997. "Constructing Instruments for Regressions with Measurement Error when no Additional Data are Available, with an Application to Patents and R&D," Econometrica, Econometric Society, vol. 65(5), pages 1201-1214, September.
    10. Smith, Richard J & Blundell, Richard W, 1986. "An Exogeneity Test for a Simultaneous Equation Tobit Model with an Application to Labor Supply," Econometrica, Econometric Society, vol. 54(3), pages 679-685, May.
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