Suppose you are interested in running the regression Yi=0+1Xi+ui, and you know that the OLS assumptions hold (E[uiXi]=0 or cov(Xi,ui)=0). But you cannot observe Yi directly. Instead, you observe a variable Yi which is the sum of Yi and a measurement error wi. As you only observe Yi, you can only run the regression Y~i=0+1Xi+vi. a) Express the error term vi in terms of the measurement error wi and the error term ui. b) Suppose the error wi is classical measurement error (ie. that cov(wi,ui)=0 and cov(wi,Xi)=0 ). In order to know whether 1 is biased, we need to know whether cov(Xi,vi)=0. Let's derive this covariance. i. Express cov(Xi,vi) in terms of cov(Xi,wi) and cov(Xi,ui) ii. What does cov(Xi,ui) equal? iii. What does cov(Xi,wi) equal? iv. As a result, what does cov(Xi,vi) equal? c) Given your answer in b), is 1 biased? If so, what is the direction of the bias? On what does the direction depend on? Is this consistent with what we discussed in lecture