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Nonparametric Instrumental Regression With Errors In Variables

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  • Adusumilli, Karun
  • Otsu, Taisuke

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

  • Adusumilli, Karun & Otsu, Taisuke, 2018. "Nonparametric Instrumental Regression With Errors In Variables," Econometric Theory, Cambridge University Press, vol. 34(6), pages 1256-1280, December.
    • Handle: RePEc:cup:etheor:v:34:y:2018:i:06:p:1256-1280_00
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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. 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.
    4. 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.
    5. 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.
    6. 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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