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Estimating nonseparable models with mismeasured endogenous variables

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  • Suyong Song
  • Susanne M. Schennach
  • Halbert White
Abstract
We study the identification and estimation of covariate‐conditioned average marginal effects of endogenous regressors in nonseparable structural systems when the regressors are mismeasured. We control for the endogeneity by making use of covariates as control variables; this ensures conditional independence between the endogenous causes of interest and other unobservable drivers of the dependent variable. Moreover, we recover distributions of the underlying true causes from their error‐laden measurements to deliver consistent estimators. We obtain uniform convergence rates and asymptotic normality for estimators of covariate‐conditioned average marginal effects, faster convergence rates for estimators of their weighted averages over instruments, and root‐n consistency and asymptotic normality for estimators of their weighted averages over control variables and regressors. We investigate their finite‐sample behavior using Monte Carlo simulation and apply new methods to study the impact of family income on child achievement measured by math and reading scores, using a matched mother–child subsample of the National Longitudinal Survey of Youth. Our findings suggest that these effects are considerably larger than previously recognized, and depend on parental abilities and family income. This underscores the importance of measurement errors, endogeneity of family income, nonlinearity of income effects, and interactions between causes of child achievement.

Suggested Citation

  • Suyong Song & Susanne M. Schennach & Halbert White, 2015. "Estimating nonseparable models with mismeasured endogenous variables," Quantitative Economics, Econometric Society, vol. 6(3), pages 749-794, November.
    • Handle: RePEc:wly:quante:v:6:y:2015:i:3:p:749-794
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    Cited by:

    1. Kengo Kato & Yuya Sasaki & Takuya Ura, 2021. "Robust inference in deconvolution," Quantitative Economics, Econometric Society, vol. 12(1), pages 109-142, January.
    2. 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.
    3. 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.
    4. Takahide Yanagi, 2019. "Inference on local average treatment effects for misclassified treatment," Econometric Reviews, Taylor & Francis Journals, vol. 38(8), pages 938-960, September.
    5. Shiu, Ji-Liang, 2016. "Identification and estimation of endogenous selection models in the presence of misclassification errors," Economic Modelling, Elsevier, vol. 52(PB), pages 507-518.
    6. Denni Tommasi & Arthur Lewbel & Rossella Calvi, 2017. "LATE with Mismeasured or Misspecified Treatment: An application to Women's Empowerment in India," Working Papers ECARES ECARES 2017-27, ULB -- Universite Libre de Bruxelles.
    7. Karun Adusumilli & Taisuke Otsu, 2015. "Nonparametric instrumental regression with errors in variables," STICERD - Econometrics Paper Series /2015/585, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    8. 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.

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