Instrumental variable treatment of nonclassical measurement error models

• 成果类型: Article
• 署名作者: Hu, Yingyao; Schennach, Susanne M.
• 署名单位: Johns Hopkins University; University of Chicago
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.1111/j.0012-9682.2008.00823.x
• 发表日期: 2008
• 页码: 195-216
• 关键词: Nonseparable models; IN-VARIABLES; identification; misclassification; regressors

摘要

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.