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Nonparametric instrumental regression with errors in variables

Author

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  • Karun Adusumilli
  • Taisuke Otsu

Abstract

This paper considers nonparametric instrumental variable regression when the endogenous variable is contaminated with classical measurement error. Existing methods are inconsistent in the presence of measurement error. We propose a wavelet deconvolution estimator for the structural function that modifies the generalized Fourier coefficients of the orthogonal series estimator to take into account the measurement error. We establish the convergence rates of our estimator for the cases of mildly/severely ill-posed models and ordinary/super smooth measurement errors. We characterize how the presence of measurement error slows down the convergence rates of the estimator. We also study the case where the measurement error density is unknown and needs to be estimated, and show that the estimation error of the measurement error density is negligible under mild conditions as far as the measurement error density is symmetric.

Suggested Citation

  • 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.
  • Handle: RePEc:cep:stiecm:/2015/585
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Babii, Andrii, 2017. "Honest confidence sets in nonparametric IV regression and other ill-posed models," TSE Working Papers 17-803, Toulouse School of Economics (TSE).
    2. Qiying Wang & Peter C.B. Phillips & Ioannis Kasparis, 2017. "Latent Variable Nonparametric Cointegrating Regression," Cowles Foundation Discussion Papers 3011, Cowles Foundation for Research in Economics, Yale University.

    More about this item

    Keywords

    Nonparametric instrumental variable regression; measurement error; inverse problem; deconvolution; measurement error;

    JEL classification:

    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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