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 root-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.

翻译：我们开发了一种在广义矩方法（GMM）框架中处理变量含误差（EIV）问题的实用方法。我们重点关注EIV变异性占测量变量变异性一定比例的情形，这是实证应用中的典型情况。对于任何初始矩条件集，我们的方法提供了一组对EIV具有稳健性的"修正"矩条件。我们证明，基于这些矩的GMM估计量是根号n一致的，且标准检验和置信区间能够提供有效的推断。即使当EIV严重到使忽略该问题的朴素估计量产生严重偏误且其置信区间覆盖率为0%时，该结论依然成立。我们的方法无需任何非参数估计，这对于包含大量协变量的应用场景，以及涉及多元或非经典EIV的情形尤为重要。特别地，该方法使得在非线性模型中利用工具变量处理EIV问题变得简便易行。