Nonparametric instrumental regression with errors in variables

Adusumilli, Karun and Otsu, Taisuke ORCID: 0000-0002-2307-143X (2018) Nonparametric instrumental regression with errors in variables. Econometric Theory, 34 (6). pp. 1256-1280. ISSN 0266-4666

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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.

Item Type:	Article
Official URL:	https://www.cambridge.org/core/journals/econometri...
Additional Information:	© 2017 Cambridge University Press
Divisions:	Economics
Subjects:	H Social Sciences > H Social Sciences (General) H Social Sciences > HB Economic Theory Q Science > Q Science (General)
Date Deposited:	29 Nov 2017 10:27
Last Modified:	01 Nov 2024 05:09
Projects:	SNP 615882
Funders:	Economic Research Council
URI:	http://eprints.lse.ac.uk/id/eprint/85871

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