IDENTIFICATION OF LINEAR REGRESSIONS WITH ERRORS IN ALL VARIABLES
研究了所有变量都有测量误差的线性回归模型，给出了系数可识别的充要条件，并提出一种基于对数特征函数二阶导数的连续矩估计量，模拟表现良好且稳健。
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.