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Simple estimation of semiparametric models with measurement errors

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  • Andrei Zeleneev
  • Kirill Evdokimov

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 naïve estimators (that ignore the EIV problem) may be heavily biased with the confidence intervals having 0% coverage. Our approach involves no nonparametric estimation, which is particularly important for applications with multiple covariates, and settings with multivariate, serially correlated, or non-classical EIV.

Suggested Citation

  • Andrei Zeleneev & Kirill Evdokimov, 2023. "Simple estimation of semiparametric models with measurement errors," CeMMAP working papers 10/23, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:10/23
    DOI: 10.47004/wp.cem.2023.1023
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    1. 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.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    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. Stéphane Bonhomme & Martin Weidner, 2022. "Minimizing sensitivity to model misspecification," Quantitative Economics, Econometric Society, vol. 13(3), pages 907-954, July.
    5. Wen, Chieh-Hua & Koppelman, Frank S., 2001. "The generalized nested logit model," Transportation Research Part B: Methodological, Elsevier, vol. 35(7), pages 627-641, August.
    6. Yuichi Kitamura & Taisuke Otsu & Kirill Evdokimov, 2013. "Robustness, Infinitesimal Neighborhoods, and Moment Restrictions," Econometrica, Econometric Society, vol. 81(3), pages 1185-1201, May.
    7. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    8. Frank Kleibergen, 2005. "Testing Parameters in GMM Without Assuming that They Are Identified," Econometrica, Econometric Society, vol. 73(4), pages 1103-1123, July.
    9. 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.
    10. 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.
    11. Daniel Wilhelm, 2018. "Testing for the presence of measurement error," CeMMAP working papers CWP45/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. Andrew Chesher & Christian Schluter, 2002. "Welfare Measurement and Measurement Error," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(2), pages 357-378.
    13. Isaiah Andrews & Matthew Gentzkow & Jesse M. Shapiro, 2017. "Measuring the Sensitivity of Parameter Estimates to Estimation Moments," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 132(4), pages 1553-1592.
    14. Song, Suyong, 2015. "Semiparametric estimation of models with conditional moment restrictions in the presence of nonclassical measurement errors," Journal of Econometrics, Elsevier, vol. 185(1), pages 95-109.
    15. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    16. Battistin, Erich & Chesher, Andrew, 2014. "Treatment effect estimation with covariate measurement error," Journal of Econometrics, Elsevier, vol. 178(2), pages 707-715.
    17. Isaiah Andrews & Anna Mikusheva, 2016. "Conditional Inference With a Functional Nuisance Parameter," Econometrica, Econometric Society, vol. 84(4), pages 1571-1612, July.
    18. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, January.
    19. 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.
    20. Isaiah Andrews, 2016. "Conditional Linear Combination Tests for Weakly Identified Models," Econometrica, Econometric Society, vol. 84, pages 2155-2182, November.
    21. Hu, Yingyao & Sasaki, Yuya, 2015. "Closed-form estimation of nonparametric models with non-classical measurement errors," Journal of Econometrics, Elsevier, vol. 185(2), pages 392-408.
    22. Koppelman, Frank S. & Wen, Chieh-Hua, 2000. "The paired combinatorial logit model: properties, estimation and application," Transportation Research Part B: Methodological, Elsevier, vol. 34(2), pages 75-89, February.
    23. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
    24. 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).
    25. McFadden, Daniel, 1974. "The measurement of urban travel demand," Journal of Public Economics, Elsevier, vol. 3(4), pages 303-328, November.
    26. 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.
    27. Isaiah Andrews & Anna Mikusheva, 2016. "Conditional Inference With a Functional Nuisance Parameter," Econometrica, Econometric Society, vol. 84, pages 1571-1612, July.
    28. 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.
    29. Li, Tong & Vuong, Quang, 1998. "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 139-165, May.
    30. Wang, Liqun & Hsiao, Cheng, 2011. "Method of moments estimation and identifiability of semiparametric nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 165(1), pages 30-44.
    31. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    32. Rivers, Douglas & Vuong, Quang H., 1988. "Limited information estimators and exogeneity tests for simultaneous probit models," Journal of Econometrics, Elsevier, vol. 39(3), pages 347-366, November.
    33. Kadane, Joseph B, 1971. "Comparison of k-Class Estimators when the Disturbances are Small," Econometrica, Econometric Society, vol. 39(5), pages 723-737, September.
    34. Erickson, Timothy & Whited, Toni M., 2002. "Two-Step Gmm Estimation Of The Errors-In-Variables Model Using High-Order Moments," Econometric Theory, Cambridge University Press, vol. 18(3), pages 776-799, June.
    35. Xiaohong Chen & Han Hong & Elie Tamer, 2005. "Measurement Error Models with Auxiliary Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(2), pages 343-366.
    36. Xiaohong Chen & Han Hong & Denis Nekipelov, 2011. "Nonlinear Models of Measurement Errors," Journal of Economic Literature, American Economic Association, vol. 49(4), pages 901-937, December.
    37. Joshua D. Angrist & Kathryn Graddy & Guido W. Imbens, 2000. "The Interpretation of Instrumental Variables Estimators in Simultaneous Equations Models with an Application to the Demand for Fish," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(3), pages 499-527.
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