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Smoothed Estimating Equations for Instrumental Variables Quantile Regression

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Abstract

The moment conditions or estimating equations for instrumental variables quantile regression involves the discontinuous indicator function. We instead use smoothed estimating equations, with bandwidth h. This is known to allow higher-order expansions that justify bootstrap refinements for inference. Computation of the estimator also becomes simpler and more reliable, especially with (more) endogenous regressors. We show that the mean squared error of the vector of estimating equations is minimized for some h > 0, which also reduces the mean squared error of the parameter estimators. The same h also minimizes higher-order type I error for a χ2 test, leading to improved size-adjusted power. Our plug-in bandwidth consistently reproduces all of these properties in simulations.

Suggested Citation

  • David M. Kaplan & Yixiao Sun, 2013. "Smoothed Estimating Equations for Instrumental Variables Quantile Regression," Working Papers 1314, Department of Economics, University of Missouri.
  • Handle: RePEc:umc:wpaper:1314
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    File URL: https://economics.missouri.edu/working-papers/2013/wp1314_kaplan.pdf
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Le-Yu Chen & Sokbae (Simon) Lee, 2017. "Exact computation of GMM estimators for instrumental variable quantile regression models," CeMMAP working papers CWP52/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Luciano de Castro & Antonio F. Galvao & David M. Kaplan & Xin Liu, 2017. "Smoothed GMM for quantile models," Papers 1707.03436, arXiv.org, revised Feb 2018.
    3. Fernandes, Marcelo & Guerre, Emmanuel & Horta, Eduardo, 2017. "Smoothing quantile regressions," Textos para discussão 457, FGV/EESP - Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
    4. Anthony A. Smith, Jr. & Michael Keane, 2004. "Generalized Indirect Inference for Discrete Choice Models," Econometric Society 2004 North American Winter Meetings 512, Econometric Society.
    5. Kaspar Wüthrich, 2015. "Semiparametric estimation of quantile treatment effects with endogeneity," Diskussionsschriften dp1509, Universitaet Bern, Departement Volkswirtschaft.
    6. Su, Liangjun & Hoshino, Tadao, 2016. "Sieve instrumental variable quantile regression estimation of functional coefficient models," Journal of Econometrics, Elsevier, vol. 191(1), pages 231-254.
    7. Armstrong, Christopher S. & Blouin, Jennifer L. & Jagolinzer, Alan D. & Larcker, David F., 2015. "Corporate governance, incentives, and tax avoidance," Journal of Accounting and Economics, Elsevier, vol. 60(1), pages 1-17.

    More about this item

    Keywords

    bandwidth choice; higher-order properties; instrumental variables; quantile regression; smoothing;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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