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Identifiability of mean‐reverting measurement error with instrumental variable
Author(s) -
Li Qing
Publication year - 2014
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/stan.12025
Subject(s) - observational error , identifiability , instrumental variable , errors in variables models , statistics , econometrics , mathematics , covariance , context (archaeology) , variance (accounting) , variable (mathematics) , identification (biology) , economics , paleontology , mathematical analysis , accounting , biology , botany
In the context where one main regressor is measured with error and at least one instrumental variable is available for the correction of measurement error, this paper provides, to the best of our knowledge, a first point‐identification result on the variance of measurement error, the variance of latent variable, and their covariance. We show that the parameters are identified if the regression model is not de facto linear. We illustrate the method in an application to identify mean‐reverting measurement error, a typical issue in reported income where the measurement error of income is negatively correlated with the true income.