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Semiparametric estimation of models with conditional moment restrictions in the presence of nonclassical measurement errors

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  • Song, Suyong

Abstract

This paper develops a framework for the analysis of semiparametric conditional moment models with endogenous and mismeasured causes, which is of empirical importance. We show that one set of valid instruments is sufficient to control for both endogeneity and measurement errors of the causes of interest, which has been observed in linear parametric models. Two-step consistent estimators of the parameters of interest are proposed. We also show that the proposed estimators are consistent with a rate faster than n−1/4 under a certain metric, and the proposed estimators of the finite-dimensional unknown parameters obtain root-n asymptotic normality. Monte Carlo evidences show that the proposed estimators perform well under a variety of identification conditions. An application to instrumental variables estimation of Engel curves illustrates the usefulness of our method. It supports that correcting for both endogeneity and measurement errors on total expenditure is substantial in estimating economically meaningful Engel curves.

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  • 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.
  • Handle: RePEc:eee:econom:v:185:y:2015:i:1:p:95-109
    DOI: 10.1016/j.jeconom.2014.10.007
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    2. Francis DiTraglia & Camilo Garcia-Jimeno, 2015. "On Mis-measured Binary Regressors: New Results And Some Comments on the Literature, Second Version," PIER Working Paper Archive 15-039, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 11 Nov 2015.
    3. Francis DiTraglia & Camilo Garcia-Jimeno, 2015. "On Mis-measured Binary Regressors: New Results And Some Comments on the Literature, Third Version," PIER Working Paper Archive 15-040, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 24 Nov 2015.
    4. DiTraglia, Francis J. & García-Jimeno, Camilo, 2019. "Identifying the effect of a mis-classified, binary, endogenous regressor," Journal of Econometrics, Elsevier, vol. 209(2), pages 376-390.
    5. Suyong Song & Stephen S. Baek, 2019. "Shape Matters: Evidence from Machine Learning on Body Shape-Income Relationship," Papers 1906.06747, arXiv.org.
    6. Francis J. DiTraglia & Camilo García-Jimeno, 2017. "Mis-classified, Binary, Endogenous Regressors: Identification and Inference," NBER Working Papers 23814, National Bureau of Economic Research, Inc.
    7. Andrews, Donald W.K., 2017. "Examples of L2-complete and boundedly-complete distributions," Journal of Econometrics, Elsevier, vol. 199(2), pages 213-220.
    8. Andrei Zeleneev & Kirill Evdokimov, 2023. "Simple estimation of semiparametric models with measurement errors," CeMMAP working papers 10/23, Institute for Fiscal Studies.
    9. Kirill S. Evdokimov & Andrei Zeleneev, 2023. "Simple Estimation of Semiparametric Models with Measurement Errors," Papers 2306.14311, arXiv.org, revised Mar 2024.
    10. Kim, Kyoo il & Petrin, Amil & Song, Suyong, 2016. "Estimating production functions with control functions when capital is measured with error," Journal of Econometrics, Elsevier, vol. 190(2), pages 267-279.

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    More about this item

    Keywords

    Semiparametric conditional moment restrictions; Method of sieve; Endogeneity; Nonclassical measurement error; Instrumental variable;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General

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