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Nonparametric instrumental regression with errors in variables

Author

Listed:
  • 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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    Cited by:

    1. Dong, Hao & Otsu, Taisuke & Taylor, Luke, 2022. "Estimation of varying coefficient models with measurement error," Journal of Econometrics, Elsevier, vol. 230(2), pages 388-415.
    2. Wang, Qiying & Phillips, Peter C.B. & Kasparis, Ioannis, 2021. "Latent Variable Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 37(1), pages 138-168, February.
    3. Babii, Andrii, 2020. "Honest Confidence Sets In Nonparametric Iv Regression And Other Ill-Posed Models," Econometric Theory, Cambridge University Press, vol. 36(4), pages 658-706, August.
    4. Kurisu, Daisuke & Otsu, Taisuke, 2022. "On the uniform convergence of deconvolution estimators from repeated measurements," LSE Research Online Documents on Economics 107533, London School of Economics and Political Science, LSE Library.
    5. Hao Dong & Yuya Sasaki, 2022. "Estimation of average derivatives of latent regressors: with an application to inference on buffer-stock saving," Departmental Working Papers 2204, Southern Methodist University, Department of Economics.
    6. 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.
    7. Daisuke Kurisu & Taisuke Otsu, 2019. "On the uniform convergence of deconvolution estimators from repeated measurements," STICERD - Econometrics Paper Series 604, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

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    More about this item

    Keywords

    Nonparametric instrumental variable regression; measurement error; inverse problem; deconvolution; measurement error;
    All these keywords.

    JEL classification:

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

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