Simple estimation of semiparametric models with measurement errors

We develop a practical way of addressing the Errors-In-Variables (EIV) problem in the Generalized Method of Moments (GMM) framework. We focus on the settings in which the variability of the EIV is a fraction of that of the mismeasured variables, which is typical for empirical applications. For any initial set of moment conditions our approach provides a “corrected” set of moment conditions that are robust to the EIV. We show that the GMM estimator based on these moments is √n-consistent, with the standard tests and confidence intervals providing valid inference. This is true even when the EIV are so large that naive estimators (that ignore the EIV problem) are heavily biased with their confidence intervals having 0% coverage. Our approach involves no nonparametric estimation, which is especially important for applications with many covariates, and settings with multivariate or non-classical EIV. In particular, the approach makes it easy to use instrumental variables to address EIV in nonlinear models.