This paper studies measurement errors that subtract signal from true variables of interest, labeled lack of signal … errors (LoSE). The effect on OLS regression of LoSE is opposite the conventional wisdom about classical measurement errors …

average treatment effect of interest will typically fail. While the form of this measurement error varies across applications …, in many cases the measurement error structure is heterogeneous across different groups of observations. We develop a … novel measurement error correction procedure capable of addressing heterogeneous mismeasurement structures by leveraging …