Nonparametric instrumental regression with errors in variables

Karun Adusumilli and Taisuke Otsu

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

JEL-codes: J1 (search for similar items in EconPapers)
Date: 2018-02-14
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Citations: View citations in EconPapers (9)

Published in Econometric Theory, 14, February, 2018, 34(6), pp. 1256-1280. ISSN: 0266-4666

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http://eprints.lse.ac.uk/85871/ Open access version. (application/pdf)

Related works:
Working Paper: Nonparametric instrumental regression with errors in variables (2015)
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