In the model 3t = 3x+ + uti t = 1,...,1 X is measured with error. Date is only available on x, where t=1,1 and Eue = Ev = 0, E(440) = E(X+Ut) = E(XV:) = 0. Eu = 0 and Ev = 0; y. and x have zero means. (a) If 3 is the ordinary least squares (OLS) estimator of 8 from regressing y on x;, show that B is inconsistent. Interpret your result. What determines the level of inconsistency? (10 marks) (b) In the above given model, suppose x was measured without error but y was measured with error and data was only available on y: . where y = y + wt, and E(w:) = 0: E(uwt) = E(X+Wt) = 0, Elv:W.) = 0, E(w) = oLet 3 be the OLS estimator for 3 from regression y on Xt. Show that B is consistent. Explain in detail. Discuss why you would nevertheless prefer to run the regression without measurement error. (10 marks] (C) Suppose in the above given model both y and x are measured with errors and data is available only on y; and x; where x; and y, are defined above. respectively. Discuss (without derivation) whether the OLS estimator of B, from regression y; on x; will be consistent or inconsistent. [5 marks] In the model 3t = 3x+ + uti t = 1,...,1 X is measured with error. Date is only available on x, where t=1,1 and Eue = Ev = 0, E(440) = E(X+Ut) = E(XV:) = 0. Eu = 0 and Ev = 0; y. and x have zero means. (a) If 3 is the ordinary least squares (OLS) estimator of 8 from regressing y on x;, show that B is inconsistent. Interpret your result. What determines the level of inconsistency? (10 marks) (b) In the above given model, suppose x was measured without error but y was measured with error and data was only available on y: . where y = y + wt, and E(w:) = 0: E(uwt) = E(X+Wt) = 0, Elv:W.) = 0, E(w) = oLet 3 be the OLS estimator for 3 from regression y on Xt. Show that B is consistent. Explain in detail. Discuss why you would nevertheless prefer to run the regression without measurement error. (10 marks] (C) Suppose in the above given model both y and x are measured with errors and data is available only on y; and x; where x; and y, are defined above. respectively. Discuss (without derivation) whether the OLS estimator of B, from regression y; on x; will be consistent or inconsistent. [5 marks]