cemmap working paper, Centre for Microdata Methods and Practice CWP17/06
While the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary dataset containing correctly measured observations, this paper establishes that the availability of instruments enables the identification of a large class of nonclassical nonlinear errors-in-variables models with continuously distributed variables. The 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 order the eigenfunctions so that the decomposition is unique. The authors propose a convenient sieve-based estimator, derive its asymptotic properties and investigate its finite-sample behavior through Monte Carlo simulations. An example of application to the relationship between earnings and divorce rates is also provided.
Nonclassical measurement error , nonlinear errors-in-variables model , instrumental variable , operator , semiparametric estimator , sieve maximum likelihood