Suppose the true model is given by yi = 0 1xi ui and we are interested in estimating 1. Suppose our sample is i.i.d and E[ui|xi] = 0. Unfortu- nately, we only have a noisy measure of xi. That is, we observe x i = x i i Assume E[i] = 0 and that i is independent from everything. In this context, i is our mea- surement error for observation i. This measurement error is not systematic, and is not related to any of the parameters we are interested in estimating. (So, it has zero covariance with any of the variables we are interested in). As we don't have access to the "real" value of xi, we run the following regression