Empirical Bayes shrinkage (mostly) does not correct the measurement error in regression
经验贝叶斯收缩通常不能纠正回归中的测量误差
In the value-added literature, it is often claimed that regressing on empirical Bayes shrinkage estimates corrects for the measurement error problem in linear regression. We clarify the conditions needed; we argue that these conditions are stronger than the those needed for classical measurement error correction, which we advocate for instead. Moreover, we show that the classical estimator cannot be improved without stronger assumptions. We extend these results to…