Econometrica

Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

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.


Log In To View Full Content

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.

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.

Journal News

View