This paper analyzes the classical linear regression model with measurement errors in all the variables. First, we provide necessary and sufficient conditions for identification of the coefficients. We show that the coefficients are not identified if and only if an independent normally distributed linear combination of regressors can be transferred from the regressors to the errors. Second, we introduce a new estimator for the coefficients using a continuum of moments that are based on second derivatives of the log characteristic function of the observables. In Monte Carlo simulations, the estimator performs well and is robust to the amount of measurement error and number of mismeasured regressors. In an application to firm investment decisions, the estimates are similar to those produced by a generalized method of moments estimator based on third to fifth moments.

中文翻译：

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识别所有变量中存在误差的线性回归

本文分析了所有变量均存在测量误差的经典线性回归模型。首先，我们为系数的识别提供了充要条件。我们表明，当且仅当回归量的独立正态分布线性组合可以从回归量转移到误差时，系数才会被识别。其次，我们使用基于可观察量的对数特征函数的二阶导数的连续矩引入了一种新的系数估计器。在蒙特卡罗模拟中，估计器表现良好，并且对测量误差量和误测回归量的数量具有鲁棒性。在申请坚定的投资决策时，