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NONPARAMETRIC INSTRUMENTAL REGRESSION WITH ERRORS IN VARIABLES

Published online by Cambridge University Press:  14 February 2018

Karun Adusumilli
Affiliation:
London School of Economics and Political Science
Taisuke Otsu*
Affiliation:
London School of Economics and Political Science
*
*Address correspondence to Taisuke Otsu, Department of Economics, London School of Economics, Houghton Street, London, WC2A 2AE, UK; e-mail: t.otsu@lse.ac.uk.

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.

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ARTICLES
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

The authors would like to thank three anonymous referees and a co-editor for helpful comments. Otsu gratefully acknowledges financial support from the ERC Consolidator Grant (SNP 615882).

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