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Consider the simple linear regression model, where X; and Y; are scalar random variables: Yi = Bo + B1Xi + ui Suppose that the regressor X; is endogenous, i.e., that E(u;|X;) # 0; however, we have a valid (scalar) instrument Z; which satisfies E(uilZi) = 0. a) Show using the Law of Iterated Expectations (LIE) that E(u; |X;, Zi) # 0. (Hint: You can do this as a "proof by contradiction". That is, suppose that E(u; |Xi, Zi) = 0, apply the LI, and show that it leads to a contradiction of one of the assumptions stated above.) b) Consider the linear IV estimator defined in Notes 16. Show algebraically that BIV = B1+ nLizqui (Zi - Z) nZi=1(xi - x) (Zi - Z) c) Using LIE, show that the IV estimator B1 is biased, i.e., in general, E(BIV) * B1. (Hint: First extend your argument from a) to show E (uilX1, ..., Xn, Z1, ..., Zn) # 0. So strict exogeneity fails if we condition on all values of X and Z