INTRODUCTION

The benchmark measurement error model is the bivariate linear errors-invariables (EIV) regression model with additive measurement errors in both the dependent variable and the regressor variable. The measurement errors are assumed to be classical, meaning that they are uncorrelated with the true value and have mean zero. Then the OLS estimator is inconsistent, with a bias toward zero. The measurement error is often large enough for this bias to be substantial; see, for example, Bound, Brown, and Mathiowetz (2001).

For nonlinear models the attenuation result does not necessarily hold, but measurement error still leads to inconsistency because the identified parameter is not the parameter of interest in the model free of measurement error. The essential problem lies in the correlation between the observed regressor variable and the measurement error. This leads to loss of identification and distorted inferences about the role of the covariate. A key objective of analysis is to establish an identification strategy for the parameter of interest.

There are important differences between nonlinear and linear measurement errors models. It is more difficult in nonlinear models to correct for classical measurement error in the regressors. Furthermore, in nonlinear models it may be more natural to allow measurement errors to be nonclassical and nonadditive. And although in linear models classical measurement error in the dependent variable is innocuous because it just contributes to the equation error as additive noise, in nonlinear models the presence of even classical measurement error in the dependent variable leads to loss of identification of model parameters.