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) may be heavily biased with the confidence intervals having 0% coverage. Our approach involves no nonparametric estimation, which is particularly important for applications with multiple covariates, and settings with multivariate, serially correlated, or non-classical EIV.

翻译：我们提出了一种在广义矩方法（GMM）框架下处理变量含误差（EIV）问题的实用方法。我们重点关注EIV波动性占测量变量波动性一部分的情形，这在实际应用中具有典型性。对于任意初始矩条件集，我们的方法提供了一个对EIV具有稳健性的修正矩条件集。研究表明，基于这些矩条件的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推断。即便在EIV如此之大以至于忽略EIV问题的朴素估计量可能严重有偏（其置信区间覆盖率为0%）的情况下，上述结论依然成立。我们的方法无需进行非参数估计，这在涉及多个协变量以及多元、序列相关或非经典EIV的应用场景中尤为重要。