Econometrica: Jan 2008, Volume 76, Issue 1

Instrumental Variable Treatment of Nonclassical Measurement Error Models

https://doi.org/10.1111/j.0012-9682.2008.00823.x
p. 195-216

Yingyao Hu, Susanne M. Schennach

While the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary data set containing correctly measured observations, we establish that the availability of instruments enables the identification of a large class of nonclassical nonlinear errors‐in‐variables models with continuously distributed variables. Our main identifying assumption is that, conditional on the value of the true regressors, some “measure of location” of the distribution of the measurement error (e.g., its mean, mode, or median) is equal to zero. The proposed approach relies on the eigenvalue–eigenfunction decomposition of an integral operator associated with specific joint probability densities. The main identifying assumption is used to “index” the eigenfunctions so that the decomposition is unique. We propose a convenient sieve‐based estimator, derive its asymptotic properties, and investigate its finite‐sample behavior through Monte Carlo simulations.

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Supplemental Material

Supplement to "Instrumental Variable Treatment of Nonclassical Measurement Error Models"

This Supplementary Material contains some of the more technical details omitted from the main paper.

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