Nonparametric Instrumental Regression with Errors in Variables

Karun Adusumilli, Taisuke Otsu

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)1256-1280
Number of pages25
JournalEconometric Theory
Volume34
Issue number6
DOIs
Publication statusPublished - 2018 Dec 1
Externally publishedYes

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regression
Errors in variables
Measurement error
Estimator
Rate of convergence

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Economics and Econometrics

Cite this

Nonparametric Instrumental Regression with Errors in Variables. / Adusumilli, Karun; Otsu, Taisuke.

In: Econometric Theory, Vol. 34, No. 6, 01.12.2018, p. 1256-1280.

Research output: Contribution to journalArticle

Adusumilli, Karun ; Otsu, Taisuke. / Nonparametric Instrumental Regression with Errors in Variables. In: Econometric Theory. 2018 ; Vol. 34, No. 6. pp. 1256-1280.
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